Handbook of Optimization

Solving a dynamic optimization problem means that the obtained results depend explicitly on time as a parameter. There are two major branches in which dynamic optimization occurs: (i) in dynamic programming and optimal control, and (ii) in dynamic fitness landscapes and evolutionary computation. In both fields, solving such problems is established practice while at the same time special and advanced aspects are still subject of research. In this chapter, we intend to give a comparative study of the two branches of dynamic optimization. We review both problem settings, define them, and discuss approaches for and issues in solving them. The main focus here is to highlight the connections and parallels. In particular, we show that optimal control problems can be understood as dynamic fitness landscapes, where for linear systems this relationship can even be expressed analytically.

This chapter presents the Bounded Dual Simplex Algorithm, which is one of the most frequently used linear programming algorithms for solving real-world problems. A solution structure of the bounded dual simplex method (used to solve linear programming problems) is presented. The main advantage of this algorithm is its use in finding solutions for large-scale problems, and its robustness and efficiency are identified in this chapter. One application of this algorithm in the area of electrical engineering is provided: namely, solving the transmission network expansion planning where the normal operation conditions of the system are continually evaluated by solving linear programming problems. The method is explained step-by-step, so that the methodology can be adapted to other problems. Finally, some conclusions are drawn.

This chapter deals with variational inclusions of the form 0 ∈ 

f

(

x

) + 

g

(

x

) + 

F

(

x

) where f is a locally Lipschitz and subanalytic function, g is a Lipschitz function, F is a set-valued map, acting all in ℝ

n

and

n

is a positive integer. The study of the previous variational inclusion depends on the properties of the function

g

. The behaviour as been examinated in different cases : when

g

is the null function, when

g

possesses divided differences and when

g

is not smooth and semismooth. We recall and give a summary of some known methods and the last section is very original and is unpublished. In this last section we combine a Newton type method (applied to

f

) with a secant type method (applied to

g

) and we obtain superlinear convergence to a solution of the variational inclusion. Our study in the present chapter is in the context of subanalytic functions, which are semismooth functions and the usual concept of derivative is replaced here by the the concept of Clarke’s Jacobian.

Many NP-complete optimization problems may be approximately solved by stochastic or deterministic heuristic methods and it is necessary to find their efficient data representation to minimize iteration computational time. In this chapter, we will touch the Minimum Steiner Tree Problems in Graphs (or Network Steiner Tree Problem), which can be solved by heuristics based on the Minimum Spanning Tree Problem and/or the Shortest Path Problem using a binary heap that enables to implement a priority queue that substantially increases the algorithm efficiency. We will also show a Delaunay triangulation-based way of finding minimal networks connecting a set of given points in the Euclidean plane using straight lines (minimum spanning tree) and its more general case (Steiner minimum tree) where additional points can be considered. Finally, we will deal with visibility graphs, Voronoi diagrams and rapidly exploring trees and focus on their applications in robot motion planning, where the robot should pass around obstacles from a given starting position to a given target position, touching none of them.

In this chapter we present an algorithm of quasi-linear complexity, based on the calculation of the infimal convolution of convex quadratic functions, that leads to the determination of the analytical optimal solution of the Continuous Quadratic Knapsack problem. The algorithm both exactly and simultaneously solves a separable uniparametric family of quadratic programming problems resulting from varying the equality constraint. We prove that the analytical solution of the problem is piecewise quadratic, continuous and, under certain conditions, belongs to the class

C

1

. Moreover we analyze the complexity of the algorithm presented and prove that the complexity is quasi-linear in order. We demonstrate that our algorithm is able to deal with large-scale quadratic programming problems of this type. We present a very important application: the classical Problem of Economic Dispatch. Finally, we release the source code for our algorithm in the computer language Mathematica.

We introduce a new node spreading bio-inspired game (BioGame) which combines genetic algorithms and traditional game theory. The goal of the BioGame is to maximize the area covered by mobile ad hoc network nodes to achieve a uniform node distribution while keeping the network connected. BioGame is fully distributed, scalable, and does not require synchronization among nodes. Each mobile node runs BioGame autonomously to make movement decisions based solely on local data. First, our force-based genetic algorithm (FGA) finds a set of preferred next locations to move. Next, favorable locations identified by FGA are evaluated by the spatial game set up among a moving node and its current neighbors. In this chapter, we present the FGA and the spatial game elements of our BioGame. We prove the basic properties of BioGame, including its convergence and area coverage characteristics. Simulation experiments demonstrate that BioGame performs well with respect to network area coverage, uniform distribution of mobile nodes, the total distance traveled by the nodes, and convergence speed. Our BioGame outperforms FGA and successfully distributes mobile nodes over an unknown geographical terrain without requiring global network information nor a synchronization among the nodes. BioGame is a good candidate for self-spreading autonomous nodes that provides a power-efficient solution for many military and civilian applications.

