Advances in Swarm Intelligence

Swarm-based metaheuristic algorithms inspired from swarm systems in nature have produced remarkable results while solving complex optimization problems. This is due to their capability of decentralized control of search agents able to explore search environment more effectively. The large number of metaheuristics sometimes puzzle beginners and practitioners where to start with. This experimental study covers 10 swarm-based metaheuristic algorithms introduced in last decade to be investigated on their performances on 12 test functions of high dimensions with diverse features of modality, scalability, and valley landscape. Based on simulations, it can be concluded that firefly algorithm outperformed rest of the algorithms while tested unimodal functions. On multimodal functions, animal migration algorithm produced outstanding results as compared to rest of the methods. In future, further investigation can be conducted on relating benchmark functions to real-world optimization problem so that metaheuristic algorithms can be grouped according to suitability of problem characteristics.

The mathematical model described here is an evolution of the one constructed within the studies [1–3] by De Santos and Villa, among others. This paper aims to formalize the concept of knowledge and its properties as a basis for creating generalized economic value functions [4], focusing on the business models of the current technological sector as the application environment. The main conclusions reached are focused on the improvement of the value of information and knowledge under the assumption of collective cooperation amongst information system agents, as well as the properties of the knowledge space derived from the model.

Consider the interaction of populations, in which there are exactly two species, one of which the predators eat the preys thereby affecting each other. In the study of this interaction Lotka-Volterra models have been used. This paper proposes a formal modelling and verification analysis methodology, which consists in representing the interaction behavior by means of a formula of the first order logic. Then, using the concept of logic implication, and transforming this logical implication relation into a set of clauses, called Skolem standard form, qualitative methods for verification (satisfiability) as well as performance issues, for some queries, are applied.

Both the original Cucker-Smale flocking model and a more recent version with collision avoidance do not have any control over how tightly the system of agents flock, which is measured by the flock diameter. In this paper, a cohesive force is introduced to potentially reduce the flock diameter. This cohesive force is similar to the repelling force used for collision avoidance. Simulation results show that this cohesive force can reduce or control the flock diameter. Furthermore, we show that for any set of model parameters, the cohesive force coefficient is the single determining factor of this diameter. The ability of this modified collision-avoiding Cucker-Smale model to provide control of the flock diameter could have significance when applied to robotic flocks.

Evolutionary computation (EC) is called “human-based EC” especially when its all main operators, which are selection, crossover, and mutation, are executed by humans. One type of human-based EC is distributed human-based EC, in which humans independently manage their solution candidates and share them by direct communication between the humans. It is expected that the EC solves problems in human organizations. However, it is not easy to conduct real experiments to investigate the effect of human behaviors on the performance of the EC because such experiments needs many cooperative people. In the paper, we, therefore, first model human behaviors and then build a simulation model including the model. The model of human behaviors focuses on physical movement and free will to decide a time of interactions with others. Furthermore, we attempt to understand the EC though simulations using the built simulation model.

Time characteristics of algorithm interpretation by Von-Neumann computers are investigated. With use of semi-Markov process fundamental apparatus the analytical model of program runtime evaluation is worked out. It is shown that external interruptions are the result of functioning of independent random process, which develops in parallel with algorithm interpretation. For description of interaction of main program, interruption generator and interruption handler apparatus of Petri-Markov nets is used. Basic structural-parametric model of computer functioning in the presence of interruptions is worked out. It is shown that in common case Petri-Markov model is an infinite one. The recursive procedure of wandering through Petri-Markov net for case under investigation is worked out. It is shown that process of wandering through the net is not quite semi-Markov one. The method of transformation of Petri-Markov model onto strictly semi-Markov process is proposed.

A novel nature-inspired deterministic derivative-free global optimization method, namely the dolphin pod optimization (DPO), is presented for solving simulation-based design optimization problems with costly objective functions. DPO implements, using a deterministic approach, the global search ability provided by a cetacean intelligence metaphor. The method is intended for unconstrained single-objective minimization and is based on a simplified social model of a dolphin pod in search for food. A parametric analysis is conducted to identify the most promising DPO setup, using 100 analytical benchmark functions and three performance criteria, varying the algorithm parameters. The most promising setup is compared with a deterministic particle swarm optimization and a DIviding RECTangles algorithm, and applied to two hull-form optimization problems, showing a very promising performance.

Teaching-learning-based Optimization (TLBO) is a popular meta-heuristic optimisation method that has been used in solving a number of scientific and engineering problems. In this paper, a new variant, namely Teaching-learning-feedback-based Optimization (TLFBO) is proposed. In addition to the two phases in the canonical TLBO, an additional feedback learning phase is employed to further speed up the convergence. The teacher in the previous generation is recorded and communicates with the current teacher to provide combined feedbacks to the learners and supervise the learning direction to avoid wasting computational efforts incurred in the previous generations. Numerical experiments on 10 well-known benchmark functions are conducted to evaluate the performance of the TLFBO, and experimental results show that the proposed TLFBO has a superior and competitive capability in solving continuous optimisation problems.

In this paper, an improved magnetotactic bacteria optimization algorithm (IMBOA) is proposed to solve unconstrained optimization problems. IMBOA uses an archive to keep some better solutions in order to guide the moving of the whole population in each generation. And it uses a kind of efficient interaction energy to enhance diversity of the population for encouraging broader exploration. The proposed algorithm is compared with some relative optimization algorithms on the CEC 2013 real-parameter optimization benchmark functions. Experimental results show that the proposed algorithm IMBOA has better performance than the compared algorithms on most of the benchmark problems.

