Simulated Evolution and Learning

For computational solutions of convex optimization problems, a rich body of knowledge including theory, algorithms, and computational experience is now available. In contrast, nothing of comparable depth and completeness can be offered at the present time, for non-convex problems. The field of convex optimization benefited immensely from pre-existing body of concepts and knowledge from pure mathematics, while non-convex problems seems to require formulation and exploration of entirely new mathematical concepts, as well as new models of computation. The intent of this paper is to describe our efforts in this direction, at a philosophical or conceptual level, without going into specific applications or implementation in software. We also point out connections with other areas, particularly mathematical physics.

To simultaneously optimize multiple objective functions, several evolutionary multiobjective optimization (EMO) algorithms have been proposed. Nowadays, often set quality indicators are used when comparing the performance of those algorithms or when selecting “good” solutions during the algorithm run. Hence, characterizing the solution sets that maximize a certain indicator is crucial—complying with the optimization goal of many indicator-based EMO algorithms. If these optimal solution sets are upper bounded in size, e.g., by the population size

μ

, we call them

optimal μ

-distributions

. Recently, optimal

μ

-distributions for the well-known hypervolume indicator have been theoretically analyzed, in particular, for bi-objective problems with a linear Pareto front. Although the exact optimal

μ

-distributions have been characterized in this case, not all possible choices of the hypervolume’s reference point have been investigated. In this paper, we revisit the previous results and rigorously characterize the optimal

μ

-distributions also for all other reference point choices. In this sense, our characterization is now exhaustive as the result holds for any linear Pareto front and for any choice of the reference point and the optimal

μ

-distributions turn out to be always unique in those cases. We also prove a tight lower bound (depending on

μ

) such that choosing the reference point above this bound ensures the extremes of the Pareto front to be always included in optimal

μ

-distributions.

We consider unconstrained minimax problem where the objective function is the maximum of a finite number of smooth convex functions. We present an iterative method to compute the optimal solution for the unconstrained convex finite minimax problem. The algorithm developed estimates the direction of steepest-descent rapidly and using Armijo’s condition proceeds towards the solution. Owing to the highly parallel nature of the algorithm, it is highly suitable for large minimax problems. Algorithm is implemented on Nvidia Tesla C1060 graphics card using CUDA and numerical comparisons with RGA & CFSQP are presented.

Negative Selection Algorithm (NSA) is one of several algorithms inspired by the principles of natural immune system. The algorithm received the researchers attention due to its applicability in various research areas and a number of valuable efforts are made to increase the effectiveness and efficiency of it. The heart of NSA is to somehow find rules called detectors to discriminate self and anomaly areas. Each detector in NSA defines a subspace of problem space where no self data is located. One of the major issues in NSA is detector’s shape or representation of detectors which can affect the detection performance significantly. This paper for the first time proposes a new representation for detectors based on convex hull. Since convex hull is a general form of other geometric shapes, it retains the benefits of other shapes meanwhile it provides some new features like the asymmetric shape. Experimental results show a significant enhancement in the accuracy of negative selection algorithm compared to other common representation shapes.

Learning classifier systems (LCSs) are evolutionary learning mechanisms that combine genetic algorithms (GAs) with the power of the reinforcement learning paradigm. XCS, eXtended Classifier System, is currently considered as state of the art learning classifier systems due to its effectiveness in data analysis and its success in applying to varieties of learning problems. Generalization and the size of evolved population in XCS is one of the most challenging issues in XCS. This paper suggests that rule representation in XCS is not matured to the point where the condition parts of classifiers are covering the problem space in an effective manner with minimum redundancy. The key idea in the proposed system, named XCS-HT, is to use a novel representation scheme based on presenting a subspace of problem space with two kinds of regions named certain and vague regions. Using such mechanism significantly boils the number of evolved XCS-HT’s classifiers down, while changing the performance only marginally. The experimental results show that XCS-HT has a better ability to solve problems having indistinguishable class boundaries comparing to XCSR, a common extension of XCS standing for handling real valued data.

Platooning technology is becoming a future task which suggests as a way of reducing carbon dioxide emissions and realizing safe driving at a high velocity. This paper presents a unique optimal control method of velocity and distance for platooning using model predictive control. The vehicle-platoon’s distance model which is based on the road condition and weather condition is used in this rigorous approach of deriving the control input. A combination of Continuation and Generalized Minimum Residual Methods is used to optimize the sequence of vehicle control commands which is required in the prediction horizon aiming at minimizing the relative velocity and keeping safe distance of the vehicle-platoon while the vehicle-platoon is on a high velocity driving.

In this paper we derive theoretical expressions to compute expected population variance for Differential Evolution (DE) variants –

DE/best/1/bin, DE/rand/2/bin

and

DE/best/2/

bin by directly extending Zaharie’s work on

DE/rand/1/bin.

The study includes comparing the theoretical and empirical evolution of population variance of three DE variants. This work provides insight about the explorative power of the variants and explains their behavior.

In this paper, the authors compare a Monte Carlo method and an optimization-based approach using genetic algorithms for sequentially generating space-filling experimental designs. It is shown that Monte Carlo methods perform better than genetic algorithms for this specific problem.

Extending Estimation of distribution algorithms (EDAs) to the continuous field is a promising and challenging task. With a single probabilistic model, most existing continuous EDAs usually suffer from the local stagnation or a low convergence speed. This paper presents an enhanced continuous EDA with multiple probabilistic models (MP-EDA). In the MP-EDA, the population is divided into two subpopulations. The one involved by histogram model is used to roughly capture the global optima, whereas the other involved by Gaussian model is aimed at finding highly accurate solutions. During the evolution, a migration operation is periodically carried out to exchange some best individuals of the two subpopulations. Besides, the MP-EDA adaptively adjusts the offspring size of each subpopulation to improve the searching efficiency. The effectiveness of the MP-EDA is investigated by testing ten benchmark functions. Compared with several state-of-the-art evolutionary computations, the proposed algorithm can obtain better results in most test cases.