Multilocal programming aims to identify all local maximizers of unconstrained or constrained nonlinear optimization problems. The multilocal programming theory relies on global optimization strategies combined with simple ideas that are inspired in deflection or stretching techniques to avoid convergence to the already detected local maximizers. The most used methods to solve this type of problems are based on stochastic procedures. In general, population-based methods are computationally expensive but rather reliable in identifying all local solutions. Stochastic methods based on point-to-point strategies are faster to identify the global solution, but sometimes are not able to identify all the optimal solutions of the problem. To handle the constraints of the problem, some penalty strategies are proposed. A well-known set of test problems is used to assess the performance of the algorithms. In this chapter, a review on recent techniques for both unconstrained and constrained multilocal programming is presented. Some real-world multilocal programming problems based on chemical engineering process design applications are described.

After an introduction that includes a discussion of the classic random walk, this paper presents a step-by-step development of the differential evolution (DE) global numerical optimization algorithm. Five fundamental DE strategies, each more complex than the last, are evaluated based on their conformance to invariance and symmetry principles, degree of control parameter dependence, computational efficiency and response to randomization. Optimal control parameter settings for the family of convex, quadratic functions are empirically derived.

This chapter presents a novel method for visualizing the dynamics of evolutionary algorithms in the form of complex networks. The analogy between individuals in populations in an arbitrary evolutionary algorithm and vertices of a complex network is discussed, as well as between edges in a complex network and communication between individuals in a population. The possibility of visualizing the dynamics of a complex network using the coupled map lattices method and control by means of chaos control techniques are also discussed.

Decision support system described here makes it possible to carry out multicriterial selection of hundreds of projects simultaneously, with tens of criterion functions with bivalent variables including polynomial ones and quotients of linear functions, and tens of resources limitations. Stewart’s idea [21] of the special scalarizing function based on the modified reference point approach, which has been hitherto applied for linear benefits and for balance criteria functions only, and its optimization by effective gradient method is used here in the situation described by Santhanam and Kyparisis [19], involving synergistic effects of second- and third-orders in benefit and cost criterion function, and in resource requirements respecting resource sharing and hierarchical contingency relationships among candidate projects. In addition, the system enables us making the dialogue of the solution in a way of adaptive creation of weights of criterion functions and also flexible projects portfolio changes. A test of efficiency is presented. Our method presented here has been published in [12].

An evolutionary metaphor of genetic programming for a symbolic regression of Boolean functions, which represent logic circuits, is studied. These functions are coded by acyclic oriented graphs with vertices corresponding to elementary Boolean operations, e. g. negation, conjunction, disjunction (both inclusive and exclusive), and their negations. The used acyclic oriented graphs are represented by the so-called column tables. Basic “genetic” operations of mutation and crossover are performed over these column tables. Preliminary results indicate that the proposed version of genetic programming with column tables is an effective evolutionary tool for a construction of optimized Boolean functions that are specified by tables of functional values for all possible combinations of arguments.

Fuzzy inference systems have found a very spread application field, especially in areas, which interact with humans. However, they lack any self-learning capabilities for design of their knowledge bases. Beside such means as neural networks and interpolation methods also genetic algorithms are used in this area. First of all the conventional approaches of genetic algorithms have found use in rule-based fuzzy inference systems. In addition, other approaches, as parts of a broader group of evolutionary algorithms, like particle swarm optimization and simulated annealing were applied for this area. Finally, various other promising approaches like fuzzy cognitive maps were adapted for fuzzy logic, too. Therefore, the structure of this chapter has three basic parts and it deals at first with adaptation and knowledge acquisition possibilities of fuzzy inference systems in general. Consecutively, methods of using genetic algorithms for the design of rule-based fuzzy inference systems are described. In the last part the scope of fuzzy cognitive maps is analysed and some adaptation approaches based on evolutionary algorithms are introduced.