As new roads constructed frequently, it is necessary to optimize the current guide sign system. To solve the problem scientifically and systematically, this paper proposes an optimization model for current guide sign system in the situation of adding a road, which is solved by Bird Mating Optimizer (BMO). The optimization model first selects several important entrances as optimized starting nodes. Next the set of guiding routes with the best costs from these starting nodes to the targeted road are solved by BMO. The costs consider travel time costs, usage costs for vehicles and reconstruction costs for the guide signs. Then deploy guide signs in the guiding routes considering driving habits. In addition, perfect the optimized project by deploying several necessary directly-guiding items in other entrances of the targeted road. Finally, the model is applied in Huacheng Avenue in Guangzhou for comparison with current deployment. Guiding accessibility to Huacheng Avenue improves from 77.9% to 88.9%.

Grey wolf optimization (GWO) algorithm is a novel nature-inspired heuristic paradigm. GWO was inspired by grey wolves, which mimics the leadership hierarchy and hunting mechanism of grey wolves in nature. It has exhibited promising performance in many fields. However, GWO algorithm has the drawback of slow convergence and low precision. In order to overcome this drawback, we propose an improved version of GWO enhanced by the Lévy-flight strategy, termed as LGWO. Lévy-flight strategy was introduced into the GWO to find better solutions when the grey wolves fall into the local optimums. The effectiveness of LGWO has been rigorously evaluated against ten benchmark functions. The experimental results demonstrate that the proposed approach outperforms the other three counterparts.

In general, the population of most metaheuristic algorithms is randomly initialized at the start of search. Monarch Butterfly Optimization (MBO) with a randomly initialized population, as a kind of metaheuristic algorithm, is recently proposed by Wang et al. In this paper, a new population initialization strategy is proposed with the aim of improving the performance of MBO. Firstly, the whole search space is equally divided into NP (population size) parts at each dimension. And then, in order to add the diversity of the initialized population, two random distributions (T and F distribution) are used to mutate the equally divided population. Accordingly, five variants of MBOs are proposed with new initialization strategy. By comparing five variants of MBOs with the basic MBO algorithm, the experimental results presented clearly demonstrate five variants of MBOs have much better performance than the basic MBO algorithm.

This paper investigates the effect of problem size on the roaming behaviour of particles in the particle swarm optimization (PSO) algorithm. Both the extent and impact of the roaming behaviour in the absence of boundary constraints is investigated, as well as the PSO algorithm’s ability to find good solutions outside of the area in which particles are initialized. Four basic PSO variations and a diverse set of real parameter benchmark problems were used as basis for the investigation. Problem size was found to have a significant impact on algorithm performance and roaming behaviour. The larger the problem is that is being considered, the more important it is to address roaming behaviour.

Particle swarm optimization has been applied to solve many optimization problems because of its simplicity and fast convergence performance. In order to avoid precocious convergence and further improve the ability of exploration and exploitation, many researchers modify the parameters and the topological structure of the algorithm. However, the boundary restriction strategy to prevent the particles from flying beyond the search space is rarely discussed. In this paper, we investigate the problems of the strategy that putting the particles beyond the search space on the boundary. The strategy may cause PSO to get stuck in the local optimal solutions and even the results cannot reflect the real performance of PSO. In addition, we also compare the strategy with the random updating strategy. The experiment results prove that the strategy that putting the particles beyond the search space on the boundary is unreasonable, and the random updating strategy is more effective.

Particle swarm optimization (PSO) has gained significant attention for solving numerical optimization problems in different applications. However, the performance of PSO depends on the appropriate setting of inertia weight and the optimal setting changes with generations during the evolution. Therefore, different adaptive inertia weight strategies have been proposed. However, the best inertia weight adaptive strategy depends on the nature of the optimization problem. In this paper, different inertia weight strategies such as linear, Gompertz, logarithmic and exponential decreasing inertia weights as well as chaotic and oscillating inertia weight strategies are explored. Finally, PSO with an adaptive ensemble of linear & Gompertz decreasing inertia weights is proposed and compared with other strategies on a diverse set of benchmark optimization problems with different dimensions. Additionally, the proposed method is incorporated into heterogeneous comprehensive learning PSO (HCLPSO) to demonstrate its effectiveness.

Particle Swarm Optimization (PSO) offers efficient simultaneous global and local searches but is challenged with the problem of slow local convergence. To address this issue, a hybrid comprehensive learning PSO algorithm with adaptive starting local search (ALS-HCLPSO) is proposed. Determining when to start local search is the main of ALS-HCLPSO. A quasi-entropy index is innovatively utilized as the criterion of population diversity to depict an aggregation degree of particles and to ascertain whether the global optimum basin has been explored. This adaptive strategy ensures the proper starting of local search. The test results on eight multimodal benchmark functions demonstrate the performance superiority of ALS-HCLPSO. And comparison results on six advanced PSO variants further test the validity and superiority of ALS-HCLPSO algorithm.

Swarm intelligence algorithms are wildly used in different areas. The bare bones particle swarm optimization (BBPSO) is one of them. In the BBPSO, the next position of a particle is chosen from the Gaussian distribution. However, all particles learning from the only global best particle may cause the premature convergence and rapid diversity-losing. Thus, a BBPSO with dynamic local search (DLS-BBPSO) is proposed to solve these problems. Also, because the blind setting of local group may cause the time complexity an unpredictable increase, a dynamic strategy is used in the process of local group creation to avoid this situation. Moreover, to confirm the searching ability of the proposed algorithm, a set of well-known benchmark functions are used in the experiments. Both unimodal and multimodal functions are considered to enhance the persuasion of the test. Meanwhile, the BBPSO and several other evolutionary algorithms are used as the control group. At last, the results of the experiment confirm the searching ability of the proposed algorithm in the test functions.