In a multimodal optimization task, the main purpose is to find multiple optimal solutions, so that the user can have a better knowledge about different optimal solutions in the search space and as and when needed, the current solution may be replaced by another optimum solution. Recently, we proposed a novel and successful evolutionary multi-objective approach to multimodal optimization. Our work however made use of three different parameters which had to be set properly for the optimal performance of the proposed algorithm. In this paper, we have eliminated one of the parameters and made the other two self-adaptive. This makes the proposed multimodal optimization procedure devoid of user specified parameters (other than the parameters required for the evolutionary algorithm). We present successful results on a number of different multimodal optimization problems of upto 16 variables to demonstrate the generic applicability of the proposed algorithm.

In structure topology optimization, the applied boundary and support conditions are often fixed in a-priori. These conditions can affect the behavior and the properties of single-piece elastic structures known as compliant mechanisms. In this paper, the same aspect is explored for path generating compliant mechanisms by considering them as design variables and their values are evolved using customized NSGA-II algorithm. Three examples are solved and the innovative facts among the applied boundary and support conditions are presented. The elastic structures are also presented in this paper.

It is only relatively recently that extremal optimisation (EO) has been applied to combinatorial optimisation problems. As such, there have been only a few attempts to extend the paradigm to include standard search mechanisms that are routinely used by other techniques such as genetic algorithms, tabu search and ant colony optimisation. The key way to begin this process is to augment EO with attributes that it naturally lacks. While EO does not get confounded by local optima and is able to move through search space unencumbered, one of the major issues is to provide it with better search intensification strategies. In this paper, two strategies that compliment EO’s mechanics are introduced and are used to augment an existing solver framework. Results, for single and population versions of the algorithm, demonstrate that intensification aids the performance of EO.

In this paper the relative performance of two constraint handling techniques, namely a parameter-less adaptive penalty method (APM) and the stochastic ranking method (SR), is studied in the context of continuous parameter constrained optimization problems. Both techniques are used within the same search engine, a binary-coded genetic algorithm.

In this paper, we develop a tree adjoining grammar (TAG) to capture semantics of a story with long-distance causal dependency, and present a computational framework for story plot generation. Under this framework, TAG is derived and a story plot is represented by a derivation tree of TAG. The generated plots are then evolved using grammar guided genetic programming (GGGP) to generate creative, interesting and complex story plots. To evaluate these newly generated plots, a human-in-the-loop approach is used. An experimental study was carried out, in which this framework was used to produce creative, interesting and complex plots from a predesigned fabula based on a story known as “The magpie and the water bottle”. The experimental study demonstrated that TAG and GGGP can potentially contribute significantly to complex automatic story plot generation.

In past, only a few attempts have been made in adopting a unified outlook towards different paradigms in Evolutionary Computation. The underlying motivation of these studies was aimed at gaining better understanding of evolutionary methods, both at the level of theory as well as application, in order to design efficient evolutionary algorithms for solving wide-range complex problems. One such attempt is made in this paper, where we reinstate ‘Unified Theory Of Evolutionary Computation’, drawn from past studies, and investigate four steps –

Initialization

,

Selection

,

Generation

and

Replacement

, which are sufficient to describe common

Evolutionary Optimization Systems

such as Genetic Algorithms, Evolutionary Strategies, Evolutionary Programming, Particle Swarm Optimization and Differential Evolution. As a next step we consider Differential Evolution, a relatively new evolutionary paradigm, and discover its inability to efficiently solve unimodal problems when compared against a benchmark Genetic Algorithm. Targeted towards enhancing DE’s performance, several modifications are successfully proposed and validated through simulation results. The

Unified Approach

is found helpful in understanding the role and re-modeling of DE steps to efficiently solve unimodal problems.

This work presents a dynamic island model framework for helping the resolution of combinatorial optimization problems with evolutionary algorithms. In this framework, the possible migrations among islands are represented by a complete graph. The migrations probabilities associated to each edge are dynamically updated with respect to the last migrations impact. This new framework is tested on the well-known 0/1 Knapsack problem and MAX-SAT problem. Good results are obtained and several properties of this framework are studied.

This paper formulates the optimal coverage problem (OCP) in wireless sensor network (WSN) as a 0/1 programming problem and proposes to use evolutionary computation (EC) algorithms to solve the problem. The OCP is to determine to active as few nodes as possible to monitor the area in order to save energy while at the same time meets the surveillance requirement, e.g., the full coverage. This is a fundamental problem in the WSN which is significant for the network lifetime. Even though lots of models have been proposed for the problem and variants of approaches have been designed for the solution, they are still inefficient because of the local optima. In order to solve the problem effectively and efficiently, this paper makes the contributions to the following two aspects. First, the OCP is modeled as a 0/1 programming problem where 0 means the node is turned off whilst 1 means the node is active. This model has a very natural and intuitive map from the representation to the real network. Second, by considering that the EC algorithms have strong global optimization ability and are very suitable for solving the 0/1 programming problem, this paper proposes to use the genetic algorithm (GA) and the binary particle swarm optimization (BPSO) to solve the OCP, resulting in a direct application of the EC algorithms and an efficient solution to the OCP. Simulations have been conducted to evaluate the performance of the proposed approaches. The experimental results show that our proposed GA and BPSO approaches outperform the state-of-the-art approaches in minimizing the active nodes number.

Over the last few decades, many different variants of Genetic Algorithms (GAs) have been introduced for solving Constrained Optimization Problems (COPs). However, a comparative study of their performances is rare. In this paper, our objective is to analyze different variants of GA and compare their performances by solving the 36 CEC benchmark problems by using, a new scoring scheme introduced in this paper and, a nonparametric test procedure. The insights gain in this study will help researchers and practitioners to decide which variant to use for their problems.

A data stream is an ordered sequence of instances that can be read only once or a small number of times using limited computing and storage capabilities. Stream data analysis is a critical issue in many application areas such as network fraud detection, stock market prediction, and web searches. In this research, our previously proposed FCMAC-BYY, that uses Bayesian Ying-Yang (BYY) learning in the fuzzy cerebellar model articulation controller (FCMAC), will be advanced by evolutionary computation and dynamic rule construction. The developed FCMAC-EBYY has been applied to a real-time stream data analysis problem of traffic flow prediction. The experimental results illustrate that FCMAC-EBYY is indeed capable of producing better performance than other representative neuro-fuzzy systems.

