Showing papers on "Evolutionary computation published in 2018"

A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications

Abstract: Bilevel optimization is defined as a mathematical program, where an optimization problem contains another optimization problem as a constraint. These problems have received significant attention from the mathematical programming community. Only limited work exists on bilevel problems using evolutionary computation techniques; however, recently there has been an increasing interest due to the proliferation of practical applications and the potential of evolutionary algorithms in tackling these problems. This paper provides a comprehensive review on bilevel optimization from the basic principles to solution strategies; both classical and evolutionary. A number of potential application problems are also discussed. To offer the readers insights on the prominent developments in the field of bilevel optimization, we have performed an automated text-analysis of an extended list of papers published on bilevel optimization to date. This paper should motivate evolutionary computation researchers to pay more attention to this practical yet challenging area.

An Indicator-Based Multiobjective Evolutionary Algorithm With Reference Point Adaptation for Better Versatility

Abstract: During the past two decades, a variety of multiobjective evolutionary algorithms (MOEAs) have been proposed in the literature. As pointed out in some recent studies, however, the performance of an MOEA can strongly depend on the Pareto front shape of the problem to be solved, whereas most existing MOEAs show poor versatility on problems with different shapes of Pareto fronts. To address this issue, we propose an MOEA based on an enhanced inverted generational distance indicator, in which an adaptation method is suggested to adjust a set of reference points based on the indicator contributions of candidate solutions in an external archive. Our experimental results demonstrate that the proposed algorithm is versatile for solving problems with various types of Pareto fronts, outperforming several state-of-the-art evolutionary algorithms for multiobjective and many-objective optimization.

An Energy Efficient Ant Colony System for Virtual Machine Placement in Cloud Computing

Abstract: Virtual machine placement (VMP) and energy efficiency are significant topics in cloud computing research. In this paper, evolutionary computing is applied to VMP to minimize the number of active physical servers, so as to schedule underutilized servers to save energy. Inspired by the promising performance of the ant colony system (ACS) algorithm for combinatorial problems, an ACS-based approach is developed to achieve the VMP goal. Coupled with order exchange and migration (OEM) local search techniques, the resultant algorithm is termed an OEMACS. It effectively minimizes the number of active servers used for the assignment of virtual machines (VMs) from a global optimization perspective through a novel strategy for pheromone deposition which guides the artificial ants toward promising solutions that group candidate VMs together. The OEMACS is applied to a variety of VMP problems with differing VM sizes in cloud environments of homogenous and heterogeneous servers. The results show that the OEMACS generally outperforms conventional heuristic and other evolutionary-based approaches, especially on VMP with bottleneck resource characteristics, and offers significant savings of energy and more efficient use of different resources.

A Surrogate-Assisted Reference Vector Guided Evolutionary Algorithm for Computationally Expensive Many-Objective Optimization

Abstract: We propose a surrogate-assisted reference vector guided evolutionary algorithm (EA) for computationally expensive optimization problems with more than three objectives The proposed algorithm is based on a recently developed EA for many-objective optimization that relies on a set of adaptive reference vectors for selection The proposed surrogate-assisted EA (SAEA) uses Kriging to approximate each objective function to reduce the computational cost In managing the Kriging models, the algorithm focuses on the balance of diversity and convergence by making use of the uncertainty information in the approximated objective values given by the Kriging models, the distribution of the reference vectors as well as the location of the individuals In addition, we design a strategy for choosing data for training the Kriging model to limit the computation time without impairing the approximation accuracy Empirical results on comparing the new algorithm with the state-of-the-art SAEAs on a number of benchmark problems demonstrate the competitiveness of the proposed algorithm