In recent years, multi-layer particle swarm optimization (MLPSO) has been applied in various global optimization problems for its superior performance. However, fast convergence speed leads the algorithm easy to converge to the local minimum. Therefore, MLPSO-Powell algorithm is proposed in this paper, selecting several swarm particles by the tournament operator in each generation to run Powell algorithm. MLPSO global searching performance with Powell local searching performance forces swarm particles to search more optima as much as possible, then it will rapidly converge as soon as it gets close to the global optimum. MLPSO-Powell enhances local search ability of PSO in dealing with multi-modal problems. The experimental results shows that the proposed approach improves performance and final results.

Landslide is a frequently repeated problem in many part of the world. This study follows up on a 2015 study, which used the PSO to optimize the STABL program in the slope stability analysis and found the best result in the literature (factor of safety = 1.238). In the current study, a modification of the PSO scripts was proposed and two new parameters (cohesion intercept and frictional angle) were added to the analysis to examine the effect of soil strength parameters. Assuming a negative correlation, it was found that the cohesion intercept had a bigger influence than the frictional angle on the final outcome in the analysis of a sample homogeneous soil slope. The addition of new parameters also reduced the FS of the optimized sliding surface.

Particle Swarm Optimization (PSO) is a kind of classical population-based intelligent optimization methods that widely used in solving various optimization problems. With the increase of the dimensions of the optimized problem, the high-dimensional particle swarm optimization becomes an urgent, practical and popular issue. Based on data similarly measurement, a high-dimensional PSO algorithm is proposed to solve the high-dimensional problems. The study primarily defines a new distance paradigm based on the existing similarity measurement of high-dimensional data. This is followed by proposes a PSO variant under the new distance paradigm, namely the LPSO algorithm, which is extended from the classical Euclidean space to the metric space. Finally, it is showed that LPSO could obtain better solution at higher convergence speed in high-dimensional search space.

This paper presents a center multi-swarm cooperative PSO with ratio and proportion learning (CMCPSO-RP), employing two well-known psychology theories. In the original MCPSO-CC, the convergence speed can be accelerated which comes at decreasing the diversity of sub-swarms, suffering from premature convergence. There is no mechanism to guarantee every possible region of the search space could be searched. To tackle this problem, all best particles from each sub-swarm can be collected and sent to master swarm to maintain a population of potential solutions. This process is less prone to becoming trapped in local minima, but typically has lower efficiency of iterations. To balance the ability of exploration and exploitation, a ratio and proportion learning strategy is proposed by empowering the searching particles with human-like thinking and cognitive process, inspired by Cognitive Load Theory and Human Problem Solving Theory. In our approach, a reasonable ratio design can be not only a way to exhibit a solution quality versus speed tradeoff, but also make CMCPSO-RP more in line with the laws of regular learning in nature. Application of the newly developed PSO algorithm on several benchmark optimization problems shows a marked improvement in performance over the comparison algorithms on all test functions.

Although combinatorial auctions make trading goods between buyers and sellers more conveniently, the winner determination problem (WDP) in combinatorial auctions poses a challenge due to computation complexity. In this paper, we consider combinatorial auction problem with transaction costs, supply constraints and non-negative surplus constraints. We formulate the WDP of combinatorial auction problem as an integer programming problem formulation. To deal with computational complexity of the WDP for combinatorial auctions, we propose an algorithm for finding solutions based on discrete PSO (DPSO) approach. The effectiveness of the proposed algorithm is also demonstrated by several numerical examples.

In this paper, we propose an algorithm for the registration of the GPS sensor and the stereo camera for vehicle localization within 3D dense point clouds. We adopt the particle swarm optimization algorithm to perform the sensor registration and the vehicle localization. The registration of the GPS sensor and the stereo camera is performed to increase the robustness of the vehicle localization algorithm. In the standard GPS-based vehicle localization, the algorithm is affected by noisy GPS signals in certain environmental conditions. We can address this problem through the sensor fusion or registration of the GPS and stereo camera. The sensors are registered by estimating the coordinate transformation matrix. Given the registration of the two sensors, we perform the point cloud-based vehicle localization. The vision-based localization is formulated as an optimization problem, where the “optimal” transformation matrix and corresponding virtual point cloud depth image is estimated. The transformation matrix, which is optimized, corresponds to the coordinate transformation between the stereo and point cloud coordinate systems. We validate the proposed algorithm with acquired datasets, and show that the algorithm robustly localizes the vehicle.

Translation is normally the main working mode of tunnel element transportation, which is one of key techniques in immersed tunnel. An approach which can decide the magnitudes and directions of towing forces is presented in no-power immersed tunnel element’s translation control under current flow. A particle swarm-based control method, which exploits a sort of linear weighted logarithmic function to avoid weak subgoals, is utilized. In simulation, the performance of the particle swarm-based control method is evaluated in the case of Hong Kong-Zhuhai-Macao Bridge project.