The group interaction parameter prediction of Ionic Liquids(IL’s) with thiophene (C

4

H

4

S) and other hydrocarbons are essential to generate (Liquid Liquid Equilibria) LLE through UNIFAC model. UNIFAC model is highly non-convex and can have several local extrema. In this work, the structural group interaction parameters have been calculated for [OMIM][BF

4

] + thiophene + hydrocarbons and [OMIM] [BTI] + thiophene + hydrocarbons systems through regression using GA.The obtained LLE data has been correlated with reported values and it was observed that the cumulative RMSD(root mean square deviation) of ten ternary systems used for regression were 3.01% and 3.65% for [OMIM][BF

4

] and [OMIM]BTI] based system respectively. Further, the obtained interaction parameters were used to correlate the experimental LLE data for four ternary systems which were not used for regression. These systems having a total of 40 tie lines gave a very satisfactory RMSD of 1.76 to 3.99% between reported and predicted composition.

There has been considerable interest in using evolutionary algorithms based techniques to design creative systems. However,these techniques suffer from either being too creative and violating design constraints of the domain or those catering to a limited search space, but operating within design constraints. We have designed a new evolutionary system ‘HIER-HEIR’, which is not only creative (searches a large space effectively), but creates only such designs which are

valid

with respect to the design domain. Inspired by human design methodology, the representation is a hierarchy of components and variation acts at all levels of hierarchy intelligently, facilitating effective search in the design space with explicit control over exploitation and exploration. We have explained our technique with the metaphor of automatic design of a fashion dress in this paper. The experimental results validate our hypotheses with regard to the system. With regard to previous work, our technique is new both with regard to previously published hierarchical systems and those designed for evolving fashion designs.

Gene expression programming (GEP) is a novel evolutionary algorithm, which combines the advantages of simple genetic algorithm (SGA) and genetic programming (GP). Owing to its special structure of linear encoding and nonlinear decoding, GEP has been applied in various fields such as function finding and data classification. In this paper, we propose a modified GEP (Mod-GEP), in which, two strategies including population updating and population pruning are used to increase the diversity of population. Mod-GEP is applied into two practical function finding problems, the results show that Mod-GEP can get a more satisfactory solution than that of GP, GEP and GEP based on statistical analysis and stagnancy (AMACGEP).

This paper presents an important real-world application of both evolutionary computation and learning, an application to the search for optimal catalytic materials. In this area, evolutionary and especially genetic algorithms are encountered most frequently. However, their application is far from any standard methodology, due to problems with mixed optimization and constraints. The paper describes how these difficulties are dealt with in the evolutionary optimization system GENACAT, recently developed for searching optimal catalysts. It also recalls that the costly evaluation of objective functions in this application area can be tackled through learning suitable regression models of those functions, called surrogate models. Ongoing integration of neural-networks-based surrogate modelling with GENACAT is illustrated on two brief examples.

Mainstream surrogate approaches for multi-objective problems build one approximation for each objective. Mono-surrogate approaches instead aim at characterizing the Pareto front with a single model. Such an approach has been recently introduced using a mixture of regression Support Vector Machine (SVM) to clamp the current Pareto front to a single value, and one-class SVM to ensure that all dominated points will be mapped on one side of this value. A new mono-surrogate EMO approach is introduced here, relaxing the previous approach and modelling Pareto dominance within the rank-SVM framework. The resulting surrogate model is then used as a filter for offspring generation in standard Evolutionary Multi-Objective Algorithms, and is comparatively validated on a set of benchmark problems.

This paper presents results of experiments concerning the scalability of two-dimensional cellular automata rules in pattern reconstruction task. The proposed cellular automata based algorithm runs in two phases: the learning phase and the normal operating phase. The learning phase is conducted with use of a genetic algorithm and its aim is to discover efficient cellular automata rules. A real quality of discovered rules is tested in the normal operating phase. Experiments show a very good performance of discovered rules in solving the reconstruction task.

Evolutionary algorithms have been successfully applied to optimize the rulebase of fuzzy systems. This has lead to powerful automated systems for financial applications. We experimentally evaluate the approach of learning fuzzy rules by evolutionary algorithms proposed by Kroeske et al. [10]. The results presented in this paper show that the optimization of fuzzy rules may be universally simplified regardless of the complex fitness surface for the overall optimization process. We incorporate a local search procedure that makes use of these theoretical results into an evolutionary algorithms for rule-base optimization. Our experimental results show that this improves a state of the art approach for financial applications.

This paper presents a niched genetic programming tool, called DMGeo, which uses elitism and another techniques designed to efficiently perform classification rule mining in geographic databases. The main contribution of this algorithm is to present a way to work with geographical and conventional data in data mining tasks. In our approach, each individual in the genetic programming represents a classification rule using a boolean predicate. The adequacy of the individual to the problem is assessed using a fitness function, which determines its chances for selection. In each individual, the predicate combines conventional attributes (boolean, numeric) and geographic characteristics, evaluated using geometric and topological functions. Our prototype implementation of the tool was compared favorably to other classical classification ones. We show that the proposed niched genetic programming algorithm works efficiently with databases that contain geographic objects, opening up new possibilities for the use of genetic programming in geographic data mining problems.

It is necessary to estimate the weld bead width and depth of penetration using suitable sensors during welding to monitor weld quality. Infra red sensing is the natural choice for monitoring welding processes as welding is inherently a thermal processing method. An attempt has been made to estimate the bead width and depth of penetration from the infra red thermal image of the weld pool using artificial neural network models. Real time infra red images were captured using IR camera during A-TIG welding. The image features such as length and width of the hot spot, peak temperature and other features are extracted using image processing techniques. These parameters along with their respective current values are used as inputs while the measured bead width and depth of penetration are used as output of the neural network models. Accurate ANN models predicting weld bead width and depth of penetration have been developed.