Fundamentals Of Natural Computing: Basic Concepts, Algorithms, And Applications

Abstract: Introduction A Small Sample of Ideas The Philosophy of Natural Computing The Three Branches: A Brief Overview When to Use Natural Computing Approaches Conceptualization General Concepts PART I - COMPUTING INSPIRED BY NATURE Evolutionary Computing Problem Solving as a Search Task Hill Climbing and Simulated Annealing Evolutionary Biology Evolutionary Computing The Other Main Evolutionary Algorithms From Evolutionary Biology to Computing Scope of Evolutionary Computing Neurocomputing The Nervous System Artificial Neural Networks Typical ANNS and Learning Algorithms From Natural to Artificial Neural Networks Scope of Neurocomputing Swarm Intelligence Ant Colonies Swarm Robotics Social Adaptation of Knowledge Immunocomputing The Immune System Artificial Immune Systems Bone Marrow Models Negative Selection Algorithms Clonal Selection and Affinity Maturation Artificial Immune Networks From Natural to Artificial Immune Systems Scope of Artificial Immune Systems PART II - SIMULATION AND EMULATION OF NATURAL PHENOMENA IN COMPUTERS Fractal Geometry of Nature The Fractal Geometry of Nature Cellular Automata L-Systems Iterated Function Systems Fractional Brownian Motion Particle Systems Evolving the Geometry of Nature From Natural to Fractal Geometry Artificial Life Concepts and Features of Artificial Life Systems Examples of Artificial Life Projects Scope of Artificial Life From Artificial Life to Life-As-We-Know-It PART III - COMPUTING WITH NATURAL MATERIALS DNA Computing Basic Concepts from Molecular Biology Filtering Models Formal Models: A Brief Description Universal DNA Computers Scope of DNA Computing From Classical to DNA Computing Quantum Computing Basic Concepts from Quantum Theory Principles from Quantum Mechanics Quantum Information Universal Quantum Computers Quantum Algorithms Physical Realizations of Quantum Computers: A Brief Description Scope of Quantum Computing From Classical to Quantum Computing Afterwords New Prospects The Growth of Natural Computing Some Lessons from Natural Computing Artificial Intelligence and Natural Computing Visions Appendix A: Glossary of Terms Appendix B: Theoretical Background Linear Algebra Statistics Theory of Computation and Complexity Other Concepts Bibliography Appendix C: A Quick Guide to the Literature Introduction Conceptualization Evolutionary Computing Neurocomputing Swarm Intelligence Immunocomputing Fractal Geometry of Nature Artificial Life DNA Computing Quantum Computing Index *All Chapters contain an Introduction, Summaries, Discussions, Exercises, and References

Localized Weighted Sum Method for Many-Objective Optimization

Abstract: Decomposition via scalarization is a basic concept for multiobjective optimization. The weighted sum (WS) method, a frequently used scalarizing method in decomposition-based evolutionary multiobjective (EMO) algorithms, has good features such as computationally easy and high search efficiency, compared to other scalarizing methods. However, it is often criticized by the loss of effect on nonconvex problems. This paper seeks to utilize advantages of the WS method, without suffering from its disadvantage, to solve many-objective problems. A novel decomposition-based EMO algorithm called multiobjective evolutionary algorithm based on decomposition LWS (MOEA/D-LWS) is proposed in which the WS method is applied in a local manner. That is, for each search direction, the optimal solution is selected only amongst its neighboring solutions. The neighborhood is defined using a hypercone. The apex angle of a hypervcone is determined automatically in a priori . The effectiveness of MOEA/D-LWS is demonstrated by comparing it against three variants of MOEA/D, i.e., MOEA/D using Chebyshev method, MOEA/D with an adaptive use of WS and Chebyshev method, MOEA/D with a simultaneous use of WS and Chebyshev method, and four state-of-the-art many-objective EMO algorithms, i.e., preference-inspired co-evolutionary algorithm, hypervolume-based evolutionary, $\boldsymbol {\theta }$ -dominance-based algorithm, and SPEA2+SDE for the WFG benchmark problems with up to seven conflicting objectives. Experimental results show that MOEA/D-LWS outperforms the comparison algorithms for most of test problems, and is a competitive algorithm for many-objective optimization.

Quality and Diversity Optimization: A Unifying Modular Framework

Abstract: The optimization of functions to find the best solution according to one or several objectives has a central role in many engineering and research fields. Recently, a new family of optimization algorithms, named quality-diversity (QD) optimization, has been introduced, and contrasts with classic algorithms. Instead of searching for a single solution, QD algorithms are searching for a large collection of both diverse and high-performing solutions. The role of this collection is to cover the range of possible solution types as much as possible, and to contain the best solution for each type. The contribution of this paper is threefold. First, we present a unifying framework of QD optimization algorithms that covers the two main algorithms of this family (multidimensional archive of phenotypic elites and the novelty search with local competition), and that highlights the large variety of variants that can be investigated within this family. Second, we propose algorithms with a new selection mechanism for QD algorithms that outperforms all the algorithms tested in this paper. Lastly, we present a new collection management that overcomes the erosion issues observed when using unstructured collections. These three contributions are supported by extensive experimental comparisons of QD algorithms on three different experimental scenarios.