Inverse kinematics (IK) is an optimization problem solving the path or trajectory a multi-jointed body should take for an extremity to reach a specified target location. When also considering the flow of movement, IK becomes a multi-objective optimization problem (MOP). This study proposes the use of the vector evaluated particle swarm optimization (VEPSO) algorithm to solve IK. A 3D character arm, with 7 degrees of freedom, is used during experimentation. VEPSO’s results are compared to single-objective optimizers, as well as an optimizer that uses weighted aggregation to solve MOPs. Results show that the weighted aggregation approach can outperform IK-VEPSO if the correct weight combination (that is problem dependent) has been selected. However, IK-VEPSO produces a set of possible solutions.

This paper studies the M/M/1 machine repair problem using a single service station subject to working breakdowns. This service station can be in working breakdown state only when at least one failed machine exists in the system. The matrix-analytic method is used to compute the steady-state probabilities for the number of failed machines in the system. A cost model is constructed to simultaneously determine the optimal values for the number of operating machines and two variable service rates to minimize the total expected cost per machine per unit time. The particle swarm optimization (PSO) algorithm is implemented to search for the optimal minimum value until the system availability constraint is satisfied.

Although barely explored so far, swarm intelligence can arguably have a profound impact on video games; for instance, as a simple yet effective approach for the realistic intelligent behavior of Non-Player Characters (NPCs). In this context, we describe the application of particle swarm optimization to the behavioral design of NPCs in a first-person shooter video game. The feasibility and performance of our method is analyzed through some computer experiments. They show that the proposed approach performs very well and can be successfully used in a fully automatic (i.e., without any human player) and efficient way.

The performance of an ACO depends extremely on the cognition of each subpath, which is represented by the pheromone trails. This paper designs an experiment to explore a subpath’s exact role in the full-path generation. It gives three factors, sequential similarity ratio (SSR), iterative best similarity ratio (IBSR) and global best similarity ratio (GBSR), to evaluate some selected subpaths called r-rank subpaths in each iteration. The result shows that r-rank subpaths keep a rather stable proportion in the found best route. And then, by counting the crossed ants of a subpath in each iteration, a subpath-based pheromone modification rule is proposed to enhance the pheromone depositing strategy. It is combined with the iteration-best pheromone update rule to solve the traveling salesman problem (TSP), and experiments show that the new ACO has a good performance and robustness.

Interaction networks formed by foraging ants are among the most studied self-organizing multi-agent systems in nature that have inspired many practical applications. However, the vast majority of prior investigations assume pheromone trails or stigmergic strategies used by the ants to create foraging behaviors. We first review an ant network model where the direction and speed of each ant’s correlated random walk are influenced by direct and minimalist interactions, such as antennal contact. We incorporate basic ant memory with nest and food compasses, and adopt a discrete time, non-deterministic forager recruitment strategy to regulate the foraging population. The paper’s main focus is on decentralized congestion control and avoidance schemes that are activated with a quorum sensing mechanism. The model relies on individual ants’ ability to estimate a perceived avoidance sector from recent interactions. Through simulation experiments it is shown that a randomized congestion avoidance scheme improves performance over alternative static schemes.

Focus on the problem of finding the optimal path in wireless sensor networks (WSN), considering energy saving requirement, an energy-saving routing strategy based on ant colony optimization (DERS-ACO) is proposed. Our strategy designs the optimization rule of dynamic state transformation, and introduces the mechanism of rewards and penalties which further saves the search time and increase the probability of optimal path search, and prolongs lifetime of network greatly. Simulation showed that the searching probability of a global for the optimal solution is increased, and the global optimal solution is obtained quickly and effectively, furthermore the energy consumption of the nodes is saved, which will prolong the lifetime of network greatly.

A central issue in distributed formation of swarm is enabling robots with only a local view of their environment to take actions that advance global system objectives (emergence of collective behavior). This paper describes a bio-inspired control algorithm using pheromone for coordinating a swarm of identical flying robots to spatially self-organize into arbitrary shapes using local communication maintaining a certain level of density.

The pickup and delivery problem (PDP) is relevant to many real-world problems, e.g., logistic and transportation problems. The problem is to find the shortest route to gain commodities from the pickup nodes and supply them to the delivery nodes. The amount of commodities of pickup nodes and delivery nodes is usually assumed to be in equilibrium; thus, all pickup nodes have to be visited for collecting all commodities required. However, some real-world applications, such as rental bikes and wholesaling business, need only to gain sufficient commodities from certain pickup nodes. A variant of PDP, namely the selective pickup and delivery problem (SPDP), is formulated to address the above scenarios. The major difference of SPDP from PDP lies in the requirement of visiting all pickup nodes. The SPDP relaxes this requirement to achieve more efficient transportation. The goal of the SPDP is to seek the shortest path that satisfies the load constraint to supply the commodities demanded by all delivery nodes with some pickup nodes. This study proposes a max-min ant system (MMAS) to solve the SPDP. The ants aim to construct the shortest route for the SPDP considering the number of selected pickup nodes and all delivery nodes. This study conducts experiments to examine the performance of the proposed MMAS, in comparison with genetic algorithm and memetic algorithm. The experimental results validate the effectiveness and efficiency of the proposed MMAS in route length and convergence speed for the SPDP.

An improved ant-type approach, ant colony optimization (ACO) model, integrated with a heading direction scheme (HDS) to real-time collision-free navigation and mapping of an autonomous robot is proposed in this paper. The developed HDS-based ACO model for concurrent map building and safety-aware navigation is capable of remedying the shortcoming of risky distance from obstacles in combination with the Dynamic Window Approach (DWA) algorithm as a local navigator. Its effectiveness and efficiency of the developed real-time hybrid map building and safety-aware navigation of an autonomous robot have been successfully validated by simulated experiments and comparison studies.