We recently proposed swarm reinforcement learning methods in which multiple agents are prepared and they learn not only by individual learning but also by learning through exchanging information among the agents. The methods have been applied to a problem in discrete state-action space so far, and Q-learning method has been used as the individual learning. Although many studies in reinforcement learning have been done for problems in the discrete state-action space, continuous state-action space is required for coping with most real-world tasks. This paper proposes a swarm reinforcement learning method based on an actor-critic method in order to acquire optimal policies rapidly for problems in the continuous state-action space. The proposed method is applied to an inverted pendulum control problem, and its performance is examined through numerical experiments.

The eXtended Classifier System (XCS) is a rule-based evolutionary on-line learning system. Originally proposed by Wilson, XCS combines techniques from reinforcement learning and evolutionary optimization to learn a population of maximally general, but accurate condition-action rules. This paper focuses on the discovery component of XCS that is responsible for the creation and deletion of rules. A novel rule combining mechanism is proposed that infers maximally general rules from the existing population. Rule combining is evaluated for single- and multi-step learning problems using the well-known multiplexer, Woods, and Maze environments. Results indicate that the novel mechanism allows for faster learning rates and a reduced population size compared to the original XCS implementation.

A new approach to evolutionary robotics is presented. Neural networks are abstracted and supplanted by a system of ordinary differential equations that govern the changes in controller outputs. The equations are evolved as trees using an evolutionary algorithm based on symbolic regression in genetic programming. Initial proof-of-concept experiments are performed using a simulated two-wheeled robot that must drive a straight line while wheel response properties vary. Evolved controllers demonstrate the ability to learn and adapt to a changing environment, as well as the ability to generalize and perform well in novel situations.

Evolutionary algorithms have been successfully applied to design fuzzy rule-based classifiers. They are used for attribute selection, fuzzy set selection, rule selection, membership function tuning, and so on. Genetics-based machine learning (GBML) is one of the promising evolutionary algorithms for classifier design. It can find an appropriate combination of antecedent sets for each rule in a classifier. Although GBML has high search ability, it needs long computation time especially for large data sets. In this paper, we apply a parallel distributed implementation to our fuzzy genetics-based machine learning. In our method, we divide not only a population but also a training data set into subgroups. These subgroups are assigned to CPU cores. Through computational experiments on large data sets, we show the effectiveness of the proposed parallel distributed implementation.

A Multi-Objective Evolutionary Algorithm (MOEA) was adapted in order to deal with problems of feature selection in data-mining. The aim is to maximize the accuracy of the classifier and/or to minimize the errors produced while minimizing the number of features necessary. A Support Vector Machines (SVM) classifier was adopted. Simultaneously, the parameters required by the classifier were also optimized. The validity of the methodology proposed was tested in the problem of bankruptcy prediction using a database containing financial statements of 1200 medium sized private French companies. The results produced shown that MOEA is an efficient feature selection approach and the best results were obtained when the accuracy, the errors and the classifiers parameters are optimized.

Pasting Systems and Tile Pasting P Systems are syntactic techniques using pasting operation generating tiling patterns and tessellations. A variant of the Parametric Tile Pasting P System equipped with multiple-edge pasting operations and geometric transformation operations has been presented here. This extension, Tile Pasting P System with Multiple-Edge Pasting (TPPSMEP) discussed in this paper with the enhanced operations increases the generative capacity to produce patterns with recurring primitives and rotated/ scaled tiling patterns unlike the earlier versions.

The present work aims at designing and implementing an automated decision making system for the treatment of diabetes. The automated medical tool has been equipped to handle the decisions regarding the care plan of the patient and also helps in diagnosis. It takes in essential parameters like glucose, cholesterol, blood pressure and devises a care plan for the patient. Fuzzy logic was used to implement the medical decision support system. A knowledge base for diabetes containing the essential concepts, treatment algorithms was created. The fuzzy logic based system used the knowledge base for constructing the collection of rules. The essential parameters from the patient database were provided as input and the decisions like the type of diabetes, diet plans, medication etc were recorded. The tool also takes the decisions and the parameters that led to the decisions to build an optimal care pathway for the patient.

Fuzzy classifiers and fuzzy rules can be informally defined as tools that use fuzzy sets or fuzzy logic for their operations. In this paper, we use genetic programming to evolve a fuzzy classifier in the form of a fuzzy search expression to predict product quality. We interpret the data mining task as a fuzzy information retrieval problem and we apply a successful information retrieval method for search query optimization to the fuzzy classifier evolution. We demonstrate the ability of the genetic programming to evolve useful fuzzy classifiers on two use cases in which we detect faulty products of a product processing plant and discover intrusions in a computer network.

This paper describes an algorithm that generates analytic functions for PID step response characteristics (i. e. rise time, overshoot, settling time, peak time and integral of time weighted absolute error) in an application of a third-order plant. The algorithm uses genetic programming for symbolic regressions and provides formal expressions composed of variables, constants, elementary operators and mathematical functions. Results show a good fitting between the desired and obtained step response for DC motor positioning problem.

This work describes the incorporation of human strategies into a genetic algorithm. Human competence and machine intelligence are merged, creating a divide and evolve approach. The approach is applied to the restoration problem of Rubik’s Cube and successfully solves this task.

This paper reports a genetic algorithm (GA) for individual assignment using multi-locus microsatellite genotyping. Its performance has been compared with existing frequency, Bayesian and distance-based methods using simulated as well as actual data. Simulated data has been generated with SIMCOAL program. Actual data has been generated from genotypes of four cattle breeds from India. The GA showed lower accuracy while assigning individuals from simulated data. Its performance was comparable to that of existing methods using actual data.

In this paper, we study the path planning for Khepera II mobile robot in a grid map environment using an extended Q-learning algorithm. The extension offers an additional benefit of avoiding unnecessary computations involved to update the Q-table. A flag variable is used to keep track of the necessary updating in the entries of the Q-table. The validation of the algorithm is studied through real time execution on Khepera-II platform. An analysis reveals that there is a significant saving in time- and space- complexity of the proposed algorithm with respect to classical Q-learning.

Analysis of artificial evolutionary systems uses post-processing to extract information from runs. Many effective methods have been developed, but format incompatibilities limit their adoption. We propose a solution combining XML and compression, which imposes modest overhead. We describe the steps to integrate our schema in existing systems and tools, demonstrating a realistic application. We measure the overhead relative to current methods, and discuss the extension of this approach into a community-wide standard representation.