Simulated annealing (SA) is a generic optimization method whose popularity stems from its simplicity and its global convergence properties; it emulates the physical process of annealing whereby a solid is heated and then cooled down to eventually reach a minimum energy configuration. Although successfully applied to many difficult problems, SA is widely reported to converge very slowly, and it is common practice to relax some of its convergence conditions as well as to allow extra freedom in its design. However, variations on the theme of annealing usually come without optimal convergence guarantees.

In this paper, we review the fundamentals of SA and we focus on acceleration techniques that come with a rigorous mathematical justification. We discuss the design of the candidate-solution generation mechanism, the issue of finite-time cooling, and the technique of acceleration by concave distortion of the objective function. We also investigate a recently introduced generalization of SA—stochastic continuation—which significantly increases the design flexibility by allowing the candidate-solution generation mechanism and the objective function to vary with temperature.

Compact algorithms are optimization algorithms belonging to the class of Estimation of Distribution Algorithms (EDAs). Compact algorithms employ the search logic of population-based algorithms but do not store and process an entire population and all the individuals therein, but on the contrary make use of a probabilistic representation of the population in order to perform the optimization process. This probabilistic representation simulates the population behaviour as it extensively explores the decision space at the beginning of the optimization process and progressively focuses the search on the most promising genotypes and narrows the search radius. In this way, a much smaller amount of parameters must be stored in the memory. Thus, a run of these algorithms requires much more limited memory devices compared to their corresponding standard population-based algorithms. This class of algorithms is especially useful for those applications characterized by a limited hardware, e.g. mobile systems, industrial robots, etc. This chapter illustrates the history of compact optimization by giving a description of the main paradigms proposed in literature and a novel interpretation of the subject as well as a design procedure. An application to space robotics is given in order to show the applicability of compact algorithms.

This chapter provides a review of methods for automatic modularization of programs evolved using genetic programming. We discuss several techniques used to establishing modularity in program evolution, including highly randomized techniques, techniques with beforehand specified structure of modules, techniques with evolvable structure and techniques with heuristic identification of modules. At first, simple techniques such as Encapsulation and Module Acquisition are discussed. The next two parts reviews Automatically Defined Functions and Automatically Defined Functions with Architecture Altering Operations that enable to evolve the structure of modules at the same time of evolving the modules itself. The following section is focused on Adaptive Representation through Learning, a technique with heuristic-based identification of modules. Next, Hierarchical Genetic Programming is described. Finally, establishing recursion and iteration, a code reuse technique closely related to modularization, is briefly surveyed.

Local optimization techniques such as gradient-based methods and the expectation-maximization algorithm have an advantage of fast convergence but do not guarantee convergence to the global optimum. On the other hand, global optimization techniques based on stochastic approaches such as evolutionary algorithms and simulated annealing provide the possibility of global convergence, which is accomplished at the expense of computational and time complexity. This chapter aims at demonstrating how these two approaches can be effectively combined for improved convergence speed and quality of the solution. In particular, a hybrid method, called hybrid simulated annealing (HSA), is presented, where a simulated annealing algorithm is combined with local optimization methods. First, its general procedure and mathematical convergence properties are described. Then, its two example applications are presented, namely, optimization of hidden Markov models for visual speech recognition and optimization of radial basis function networks for pattern classification, in order to show how the HSA algorithm can be successfully adopted for solving real-world problems effectively. As an appendix, the source code for multi-dimensional Cauchy random number generation is provided, which is essential for implementation of the presented method.

Seven up-to-date adaptive variants of differential evolution were compared in six benchmark problems of two levels of dimension (

D

 = 30 and

D

 = 100). The opposition-based optimization was also implemented to each adaptive variant and compared in experiments. It was found that all the algorithms perform very reliably in the problems of

D

 = 30, whereas their reliability rate in the problems of

D

 = 100 differs substantially among the test problems. Only two algorithms (JADE and

b6e6rl

variant of competitive DE) operate with acceptable reliability in all the problems. Considering the computational costs, the rank of the algorithms is different in various problems. When the average performance over all the problems is taken into account, JADE was the most efficient and

b6e6rl

the most reliable. The implementation of opposition-based optimization into adaptive variants of differential evolution does not increase the reliability and its positive influence on the efficiency is rare. Based on the results, recommendations to application of adaptive algorithms are formed and the source code of the algorithms is available online.