There are lots of computationally intensive tasks in optimization process of Artificial Bee Colony (ABC) algorithm, which requires large CPU processing time. To improve optimization precision and performance of the ABC algorithm, a parallel Multi-cores Parallel ABC algorithm (MPABC) was proposed based on the Fork/Join framework. The algorithm is to introduce the multi-populations’ parallel operation to guarantee population’s diversity, improve the global convergence ability and avoid falling into the local optimum. The performance of the original serial ABC algorithm and the MPABC algorithm was analyzed and compared based on four benchmark objective functions. The results show that the MPABC algorithm can achieve the speedup of 3.795 and the efficiency of 94.87% in solving complex problems. It can make full use of multi-core resources, improve the solution’s quality and efficiency, and have the advantages of low parallel cost and simple realizing process.

RNA molecules folded into secondary structure are found to have structure related functionalities. Efficient computational techniques are required for common structural motif identification due to its relevance in the study of various functional aspects. In this work we focus on finding the most frequent descriptor motif inherent in given set of RNA sequences. Our approach uses an efficient computational method incorporating Nature inspired optimization algorithm. The motif skeletons are obtained by applying context free grammar defined for the descriptor motif. Then swarm intelligence based Artificial Bee Colony optimization algorithm is applied to derive the common motif with minimum and maximum length values of each motif element. Optimization process is done based on the objective function defined with the frequency of occurrence as major criterion. This method is able to generate correct motif structures in Signal Recognition Particle data set. The resultant motif is compared with the common motifs generated by other evolutionary methods.

Demand side management (DSM) is proposed to solve the contradiction between supply and demand of electricity market. To avoid the peak load, time-of-use (TOU) pricing strategy plays an important role in DSM to affect the behavior of using electricity by the users. In this paper, we proposed a mixed artificial bee colony (mABC) algorithm to TOU pricing optimization. Different from traditional research which optimizes the time division and electricity price separately, we consider these two factors together and optimize them simultaneously through the proposed mABC. The experimental results on a real-world scenario show the superiority of the mABC over traditional state-of-the-art methods.

Office-space allocation (OFA) problem is a class of complex optimization problems that distributes a set of limited entities to a set of resources subject to satisfying set of constraints. Due to the complexity of OFA, numerous metaheuristic-based techniques have been proposed. Artificial Bee Colony (ABC) algorithm is a swarm intelligence, metaheuristic techniques that have been utilized successfully to solve several formulations of university timetabling problems. This paper presents an adaptation of ABC algorithm for solving OFA problem. The adaptation process involves integration of three neighbourhood operators with the components of the ABC algorithm in order to cope with rugged search space of the OFA. The benchmark instances established by University of Nottingham namely Nothingham dataset is used in the evaluation of the proposed ABC algorithm. Interestingly, the ABC is able to produced high quality solution by obtaining two new results, one best results and competitive results in comparison with the state-of-the-art methods.

In this paper, we show that NSGA-II can be applied to GP and the Process Description Language (PDL) and describe two modifications to NSGA-II. The first modification removes individuals which have the same behaviour from GP populations. It selects for de-duplication by taking the result of each objective fitness function together to make a comparison. NSGA-II is designed to expand its Pareto front of solutions by favouring individuals who have the highest or lowest value (boundary points) in a front, for any objective. The second modification enhances exploitation by preferring individuals who occupy an extreme position for most objective fitness functions. The results show, for the first time, that NSGA-II can be used with PDL and GP to successfully solve a robot control problem and that the suggested modifications offer significant improvements over an algorithm used previously with GP and PDL and unmodified NSGA-II for our test problem.

Genetic algorithm (GA), an efficient evolutionary algorithm inspired from the science of genetics, attracts the worldwide attention for several decades. This paper tries to strengthen the search ability of the population in GA in the way of improving the distance among individuals by introducing a new solution updating strategy based on the theory of Cooperative Game. The simulation is done using fourteen benchmark functions, and the results demonstrate that this modified genetic algorithm works efficiently.

The consecutive meals planning is a combinatorial optimization problem that determines a meals plan in one period consisting of consecutive days. This paper proposes an evaluation function using a moving entropy for this problem. The function measures the appearance order of meal’s characteristics on the plan. In the numerical experiments, we apply a permutation GA to the problem. We show that our meals plan is a good solution with large variation of appearance order of meal’s characteristics for the consecutive meals planning.

As data sparsity may produce unreliable recommendations in collaborative filtering-based recommender systems, it has been addressed by many researchers in related fields. Jaccard index is regarded as effective when combined with existing similarity measures to relieve data sparsity problem. However, the index only reflects how many items are co-rated by two users, without considering whether their ratings are evaluated similar or not. This paper proposes a novel improvement of Jaccard index, reflecting not only the ratio of co-rated items but also whether the ratings of each co-rated item by two users are both high, medium, or low. A genetic algorithm is employed to find the optimal weights of the levels of evaluations and the optimal boundaries between them. We conducted extensive experiments to find that the proposed index significantly outperforms Jaccard index on moderately sparse to dense datasets, in terms of both prediction and recommendation qualities.

Most bio-inspired algorithms for solving the Steiner tree problem (STP) require the procedures of encoding and decoding. The frequent operations on both encoding and decoding inevitably result in serious time consumption and extra memory overhead, and then reduced the algorithms’ practicability. If a bio-inspired algorithm is encoding-free, its practicability will be improved. Being motivated by this thinking, this article presents an encoding-free genetic algorithm in solving the STP. To verify our proposed algorithm’s validity and investigate its performance, detailed simulations were carried out. Some insights in this article may also have significance for reference when solving the other problems related to the topological optimization.