Computational intelligence competitions have recently gained a lot of interest. These contests motivate and encourage researchers to participate on them. Computer games are interesting test beds for research in artificial intelligence that motivate researchers to apply their work areas to specific games. In this paper a structural parameter set of a car agent is optimised using particle swarm optimisation and evolution strategies. The change was for were to the TORCS competition held during the Car Setup Optimization Competition EvoStar 2010.

In this paper, we suggest a novel problem within the context of multi objective optimization. It concerns the control of solutions’ performances in multi objective spaces. The motivation for controlling these performances comes from an inspiration to improve the robustness of solutions to physical deterioration. When deterioration occurs, the solution performances degrade. In order to prevent extended degradation and loss of robustness, an active control is implemented. Naturally, in order to enable such a control, the solution (product) should have tunable parameters that would serve as the controlled variables. Optimizing the solution for such a problem means that the tunable parameters should be found and their manipulation determined. Here the optimal solutions and the controller are designed using multi and single objective evolutionary algorithms. The paper is concluded with a discussion on the high potential of the approach for research and real life applications.

Thermoelectric devices are indeed device of future as they are green cooling devices. Tough still under research, performance of these devices is main concern to engineers for their suitability for practical use. In the present work, the two main concern i.e. Coefficient of Performance (COP) and Rate of Refrigeration (ROR) of such devices are simultaneously addressed. NSGA-II is used for finding Pareto-optimal solutions under three different settings for ambient conditions. Mathematical model is considered and effect of ambient conditions on optimal performance is also highlighted.The results of optimization are verified by theoretical governing equations for Thermo-Electric Coolers (TEC). It is concluded that Bi-Objective optimization of performance of single stage TEC is possible, relevant and have huge potential for practical use by designers of TEC.

Multi-objective optimizations of various conflicting objectives in designing particle reinforced silicone rubber are conducted using evolutionary algorithms to reduce the processing time of soft tooling process. A well-established evolutionary algorithm based multi-objective optimization tool, NSGA-II is adopted to find the optimal values of design parameters. From the obtained Pareto-optimal fronts, suitable multi-criterion decision making techniques are used to select one or a small set of the optimal solution(s) of design parameter(s) based on the higher level information of soft tooling process for industrial applications.

This study investigates the applicability of two elitist multi-objective evolutionary algorithms (MOEAs), namely the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and an improved Strength Pareto Evolutionary Algorithm (SPEA2), in the voltage and reactive power optimization problem. The problem has been formulated mathematically as a nonlinear constrained multiobjective optimization problem where the real power loss, the load bus voltage deviations and the installation cost of additional reactive power (VAR) sources are to be minimized simultaneously. To assess the effectiveness of the proposed approach, different combinations of the objectives have been minimized simultaneously. The simulation results showed that the two algorithms were able to generate a whole set of well distributed Pareto-optimal solutions in a single run. Moreover, fuzzy logic theory is employed to extract the best compromise solution over the trade-off curves obtained. Furthermore, a performance analysis showed that SPEA2 found better convergence and spread of solutions than NSGA-II. However, NSGA-II found more extended trade-off curves in some cases and required less computational time than SPEA2.

During engineering design, it is often difficult to quantify product reliability because of insufficient data or information for modeling the uncertainties. In such cases, one needs a reliability estimate when the functional form of the uncertainty in the design variables or parameters cannot be found. In this work, a probabilistic method to estimate the reliability in such cases is implemented using Non-Dominated Sorting Genetic Algorithm-II. The method is then coupled with an existing RBDO method to solve a problem with both epistemic and aleatory uncertainties.

This paper presents an application of multi-objective optimisation for the design of an important component of automobiles, namely the suspension system. In particular, we focus on the

double wishbone

suspension, which is one of the most popular suspensions in use today and is commonly found on mid-range to high-end cars. The design of such mechanical systems is fairly complicated due to the large number of design variables involved, complicated kinematic model, and most importantly, multiplicity of design objectives, which show conflict quite often.

The above characteristic of the design problem make it ideally suited for a study in optimisation using non-classical techniques for multi-objective optimisation. In this paper, we use +NSGA-II+ [5] for searching an optimal solution to the design problem. We focus on two important performance parameters, namely

camber

and

toe

, and propose objective functions which try to minimise the variation of these as the wheel travels in

jounce

and

rebound

. The

pareto-optimal

front between these two objectives are obtained using multiple formulations and their results are compared.

Controlling dominance area of solutions (CDAS) relaxes the concepts of Pareto dominance with an user-defined parameter

S

. This method enhances the search performance of dominance-based MOEA in many-objective optimization problems (MaOPs). However, to bring out desirable search performance, we have to experimentally find out

S

that controls dominance area appropriately. Also, there is a tendency to deteriorate the diversity of solutions obtained by CDAS when we decrease

S

from 0.5. To solve these problems, in this work, we propose a modification of CDAS called self-controlling dominance area of solutions (S-CDAS). In S-CDAS, the algorithm self-controls dominance area for each solution without the need of an external parameter. S-CDAS considers convergence and diversity and realizes a fine grained ranking that is different from conventional CDAS. In this work, we use many-objective 0/1 knapsack problems with

m

 = 4~10 objectives to verify the search performance of the proposed method. Simulation results show that S-CDAS achieves well-balanced search performance on both convergence and diversity compared to conventional NSGA-II, CDAS, IBEA

ε

 + 

and MSOPS.

Three Multi-Objective Differential Evolutions (MODEs) that differ in their selection schemes are applied to a real-world application, i.e., the multi-objective optimum design of the balanced Surface Acoustic Wave (SAW) filter used in cellular phones. In order to verify the optimality of the Pareto-optimal solutions obtained by the best MODE, those solutions are also compared with the solutions obtained by the weighted sum method. Besides, from the Principal Component Analysis (PCA) of the Pareto-optimal solutions, an obvious relationship between the objective function space and the design parameter space is disclosed.