This chapter shows the interest of Takagi-Sugeno (T-S) fuzzy model approach to apprehend nonlinear behaviors of physical systems and its application for observers design. From mathematical nonlinear model or experimental data, a T-S representation can be obtained using different techniques. This approach is largely exploited in many fields such as control, diagnosis and fault-tolerant control. Then the design of a robust T-S observer is addressed. The chapter considers a robust observer with respect to the uncertainties as well as unknown inputs. The synthesis of sufficient design conditions are performed using Lyapunov functions and set of linear matrix inequalities (

$\mathcal{LMI}$

). Two case studies are given. An example, dealing with a turbojet plane, shows how to obtain T-S representation using optimization algorithms. The validity of the proposed observer design is based on automatic steering of vehicles.

Cellular genetic algorithms (cGAs) are a kind of genetic algorithms (GAs) with decentralized population in which interactions among individuals are restricted to the closest ones. The use of decentralized populations in GAs allows to keep the population diversity for longer, usually resulting in a better exploration of the search space and, therefore in a better performance of the algorithm. However, the use of decentralized populations supposes the need of several new parameters that have a major impact on the behavior of the algorithm. In the case of cGAs, these parameters are the population and neighborhood shapes. Hence, in this work we propose a new adaptive technique based in Cellular Automata, Game Theory and Coalitions that allow to manage dynamic neighborhoods. As a result, the new adaptive cGAs (EACO) with coalitions outperform the compared cGA with fixed neighborhood for the selected benchmark of combinatorial optimization problems.

Graph vertex coloring is one of the most studied NP-hard combinatorial optimization problems. Given the hardness of the problem, various heuristic algorithms have been proposed for practical graph coloring, based on local search, population-based approaches and hybrid methods. The research in graph coloring heuristics is very active and improved results have been obtained recently, notably for coloring large and very large graphs. This chapter surveys and analyzes graph coloring heuristics with a focus on the most recent advances.

The overall efficiency, reliability, and availability of firewalls are crucial in enforcing and administering security, especially when the network is under attack. These challenges require new designs, architecture and algorithms to optimize firewalls. Contrary to a list-based structure, a de-centralized (hierarchical) design leads to efficient organization of rule-sets, thereby significantly increasing the performance of the firewall. The objective is to transform the original list-based rule-set into more efficient and manageable structures, in order to improve the performance of firewalls. The main features of this approach are the hierarchical design, rule-set transformation approaches, online traffic adaptation mechanisms, and a strong reactive scheme to counter malicious attacks (e.g.

Denial-of-Service (DoS)

attacks [1]).

This paper presents a model that incorporates the concepts of a systems approach (theory of constraints) into supply chain network design to determine the optimal location of a new distribution center in supply chain network design. A Non-dominated sorting Particle Swarm Optimization (NSPSO) Algorithm is proposed to solve the problem at hand and two settings for handling the constraints are, also, presented and compared. Results showed improved results of the proposed formulation over published results especially with respect to the total inventory capacity throughout the supply chain.

This contribution deals with search and implementation of optimization algorithms in analyzing and evaluating objects of interest present in ultrasound images as well as assessing the progress or regressions illustrated in these objects. These objects are highly significant from a medical perspective and include atherosclerotic plaque in carotid arteries, the intima-media thickness in the distal part of the common carotid artery, cerebral cortex size and brain stem findings in cases of Parkinson disease. Here, we describe procedures employing common principles and methods for recognizing points of interest in images that may serve in finding and determining pixel coordinates and other parameters and properties of analyzed objects. We use the stochastic optimization algorithm to optimize the energy function of deformable models used to approximate the locations and shapes of object boundaries in medical images. We suppose that evolutionary algorithm called SOMA can be used to find the desired global solution. Evolutionary algorithms are based on principles of evolution found in nature and respect the Darwin‘s theory of natural selection according to the defined cost function and gene recombination and mutation. As the computation of gradient vector flow field and also the evolution of active contour are computationally very expensive, we investigate the suitability of the GPU for a parallel implementation.