An energy minimized method using genetic algorithm for solving redundancy of underwater vehicle-manipulator system is proposed in this paper. Energy minimization is here set up as an optimization problem. Under the constraints of the dynamic and kinematic equations, the inverse kinematic solution with the optimal index is formed by using the weight pseudoinverse matrix. Energy consumption function is chosen as the objective function, and then the energy minimized solution based on genetic algorithm for solving the redundancy of the system is performed. Two numerical examples are carried out to verify the proposed method and promising result is obtained.

Automatic generation of test case is an important means to improve the efficiency of software testing. As the theoretical and experimental base of the existing heuristic search algorithm, genetic algorithm shows great superiority in test case generation. However, since most of the present fitness functions are designed by a single target path, the efficiency of the generating test case is relatively low. In order to cope with this problem, this paper proposes an efficiency genetic algorithm by using a novel fitness function. By generating multiple test cases to cover multiple target paths, this algorithm needs less iterations hence exhibits higher efficiency comparing to the existing algorithms. The simulation results have also shown that the proposed algorithm is high path coverage and high efficiency.

Differential Evolution (DE) has been successfully applied to various optimization problems. The performance of DE is affected by algorithm parameters such as a scaling factor F and a crossover rate CR. Many studies have been done to control the parameters adaptively. One of the most successful studies on controlling the parameters is JADE. In JADE, the values of each parameter are generated according to one probability density function (PDF) which is learned by the values in success cases where the child is better than the parent. However, search performance might be improved by learning multiple PDFs for each parameter based on some characteristics of search points. In this study, search points are divided into plural groups according to the rank of their objective values and the PDFs are learned by parameter values in success cases for each group. The advantage of JADE with the group-based learning is shown by solving thirteen benchmark problems.

Penalty parameters play a key role when adopting the penalty function method for solution ranking. In the previous study, a corresponding relationship between the constrained optimization problems and the penalty parameters was constructed. This paper tries to verify whether the relationship is related with the evolutionary algorithms (EAs), i.e., how the EAs influence the relationship. Two differential evolution algorithms are taken as an example. Experimental results confirm the influence and show that an improved EA will enlarge the available value of corresponding penalty parameter, especially for the intermittent relationship. The findings also prove that EA can make up the shortcoming of constraint handling techniques to some extent.

In order to better solve the large scale optimization problem, we propose a cooperation coevolution differential evolutionary (CCDE) algorithm with a gradient descent strategy (GDS). The GDS based CCDE algorithm (CCDE/GDS) benefits the solution of large scale optimization problems in two critical aspects. Firstly, the optimization turned out to be far less time consuming due to that GDS is helpful for guiding the search direction on the globally best individual position. More importantly, the GDS is controlled by an elastic operator to be carried out only when the globally best individual has been trapped, making the algorithm fast respond to the large scale evolutionary environment. Secondly, GDS was reported in the literature to approximate the local best value on most object functions. Therefore, the GDS used in CCDE can promote the globally best individual position to more promising region when it is trapped into local optimum, so as to achieve high accuracy. We designed experiments on CEC2010 benchmark functions for evaluating our newly proposed algorithm, which shows that the proposed algorithm and modified framework can obtain very competitive results on the large scale optimization problem efficiently.

A new approach to solve Chance Constrained Optimization Problem (CCOP) without using the Monte Carlo simulation is proposed. Specifically, the prediction interval based on Chebyshev inequality is used to estimate a stochastic function value included in CCOP from a set of samples. By using the prediction interval, CCOP is transformed into Upper-bound Constrained Optimization Problem (UCOP). The feasible solution of UCOP is proved to be feasible for CCOP. In order to solve UCOP efficiently, a modified Differential Evolution (DE) combined with three sample-saving techniques is also proposed. Through the numerical experiments, the usefulness of the proposed approach is demonstrated.

Flow-shop scheduling covers a class of widely studied optimisation problem which focus on optimally sequencing a set of jobs to be processed on a set of machines according to a given set of constraints. Recently, greater research attention has been given to distributed variants of this problem. Here we concentrate on the distributed two machine flow-shop scheduling problem (DTMFSP), a special case of classic two machine flow-shop scheduling, with the overall goal of minimising makespan. We apply Differential Evolution to solve the DTMFSP, presenting new best-known results for some benchmark instances from the literature. A comparison to previous approaches from the literature based on the Harmony Search algorithm is also given.

This paper presents a new multi-objective differential evolution algorithm (MODEMR) to solve the QoS multicast routing problem, which is a well-known NP-hard problem in mobile Ad Hoc networks. In the MODEMR, the network lifetime, cost, delay, jitter and bandwidth are considered as five objectives. Furthermore, three QoS constraints which are maximum allowed delay, maximum allowed jitter, and minimum requested bandwidth are included. In addition, we modify the crossover and mutation operators to build the shortest-path multicast tree to maximize network lifetime and bandwidth, minimize cost, delay and jitter. In order to evaluate the performance and the effectiveness of MODEMR, the experiments are conducted and compared with other algorithms for these problems. The simulation results show that our proposed method is capable of achieving faster convergence and more preferable for multicast routing in mobile Ad Hoc networks.