We present a novel system to lessen the risk of occupational health hazards (OHH) of workers in the labor intensive industrieswith a job-combination approach. The work is carried out in a brick manufacturing (BM) unit at Hathras, India. The risk of OHH is assessed in terms of perceived discomfort level (PDL) of workers. PDL is computed with factor rating (FR) method. It is observed based on an initial survey in the BM unit that the workers, in general, aim to maximize their earnings by subjecting themselves to extreme work conditions due to economic reasons, and hence are exposed to greater risk of OHH resulting in higher values of PDL. We employ NSGA-II, an evolutionary multiobjective optimization (EMO) technique, to search for optimal PDL-earning tradeoff (PET) profile with two conflicting objectives, viz. minimization of PDL, and maximization of earnings.

Because of their numerous and diverse ranges, the tuning of process parameters of a machining process depends heavily upon operators’ technologies and experiences. Still, proper tuning cannot be expected from such a manual process, which encourages the use of an optimization tool for effective utilization of a process. In this paper, a multi-objective genetic algorithm (GA) is applied to electrochemical machining for tuning its various process parameters so that the optimum output can be achieved. An experimental dataset is used for modeling the problem through regression analysis, and then the GA is applied to a linear model and an exponential model for maximizing material removal rate and minimizing surface roughness.

Altruism may be found in sets (groups of solutions). In such cases, it may occur that individual/individuals degrade their chances of survival (with sacrifice in the extreme) to ensure survival of fitter individuals. The idea of altruism within group evolution is posed here as a multi objective problem. The aspiration of a group to survive (find an optimal solution) is posed versus the individual’s aspiration to survive. In the paper, the problem is a trajectory planning problem with the dilemma producing a Pareto set for a decision maker to choose from. It is shown that if the decision maker is ready to forfeit some of the group members, optimality may be gained. Evolutionary multi objective algorithm is implemented in order to search for this optimal set.

Monopulse antennas form an important methodology of realizing tracking radar and they are based on the simultaneous comparison of sum and differencesignals to compute the angle-error and to steer the antenna patterns in the direction of the target (i.e., the boresight direction). In this study, we consider the synthesis problem of difference patterns in monopulse antennas from the perspective of Multi-objective Optimization (MO). The synthesis problem is recast as a multi-objective optimization problem (for the first time, to the best of our knowledge), where the Maximum Side-Lobe Level (MSLL) and Beam Width (BW) of principal lobe are taken as the two objectives. The Optimal Pareto Fronts (OPF) are obtained for different number of elements and subarrays using one of the best-known evolutionary MO algorithms till date, called the Non-dominated Sorting Genetic Algorithm (NSGA-II). The quality of solutions obtained is compared with the help of Pareto fronts on the basis of the two objectives to investigate the dependence of the number of elements and the number of sub-arrays on the final solution. Then we find the best compromise solutions for 20 element array and compare the results with standard single objective algorithms such as the Differential Evolution (DE) that has been reported in literature so far for the synthesis problem.

This paper presents an improvement in performance of elitist non-dominated sorting genetic algorithm (NSGA-II) by modifying the probability distribution of crossover operator. The probability distribution of simulated binary crossover (SBX-A) operator, used in NSGA-II algorithm, is modified with lognormal distribution (SBX-LN). This algorithm is used to test twenty multi-objective functions. This NSGA-II (SBX-LN) algorithm performed well for different functions. This algorithm also performed well in optimizing a turbo-alternator design. It found more optimum solutions with better diversity in turbo-alternator design optimization.

Metamodels can speed up the optimization process. Previously evaluated designs can be used as a training set for building surrogate models. Subsequently an inexpensive

virtual

optimization can be performed. Candidate solutions found in this way need to be

validated

(evaluated by means of the real solver).

This process can be iterated in an automatic way: this is the reason of the

fast

optimization algorithms. At each iteration the newly evaluated designs enrich the training database, permitting more and more accurate metamodels to be build in an adaptive way.

In this paper a novel scheme for fast optimizers is introduced: the virtual optimization - representing an

exploitation

process - is accompanied by a virtual run of a suited space-filler algorithm - for

exploration

purposes - increasing the robustness of the fast optimizer.

A supply chain network system is to provide an optimal platform for efficient and effective supply chain management. There’s increasingly competitive, multi-channel retail world calls for a radically new strategy for evaluating supply chain network design. Retailers must abandon past practices which look to optimize the number and placement of facilities within traditional networks. A multi-objective optimization procedure which permits a trade-off evaluation for an integrated model is initially presented. This model includes elements of total cost, customer service and flexibility as its objectives and integrates facility location and inventory control decisions. Inventory control issues include economic order quantity, safety stock and inventory replenishment decisions and consider the risk pooling phenomenon to be realized from collaborative initiatives such as vendor-managed inventory. The possibility of a multi-objective evolutionary approach is developed to determine the optimal facility location portfolio and is implemented on a real large retail supply chain in Taiwan to investigate the model performance. Some preliminary results are described.

With the properties of multi-objective job shop problem (MOJSP) in mind, we integrate the multiagent systems and evolutionary algorithms to form a new algorithm, multiagent evolutionary algorithm for MOJSP (MAEA-MOJSP). In MAEA-MOJSP, an agent represents a candidate solution to MOJSP, and all agents live in a latticelike environment. Making use of three designed behaviors, the agents sense and interact with their neighbors. In the experiments, eight benchmark problems are used to test the performance of the algorithm proposed. The experimental results show that MAEA-MOJSP is effective.

From the viewpoint of decision making process, it brings inconveniences for decision makers to select one (few) proper solution(s). Thus we propose preference oriented two-layered multiagent evolutionary algorithm (TL-MAEA) to meet customers’ needs. The algorithm has a structure of two layers: in the top layer, preference relations among multiple objectives are calculated through interactions with the decision maker; while in the bottom layer, MAEA is employed to obtain the optimal solution corresponding to the preference relations. In the experimental, 12 benchmark problems are used to test the algorithm. The results show that the proposed algorithm is effective.

In this paper, we propose an adaptation to Nondominated Sorting Genetic Algorithm (NSGA-II), introducing a data structure, called

NonDominated Tree (NDT)

. The NDT is an adaptation of a Binary Search Tree and is used to identify the nondominated fronts in only one run. This structure may be used to improve even more the performance of NSGA-II and other Evolutionary Algorithms (EAs) that use nondominated sorting procedures. It reduces the number of comparisons performed by the NSGA-II nondominated sorting routine. Some tests demonstrated that the proposed structure improves the search of fronts of nondominated solutions in an efficient way.