This chapter presents a general framework of Differential Evolution algorithm for combinatorial optimization problems. We define the differences between a given pair of solutions in the differential mutation as a set of elementary movements in the discrete search space. In this way, the search mechanism and self-adaptive behavior of the differential evolution is preserved and generalized to combinatorial problems. These ideas are then applied to n-job m-machine flow shop scheduling in order to illustrate its application in an important problem in combinatorial optimization. The method was applied to the 120 Taillard instances of the permutation flow shop scheduling problem, and compared against the results obtained by other metaheuristic algorithms in the literature. Although relying only on the differential mutation and the local search performed on the best individual, dDE ranks fairly well against more sophisticated metaheuristics. The results are promising and illustrate the applicability of the proposed approach for combinatorial optimization using differential evolution.

Multi-objective optimization of industrial low density polyethylene (LDPE) tubular reactor is carried out using improved strategies of multi-objective differential evolution (MODE) algorithm (namely, MODE-III and hybrid-MODE). Two case studies consisting of two-objective optimization and four-objective optimization are considered. In case-1, two objectives namely, maximization of conversion and minimization of the sum of square of normalized side chain concentrations are considered. A set of eleven decision variables, which consists of operating variables, namely, inlet temperature (

T

in

), inlet pressure (

P

in

), the feed flow rates of -oxygen (

F

o

), -solvent (

F

S

), -initiators (

F

I,1

,

F

I,2

), and the five average jacket temperatures (

T

J,1

-

T

J,5

), are considered. Constraints on maximum temperature attained in the reactor and number average molecular weight are considered. The results of present study show that MODE-III algorithm is able to give consistent results for various control parameters. These results show the ability of the existing algorithm to produce more valuable and practical results that are important to the process plant engineer.

This chapter aims to address the challenging and demanding issue of solving a continuous nonlinear constrained global optimization problem. We propose four stochastic methods that rely on a population of points to diversify the search for a global solution: genetic algorithm, differential evolution, artificial fish swarm algorithm and electromagnetism-like mechanism. The performance of different variants of these algorithms is analyzed using a benchmark set of problems. Three different strategies to handle the equality and inequality constraints of the problem are addressed. An augmented Lagrangian-based technique, the tournament selection based on feasibility and dominance rules, and a strategy based on ranking objective and constraint violation are presented and tested. Numerical experiments are reported showing the effectiveness of our suggestions. Two well-known engineering design problems are successfully solved by the proposed methods.

This chapter will focus on the development of a system with Artificial Intelligence based on Evolutionary Computation that allow generate a quasi-optimum trace of a pipeline integrating Digital Elevation Models and Geographical Information Systems. The algorithm is conceived with optimization purposes based on the relevant characteristics of the trace without prior monetary quantification, although the last was taken into consideration.

The chapter will consist of three main sections: the description of the baseline information, a description of the design of evolutionary algorithm (EA) handling information of the first stage and finally the tasks of adjusting the parameters of EA and obtaining pipeline route quasi-optimum in the case of interest.

The tool developed in this chapter allows obtaining a quasi-optimal route trace by using a hybrid evolutionary algorithm. This development that exploits modern technologies opens new perspectives for feasibility studies of paths, reducing the total costs.

Today researchers need to solve vague defined problems working with huge data sets describing signals close to chaotic ones. Common feature of such signals is missing algebraic model explaining their nature. Genetic Algorithms and Evolutionary Strategies are suitable to optimize such models and Genetic Programming Algorithms to develop them. Hierarchical GPA-ES algorithm presented herein is used to build compact models of difficult signals including signals representing deterministic chaos. Efficiency of GPA-ES is presented in the paper. Specific group of non-linearly composed functions similar to real biomedical signals is studied in the paper. On the base of these prerequisites, models applicable in complex biomedical signals like EEG modeling are formed and studied within the contribution.

Optimization methods have had successful applications in business and public services. Nowadays the new theories of soft computing are used for these purposes. The applications in business and public services have specific features in comparison with others. The processes are focused on private corporate attempts at money making or decreasing expenses. The optimization plays very important roles especially in business because it helps to reduce costs that can lead to higher profits and to success in the competitive fight. There are various optimization methods used: classical ones and methods using soft computing. There are especially the methods such as fuzzy logic, neural networks, evolutionary algorithms, and the theory of chaos.