This study proposes an adaptive differential evolution (ADE)-based variable bias current control strategy to improve the energy efficiency of an active magnetic bearing (AMB) system. In the AMB system, the drive current is composed of a control current and a superimposed bias current in which the former is controlled by an external controller used to regulate the rotor position while the latter is set as a pre-designed constant used to improve the linearity and dynamic performance. Generally, the bias current causes power loss even if no force is required. In this regard, the ADE-based variable bias current control strategy is proposed to minimize the energy consumption of the AMB control system without altering the control performance. Experimental results demonstrate the high-accuracy control and significant energy saving performances of the proposed method. The energy improvements compared to baseline were 20.24% and 17.65% for the operation periods of 10 s and 50 s, respectively.

We propose two strategies for improving the performance of the Fireworks Algorithm (FWA). The first strategy is to decrease the amplitude of each firework according to the generation, where each firework has the same initial amplitude and decreases in size every generation rather than by dynamic allocation based on its fitness. The second strategy is a local optima-based selection of a firework in the next generation rather than the distance-based selection of the original FWA. We design a set of controlled experiments to evaluate these proposed strategies and run them with 20 benchmark functions in three different dimensions of 2-D, 10-D and 30-D. The experimental results demonstrate that both of the two proposed strategies can significantly improve the performance of the original FWA. The performance of the combination of the two proposed strategies can further improve that of each strategy in almost all cases.

Many resampling methods and non-resampling ones have been proposed to deal with noisy optimization problems. The former provides accurate fitness but demands more computational resources while the latter increases the diversity but may mislead the swarm. This paper proposes a fireworks algorithm (FWA) based framework to solve noisy optimization problems. It can gradually change its strategy from resampling to non-resampling during the evolutionary process. Experiments on CEC2015 benchmark functions with noises show that the algorithms based on the proposed framework outperform their original versions as well as their resampling versions.

Fireworks algorithm (FWA) is effective to solve optimization problems as a swarm intelligence algorithm. In this paper, the elite-leading fireworks algorithm (ELFWA) is proposed based on dynamic search in fireworks algorithm (dynFWA), which is an important improvement of FWA. In dynFWA firework is separated to two group: core-firework (CF) and non-core fireworks (non-CFs). This paper takes some beneficial information from non-CFs to reinforce the local search effect of CF. Random reinitialization and elite-leading operator are used to maintain the diversity of the non-CFs, which play an important role in global search. Based on the CEC2015 benchmark functions suite, ELFWA has a very competitive performance when comparing with state-of-the-art fireworks algorithms, such as dynFWA, dynFWACM and eddynFWA.

Maximal covering location problem is an interesting and applicable hard optimization problem. It is a facility location problem where facilities have to be placed in optimal positions to maximize coverage of the weighted demand nodes, while respecting some constraints. This hard optimization problem has been successfully tackled by swarm intelligence algorithms. In this paper we propose adjustment of the recent guided fireworks algorithm for maximal covering location problem. We tested our approach on standard benchmark data sets and compared results with other approaches from literature where our proposed algorithm proved to be more successful, both in the quality of the coverage and convergence speed.

Brain Storm Optimization (BSO) algorithm is a brand-new and promising swarm intelligence algorithm by mimicking human being’s behavior of brainstorming. This paper presents an improved BSO, i.e., BSO with learning strategy (BSOLS). It utilizes a novel learning strategy whereby the first half individuals with better fitness values maintain their superiority by keeping away from the worst ones while other individuals with worse fitness values improve their performances by learning from the excellent ones. The improved algorithm is tested on 10 classical benchmark functions. Comparative experimental results illustrate that the proposed algorithm performs significantly better than the original BSO and standard particle swarm optimization algorithm.

Brain Storm Optimization (BSO) is inspired by human being brain storm process. A novel Difference Brain Storm Optimization (DBSO) is proposed to solve combined heat and power economic dispatch (CHPED) problem in power plant. The difference mutation operation is adopted to replace the Gaussian mutation in the original BSO algorithm for increasing the diversity of the population and the speed of convergence. A test system with 7 units taken from the literature is simulated to verify the performance of the proposed algorithm. The results show that comparing with other intelligent optimization method, both BSO and DBSO can provide the better solution. The convergence speed of the DBSO is better than BSO algorithm.

Cuckoo search algorithm (CSA) is a nature-inspired meta-heuristic based on the obligate brood parasitic behavior of cuckoo species, and it has shown promising performance in solving optimization problems. Chaotic mechanisms have been incorporated into CSA to utilize the dynamic properties of chaos, aiming to further improve its search performance. However, in the previously proposed chaotic cuckoo search algorithms (CCSA), only one chaotic map is utilized in a single search iteration which limited the exploitation ability of the search. In this study, we consider to utilize multiple chaotic maps simultaneously to perform the local search within the neighborhood of the global best solution found by CSA. To realize this, three kinds of multiple chaotic cuckoo search algorithms (MCCSA) are proposed by incorporating several chaotic maps into the chaotic local search parallelly, randomly or selectively. The performance of MCCSA is verified based on 48 widely used benchmark optimization functions. Experimental results reveal that MCCSAs generally perform better than CCSAs, and the MCCSA-P which parallelly utilizes chaotic maps performs the best among all 16 compared variants of CSAs.

This paper introduces a new method to solve the IFS inverse problem for fractal images, known to be a very difficult optimization problem. Given a source binary fractal image, the method computes the IFS code of an IFS fractal whose attractor approximates the input image accurately. The proposed method is based on the cuckoo search algorithm, a powerful swarm intelligence method for continuous optimization. The good performance of the method is illustrated by its application to two examples of 2D binary fractal images.