This paper introduces a hybrid shape optimization method (M-HYBRID) for multiple objectives (MO) using Genetic Algorithm (GA) and Ant Colony Optimization (ACO) in combination with a meshless computational fluid dynamics solver. It uses the reference point based approach to reach the required optimum. This method was found to converge faster than MO optimizer based on GA alone. The constraint on the handling large number of parameters with MO optimiser based on ACO is overcome in M-HYBRID. This hybrid optimizer is good contender when a global optimum is the target.

The field of evolutionary multi-objective optimization (MOO) has witnessed an ever-growing number of studies to use artificial swarm behavior. In this paper authors have made an endeavor to minimize the computational burden, associated with global ranking methods and local selection modules used in many multi-objective particle swarm optimizers. Two different swarm strategies were employed for global and local search respectively using particle swarms and bacterial chemotaxis. In this paper the authors have shown comparative improvements of the proposed method namely MOBSO, with a benchmark evolutionary MOO method, NSGA-II. The paper also highlights the reduction in computational complexity for large populations, due to the proposed method.

This paper proposes an approach for the optimisation of web business processes using multi-objective evolutionary computing. Business process optimisation is considered as the problem of constructing feasible business process designs with optimum attribute values such as duration and cost. This optimisation framework involves the application of a series of Evolutionary Multi-objective Optimisation Algorithms (EMOAs) in an attempt to generate a series of diverse optimised business process designs for given requirements. The optimisation framework is tested to validate the framework’s capability in capturing, composing and optimising business process designs constituted of web services. The results from the web business process optimisation scenario, featured in this paper, demonstrate that the framework can identify business process designs with optimised attribute values.

In present work, multi-objective optimization of multi-stage planetary gear train is done. Optimization of multi-stage speed reducer is difficult due to involvement of integer variables. Minimizing surface fatigue life factor and minimization of volume of gear box are two conflicting objective functions under consideration. Two methods, one classical (SQP) and other non-traditional (NSGA-II) have been used for analysis to satisfy strength and other geometric criteria. Previous work is concentrated on optimization of spur or helical gears. This work is an extension to earlier work in a sense that planetary gear train with reduced speed involves more geometric constraints.

Control systems design may be based on many criteria. These optimization problems are nonconvex, therefore evolutionary multi-objective optimization algorithms (EMOA) are methods of choice. In engineering design problems it is desirable to find the one solution only as in single criterion optimisation. We describe a new method based on reduction of objectives while keeping relevant Pareto sets changes bounded. In the illustrative control design six objectives from optimal control, mixed norm robust optimization and standard control methods are reduced to three, which enables visualisation of the Pareto front.

This paper studies the probabilistic based evolutionary algorithms in dealing with bi-objective travelling salesman problem. Multi-objective restricted Boltzmann machine and univariate marginal distribution algorithm in binary representation are modified into permutation based representation. Each city is represented by an integer number and the probability distributions of the cities are constructed by running the modeling approach. A refinement operator and a local exploitation operator are proposed in this work. The probabilistic based evolutionary optimizers are subsequently combined with genetic based evolutionary optimizer to complement the limitations of both algorithms.

This paper presents a novel technique to detect irregular shell clusters using an algorithm that is inspired by Ant Colony Optimization (ACO). Till now major work on shell clustering has been based on regular shells using a fuzzy-based technique. However the proposed algorithm can separate irregular shell clusters from the solid clusters very efficiently. The algorithm is tested on seven test images and it is seen to give very good results.

The objective of this paper is to investigate optimum process parameters and tool geometries in Friction Stir Welding (FSW) to minimize temperature difference between the leading edge of the tool probe and the work piece material in front of the tool shoulder, and simultaneously maximize traverse welding speed, which conflicts with the former objective. An evolutionary multi-objective optimization algorithm (i.e. NSGA-II), is applied to find multiple trade-off solutions followed by a gradient-based local search (i.e. SQP) to improve the convergence of the obtained Pareto-optimal front. In order to reduce the number of function evaluations in the local search procedure, the obtained non-dominated solutions are clustered in the objective space and consequently, a post-optimality study is manually performed to find out some common design principles among those solutions. Finally, two reasonable design choices have been offered based on several process specific performance and cost related criteria.

Radial Basis Function Neural Network (RBFNN) is a curve fitting tool in a higher dimensional space. The nature of this surface depends mainly on the number of neurons in the hidden layer. The number of hidden neurons is decided by the number of clusters into which the data-set gets divided. It has been shown that the accuracy in prediction depends upon the quality of the clusters. To obtain good quality clusters, in this study, a hybrid optimization scheme of running a genetic algorithm in the outer loop, while simultaneously running a back-propagation algorithm in the inner loop, has been adopted. The number of hidden neurons is kept the same with that of clusters formed by an algorithm proposed here, apart from the popular fuzzy-c-means and entropy-based clustering algorithms. RBFNN developed using the proposed clustering algorithm is found to perform better than that obtained utilizing the other two clustering algorithms. The method has been successfully implemented in both forward and reverse mappings of electron beam welding process.

The Levenberg Marquardt (LM) algorithm is a popular non-linear least squares optimization technique for solving data matching problems. In this method, the damping parameter plays a vital role in determining the convergence of the system. This damping parameter is calculated arbitrarily in the classical LM, causing it to converge prematurely when used for solving real world engineering problems. This paper focuses on changes made to the classical LM algorithm to enhance its performance. This is achieved by adaptive damping, wherein the damping parameter is varied depending on the convergence of the objective function. To eliminate the need for a good initial guess, the idea of using an evolutionary algorithm in conjunction with the LM algorithm is also explored.

Constrained engineering design optimization problems are usually computationally expensive due to non-linearity and non convexity of the constraint functions. Penalty function methods are found to be quite popular due to their simplicity and ease of implementation, but they require an appropriate value of the penalty parameter. Bi-objective approach is one of the methods to handle constraints, in which the minimization of the constraint violation is included as an additional objective. In this paper, constrained engineering design optimization problems are solved by combining the penalty function approach with a bi-objective evolutionary approach which play complementary roles to help each other. The penalty parameter is approximated using bi-objective approach and a classical method is used for the solution of unconstrained penalized function. In this methodology, we have also eliminated the local search parameter which was needed in our previous study.