In this chapter, the main significant contributions are formulation of a new non-linear membership function using fuzzy approach to capture and describe vagueness in the technological coefficients of constraints in the industrial production planning problems. This non-linear membership function is flexible and convenience to the decision makers in their decision making process. Secondly, a nonlinear objective function in the form of cubic function for fuzzy optimization problems is successfully solved by two hybrid optimization techniques from the area of soft computing and classical approaches. Among the two techniques, one outstanding technique is selected based on the quality of the solution. An intelligent performance analysis is adapted to the convenience of decision makers and implementers to select the niche optimization techniques to apply in real word problem solving approach particularly related to industrial engineering problems.

This research deals with the optimization of control of Hénon Map, which is a discrete chaotic system. This work introduces and compares evolutionary approach representing tuning of parameters for an existing control method either with the standard cost function using the numerical desired state as the one of the input or blackbox type cost function, as well as meta-evolutionary approach representing synthesis of a whole control law by means of Analytic Programming (AP). These three approaches are used for the purpose of stabilization of the stable state and higher periodic orbits, which stand for oscillations between several values of chaotic system. For experimentation, Self-Organizing Migrating Algorithm (SOMA) and Differential Evolution (DE) were used.

This research introduces a method of steganalysis by means of neural networks and its structure optimization. The main aim is to explain the approach of revealing a hidden content in jpeg files by feed forward neural network with Levenberg-Marquardt training algorithm. This work is also concerned to description of data mining techniques for structure optimization of used neural network. The results showed almost 100% success of detection.

A GPU based enhanced differential evolution algorithm is presented in this chapter to solve the flow shop scheduling problem. The main premise is to show the effectiveness of using mainstream GPU hardware compared to high-end CPU, and analyze as to under what conditions it becomes viable. Both CUDA and OpenCL architecture is utilized and a comparison is done on the Mac OS X platform. The results validate that with increasing problem complexity, GPU programming becomes more viable.

The aim of this paper is to describe a new optimization method that can create control equations of general regulators. For this type of optimization a new method was created and we call it Two-Level Transplant Evolution (TLTE). This method allowed us to apply advanced methods of optimization, for example direct tree reducing of tree structure of control equation. The reduction method was named Arithmetic Tree Reducing (ART). For optimization of control equations of general controllers is suitable combine two evolutionary algorithms. Main goal in the first level of TLTE is the optimization of structure of general controllers. In the second level of TLTE the concrete parameters are optimized and the unknown abstract parameters in structure of equations are set. The method TLTE was created by combination of Transplant Evolution method (TE) and Differential Evolution method (DE). The Transplant Evolution (TE) optimizes structure of solution with unknown abstract parameters and the DE optimizes the parameters in this structure. The parameters are real numbers. The real numbers are not easy find directly in TE without DE. For evaluation of quality of found control equation are described new methods, which allow evaluate their quality. It can be used in the case when the simulation of control process cannot be finished. In results are shown some practical application. In all results we received the control equation that reached better quality of control process, than classical PID controllers and Takahashi‘s modification of PID controller.

A hybrid approach combining the unique exploration strategy of Discreet Self Organising Migration Algorithm and the robust and effective memory adaptive programming paradigm of Scatter Search is presented. The new hybrid approach is developed to solve permutative combinatorial optimization problems and it applied to the flow-shop with no-wait scheduling optimization problem. Experimentation is done with the benchmark Taillard sets and the obtained results are favorably compared with results in current literature.

Optimization approaches, inspired by different metaphors, have recently attracted the interest of the scientist community. On the other hand, circle detection over digital images has received considerable attention from the computer vision community over the last few years as tremendous efforts have been directed towards seeking for an optimal detector. This chapter presents an algorithm for the automatic detection of circular shapes embedded into cluttered and noisy images with no consideration of conventional Hough transform techniques. The approach is based on a physics-inspired technique known as the Electromagnetism-like Optimization (EMO). It follows the Electromagnetism principle regarding a attraction-repulsion mechanism which manages particles towards an optimal solution. Each particle represents a solution by holding a charge which is related to the objective function to be optimized. The algorithm uses the encoding of three non-collinear points embedded into the edge map as candidate circles. Guided by the values of the objective function, the set of encoded candidate circles (charged particles) are evolved using the EMO algorithm so that they can fit into actual circular shapes over the edge map. Experimental evidence from several tests on synthetic and natural images which provide a varying range of complexity validates the efficiency of our approach regarding accuracy, speed and robustness.