We adapt the Cuckoo Search (CS) algorithm for solving the three color Graph Coloring Problem (3-GCP). The difficulty of this task is adapting CS from a continuous to a discrete domain. Previous researches used sigmoid functions to discretize the Lévi Flight (LF) operator characteristic of CS, but this approach does not take into account the concept of Solution Distance, one of the main characteristics of LF. In this paper, we propose a new discretization of CS that maintains LF’s solution distance concept. We also simplify CS’s parasitism operator, reducing the number of evaluations necessary. We compare different combinations of the proposed changes, using GA as a baseline, on a set of randomly generated 3-GCP problems. The results show the importance of a good discretization of the LF operator to increase the success rate and provide auto-adaptation to the CS algorithm.

This study brings together two related areas: deep learning and swarm intelligence for missing data estimation in high-dimensional datasets. The growing number of studies in the deep learning area warrants a closer look at its possible application in the aforementioned domain. Missing data being an unavoidable scenario in present day datasets results in different challenges which are nontrivial for existing techniques which constitute narrow artificial intelligence architectures and computational intelligence methods. This can be attributed to the large number of samples and high number of features. In this paper, we propose a new framework for the imputation procedure that uses a deep learning method with a swarm intelligence algorithm, called Deep Learning-Cuckoo Search (DL-CS). This technique is compared to similar approaches and other existing methods. The time required to obtain accurate estimates for the missing data entries surpasses that of existing methods, but this is considered a worthy bargain when the accuracy of the said estimates in a high dimensional setting are taken into consideration.

Cuckoo Search (CS) is the powerful optimization algorithm and has been researched recently. Cuckoo Search for Dynamic Environment (D-CS) has proposed and tested in dynamic environment with multi-modality and cyclically before. It was clear that has the hold capability and can find the optimal solutions in this environment. Although these experiments only provide the valuable results in this environment, D-CS not fully explored in dynamic environment with other dynamism. We investigate and discuss the find and hold capabilities of D-CS on dynamic environment with randomness. We employed the multi-modal dynamic function with randomness and applied D-CS into this environment. We compared D-CS with CS in terms of getting the better fitness. The experimental result shows the D-CS has the good hold capability on dynamic environment with randomness. Introducing the Local Solution Comparison strategy and Concurrent Solution Generating strategy help to get the hold and find capabilities on dynamic environment with randomness.

Particle filter (PF) has been proved to be an effective tool in solving relative navigation problems. However, the sample impoverishment problem caused by resampling is the main disadvantage of PF, which strongly affect the accuracy of navigation. To solve this problem, an improved PF based on firefly algorithm (FA) is proposed. Combine with the operation mechanism of PF, the optimization mode of FA is revised, and a new update formula of attractiveness is designed. By means of firefly group’s mechanism of survival of the fittest and individual firefly’s attraction and movement behaviors, this algorithm enables the particles to move toward the high likelihood region. Thus, the number of meaningful particles can be increased, and the particles can approximate the true state of the target more accurately. Simulation results show that the improved algorithm improves the navigation accuracy and reduces the quantity of the particles required by the prediction of state value.

In this paper, we propose a novel method based on discrete firefly algorithm for traveling salesman problem. We redefine the distance of firefly algorithm by introducing swap operator and swap sequence to avoid algorithm easily falling into local solution and accelerate convergence speed. In addition, we adopt dynamic mechanism based on neighborhood search algorithm. Finally, the comparison experiment results show that the novel algorithm can search perfect solution within a short time, and greatly improve the effectiveness of solving the traveling salesman problem.

It is a hot research to explore protein complexes which are closely related to biological processes from the biological network. As a novel swarm intelligence optimization algorithm, the firefly algorithm (FA) has been verified to solve many optimization problems. In this study, we transform the protein clustering problem into an optimization problem in protein-protein interaction (PPI) network. A new method for mining protein complexes based on the firefly algorithm was proposed, called FC. A new objective function was proposed to find the high cohesion and low coupling clusters. A thorough comparison completed for different protein clustering methods has been carried out. The clustering results show that FC method outperforms the other state-of-the-art methods in accuracy of detecting complexes from PPI network.

To improve two-dimensional (2D) Otsu thresholding’s performance in both computation speed and segmentation quality, an improved 2D Otsu algorithm is proposed for low Signal-to-noise Ratio (SNR) images. A new 2D histogram is defined based on median gray-scale and Gaussian average gray-scale. By meeting better to the assumption of that the object’s probability and the background’s probability sum up to 1, the new 2D histogram enhances the thresholding algorithm’s robustness to severe noise. Then a scheme of calculating the fitness function based on firefly optimization algorithm is employed to search for optimal thresholds. The proposed algorithm is applied to typical low SNR images–microscopic images of ocean plankton, and to Lenna test image. Experiment results show that with better thresholding quality, the running time of the proposed algorithm is reduced to 2.5% of the conventional 2D Otsu.

In fruit fly optimization algorithm (FOA), the search speed of each fruit fly is fast, but when it traps into the local optimum, it is difficult to re-find a better solution. In order to overcome this drawback, we propose an improved version of FOA, termed as 3D-FOAdis. In the proposed method, three-dimensional coordinates and the disturbance mechanism were both introduced. We firstly extends the original two-dimensional coordinates to three-dimensional coordinates, where fruit flies can fly more widely so that it is more likely to jump out of the local optimum. Then we introduce a disturbance mechanism force the FOA to find better solutions when the fruit flies fall into the local optimums. The effectiveness of 3D-FOAdis has been rigorously evaluated against the nine benchmark functions. The experimental results demonstrate that the proposed approach outperforms the other two counterparts.