A novel process has been developed for reducing complexity in real-world, high-dimensional, multi-objective optimisation problems. This approach relies on being able to identify and exploit local harmony between objectives to reduce dimensionality. To achieve this, a systematic and modular process has been designed to cluster the Pareto-optimal front and apply a rule-based Principal Component Analysis including preference articulation for potential objective reduction. This many-objective optimisation decision-making process is demonstrated on a real-world, automotive diesel engine calibration optimisation problem comprising six objectives. The complexity reduction process resulted in three- and four-objective sub-problems. In the former, a significant improvement was achieved in one of the retained objectives at very little cost to the others.

In this paper, we propose a sequential decomposition method for multi-class pattern classification problems based on domain knowledge. A novel modular decision tree architecture is used to divide a

K

-class classification problem into a series of

L

smaller (binary or multi-class) sub-problems. The set of all

K

classes

c

 = {

c

1

,

c

2

, ...

c

K

} is divided into smaller subsets (

c

 = {

s

1

,

s

2

, ...

s

L

}) each of which contains classes that are related to each other. A modular approach is then used to solve (1) the binary sub-problems (

$p_i = \{s_i, \bar{s_i}\}$

) and (2) the smaller multi-class problem

s

i

 = {

c

i

1

,

c

i

2

, ...

c

in

}. Problem decomposition helps in a better understanding of the problem without compromising on the classification accuracy. This is demonstrated using the rules generated by the

C

4.5 classifier using a monolithic system and the modular system.

In this paper an application of conventional Particle Swarm Optimization (PSO) approach with alternative neighborhood topologies is proposed for the design of virtual manufacturing cells within which machines and jobs are assigned to the cells with a view to maximize productive output, whilst simultaneously minimizing the inter-cell movements due to the limited availability of machines. The PSO results are then compared with the following approaches: Binary PSO (BPSO) and Preemptive / Lexico Goal Programming. It is observed that the PSO topological variants perform well for the assumed VCM design problem.

In order to reduce the amount of wasted energy in office lighting and provide a major contribution to lowering overall energy consumption, we are developing a new energy saving system for office lighting by using adjustable lamp, ZigBee Wireless Sensor Network (WSN) and Particle Swarm Optimization (PSO). In this paper we make a prototype system which consists of one ZigBee control module, four fluorescent lamps with dimming capacity and three illumination sensors.The illumination sensors collect and send the data to the control module. After the PSO (Particle Swarm Optimization) process, the module finally sets the power of the lamps according to the PSO result. After real experiments in both sunny day and cloudy dayin a small-size office, it was proved that the system can successfully control the lights, and save considerable energy.

A global supply chain spans several regions and countries across the globe. A tremendous spurt in the extent of globalization has necessitated the need for modeling global supply chains in place of the conventional supply chains. In this paper, we propose a framework,

EcoSupply

, to analyze the supply chain ecosystem in a probabilistic setting unlike the existing methodologies, which presume a deterministic context. EcoSupply keeps track of the previous observations in order to facilitate improved prediction about the influence of uncertainties in the ecosystem, and provides a coherent mathematical exposition to construe the new associations, among the different supply chain stakeholders, in place of the existing links. To the best of our knowledge, EcoSupply is the first machine learning based paradigm to incorporate the dynamics of global supply chains.

In studying data sets for complex nonlinear relations, neural networks can be used as modeling tools. Trained fully connected networks cannot, however, reveal the relevant inputs among a large set of potential ones, so a pruning of the connections must be undertaken to reveal the underlying relations. The paper presents a general method for detecting nonlinear relations between a set of potential inputs and an output variable. The method is based on a neural network pruning algorithm, which is run repetitively to finally yield Pareto fronts of solutions with respect to the approximation error and network complexity. The occurrence of an input on these fronts is taken to reflect its relevance for describing the output variable. The method is illustrated on a simulated cell population sensitized to death-inducing ligands resulting in programmed cell death (apoptosis).

In this paper, couple of multi-objective optimization (MOO) techniques is implemented on a concept vehicle design problem. The Pareto Set Pursuing (PSP) method, proposed by Shan and Wang [1] is compared with a commercial version of the NSGA-II algorithm. PSP uses a sequential surrogate model generation and progressive importance sampling approach as compared to the NSGA-II, which uses exact function evaluations. This comparative study is initially carried out with the aid of a continuous analytical test problem followed by a mixed discrete continuous, vehicle design problem. Based on these studies, it was found that PSP performed reasonably well as compared to the NSGA-II and offered considerable savings on the number of function evaluations. Additionally, it also provided an evenly spread Pareto frontier. For the concept vehicle design problem, the performance of PSP was comparable with NSGA-II in terms of the accuracy of Pareto frontier and better in terms of the spread of the Pareto frontier.

Partitional algorithms form an extremely popular class of clustering algorithms. Primarily, these algorithms can be classified into two sub-categories: a)

k

-means based algorithms that presume the knowledge of a suitable

k

, and b) algorithms such as Leader, which take a distance threshold value,

τ

, as an input. In this work, we make the following contributions. We 1) propose a novel technique, EPIC, which is based on both the number of clusters,

k

and the distance threshold,

τ

, 2) demonstrate that the proposed algorithm achieves better performance than the standard

k

-means algorithm, and 3) present a generic scheme for integrating EPIC into different classification algorithms to reduce their training time complexity.

Suffix trees provide for efficient indexing of numerous sequence processing problems in biological databases. We address the pivotal issue of improving the search efficiency of disk-resident suffix trees by improving the storage layout from a statistical learning viewpoint. In particular, we make the following contributions: we (a) introduce the

Q

-Optimal Disk Layout(

Q

-OptDL) problem in the context of suffix trees and prove it to be NP-Hard, and (b) propose an algorithm for improving the layout of suffix trees that is guaranteed to perform asymptotically no worse than twice the optimal disk layout.