Evolutionary music composition refers to machine-based generation of musical pieces by means of evolutionary computation techniques. In this chapter we discuss machine-based music composition from several viewpoints. First, techniques used to machine-based music composition are reviewed. Second, music composition subtasks, such as generating melodies, harmonization of musical phrases and generating rhythm patterns or composition of a rhythm accompaniment are introduced. Third, two distinct approaches to the evaluation of generated music are discussed: interactive evaluation based on human mentor’s judgement and autonomous evaluation of generated musical material by the system itself. The rest of the chapter describes six recognized evolutionary systems for music composition in detail. In particular, the description is focused to the design of evolutionary algorithms behind these systems.

This chapter explores the use of the Artificial Bee Colony (ABC) algorithm to compute pixel classification for image segmentation. ABC is a heuristic algorithm motivated by the intelligent behaviour of honey-bees which has been successfully employed to solve complex optimization problems. In this approach, an image 1-D histogram is approximated through a Gaussian mixture model whose parameters are calculated by the ABC algorithm. For the approximation scheme, each Gaussian function represents a pixel class and therefore a threshold. Unlike the Expectation-Maximization (EM) algorithm, the ABC-based method shows fast convergence and low sensitivity to initial conditions. Remarkably, it also improves complex time-consuming computations commonly required by gradient-based methods. Experimental results demonstrate the algorithm’s ability to perform automatic multi-threshold selection yet showing interesting advantages by comparison to other well-known algorithms.

This chapter presents application of two popular Nature Inspired Algorithms (NIA); Particle Swarm Optimization (PSO) and Differential Evolution (DE) algorithms for solving the optimization problems that arise in the field of electrical engineering. The main focus is on efficient utilization of electrical energy and the protection of transmission lines, the most important fields of optimization in electrical engineering having nonconvex characteristics with several equality and inequality constraints. The PSO and DE variants are applied to various electrical engineering problems including over-current relay settings in transmission lines, in-situ parameter estimation of electric motors, design and control of induction motors (IM) serving to process industries and proportional-integral (PI) controller tuning in variable speed drives.

The fuzzy technology reveals that everything is a matter of degree. At the moment, many industrial production problems are solved by operational research optimization techniques. These techniques are performed under the consideration of some real assumptions. In current studies, we still have several problems that require the application of fuzzy linear, non-linear, non-continues and other mathematical programming techniques. The prime objective of this chapter is to investigate a new application to the literature and to solve the crude oil refinery production problem by using the hybrid optimization techniques such as; Tabu Search (TS), Hopfield Recurrent Artificial Neural Network (HRANN) and fuzzy approaches. In this work, the real-world problem of the refinery model (which has been developed in (Gunes, 2000)) was solved using various optimization techniques. Thorough comparative studies and results analysis was carried out as well. The final findings reveal that the hybrid optimization technique provides better, robust, efficient, flexible and stable solutions.

This paper addresses a point-to-point robotic arm path planning in complex obstacle environments. To guarantee a smoothness of a motion during a manipulation, a continuous function of a sixth degree polynomial is utilized as a joint angle path. The feasible sixth degree joint angle path will be searched utilizing a Particle Swarm Optimization (PSO). There is no information regarding the region of this feasible joint angle so that the PSO should search it first. At the first computation where the population is generated randomly, all particles commonly collide with obstacles. The searching computation will be continued till at certain iteration for which the feasible particle is met. Then, the PSO should evolve this particle to find the best one with the highest fitness value. It is very hard computation since it involves a requirement to escape from zero fitness. The most difficult computation in this case is in finding at least one particle that lies in the feasible zone. In this paper, the PSO has shown its good performance in finding the feasible motion of the sixth degree polynomial joint angle path by utilizing just the information of a forward kinematics. To simulate the proposed path planning, 3-Degree of Freedom (DOF) planar robot will be utilized.

The strength of physical science lies in its ability to explain phenomena as well as make prediction based on observable, repeatable phenomena according to known laws. Science is particularly weak in examining unique, non-repeatable events. We try to piece together the knowledge of evolution with the help of biology, informatics and physics to describe a complex evolutionary structure with unpredictable behavior. Evolution is a procedure where matter, energy, and information come together. Our research can be regarded as a natural extension of Darwin’s evolutionary view of the last century. We would like to find plausible uniformitarian mechanisms for evolution of complex systems. Workers with specialized training in overlapping disciplines can bring new insights to an area of study, enabling them to make original contributions. This chapter describes evolution of complexity as a basic principle of evolutionary computation.