Testing vision-based control systems using learnable evolutionary algorithms

Abstract: Vision-based control systems are key enablers of many autonomous vehicular systems, including self-driving cars. Testing such systems is complicated by complex and multidimensional input spaces. We propose an automated testing algorithm that builds on learnable evolutionary algorithms. These algorithms rely on machine learning or a combination of machine learning and Darwinian genetic operators to guide the generation of new solutions (test scenarios in our context). Our approach combines multiobjective population-based search algorithms and decision tree classification models to achieve the following goals: First, classification models guide the search-based generation of tests faster towards critical test scenarios (i.e., test scenarios leading to failures). Second, search algorithms refine classification models so that the models can accurately characterize critical regions (i.e., the regions of a test input space that are likely to contain most critical test scenarios). Our evaluation performed on an industrial automotive automotive system shows that: (1) Our algorithm outperforms a baseline evolutionary search algorithm and generates 78% more distinct, critical test scenarios compared to the baseline algorithm. (2) Our algorithm accurately characterizes critical regions of the system under test, thus identifying the conditions that are likely to lead to system failures.

A New Decomposition-Based NSGA-II for Many-Objective Optimization

Abstract: Multiobjective evolutionary algorithms (MOEAs) have proven their effectiveness and efficiency in solving problems with two or three objectives. However, recent studies show that MOEAs face many difficulties when tackling problems involving a larger number of objectives as their behavior becomes similar to a random walk in the search space since most individuals are nondominated with respect to each other. Motivated by the interesting results of decomposition-based approaches and preference-based ones, we propose in this paper a new decomposition-based dominance relation to deal with many-objective optimization problems and a new diversity factor based on the penalty-based boundary intersection method. Our reference point-based dominance (RP-dominance), has the ability to create a strict partial order on the set of nondominated solutions using a set of well-distributed reference points. The RP-dominance is subsequently used to substitute the Pareto dominance in nondominated sorting genetic algorithm-II (NSGA-II). The augmented MOEA, labeled as RP-dominance-based NSGA-II, has been statistically demonstrated to provide competitive and oftentimes better results when compared against four recently proposed decomposition-based MOEAs on commonly-used benchmark problems involving up to 20 objectives. In addition, the efficacy of the algorithm on a realistic water management problem is showcased.

A Level-Based Learning Swarm Optimizer for Large-Scale Optimization

Abstract: In pedagogy, teachers usually separate mixed-level students into different levels, treat them differently and teach them in accordance with their cognitive and learning abilities. Inspired from this idea, we consider particles in the swarm as mixed-level students and propose a level-based learning swarm optimizer (LLSO) to settle large-scale optimization, which is still considerably challenging in evolutionary computation. At first, a level-based learning strategy is introduced, which separates particles into a number of levels according to their fitness values and treats particles in different levels differently. Then, a new exemplar selection strategy is designed to randomly select two predominant particles from two different higher levels in the current swarm to guide the learning of particles. The cooperation between these two strategies could afford great diversity enhancement for the optimizer. Further, the exploration and exploitation abilities of the optimizer are analyzed both theoretically and empirically in comparison with two popular particle swarm optimizers. Extensive comparisons with several state-of-the-art algorithms on two widely used sets of large-scale benchmark functions confirm the competitive performance of the proposed optimizer in both solution quality and computational efficiency. Finally, comparison experiments on problems with dimensionality increasing from 200 to 2000 further substantiate the good scalability of the developed optimizer.

Evolutionary computation algorithms for feature selection of EEG-based emotion recognition using mobile sensors

Abstract: A review of state-of-the-art feature extraction methods from electroencephalogram signals.A new framework using evolutionary algorithms to find the most optimal features set and channels.Comprehensive experimental results based on two public datasets and one newly collected dataset. There is currently no standard or widely accepted subset of features to effectively classify different emotions based on electroencephalogram (EEG) signals. While combining all possible EEG features may improve the classification performance, it can lead to high dimensionality and worse performance due to redundancy and inefficiency. To solve the high-dimensionality problem, this paper proposes a new framework to automatically search for the optimal subset of EEG features using evolutionary computation (EC) algorithms. The proposed framework has been extensively evaluated using two public datasets (MAHNOB, DEAP) and a new dataset acquired with a mobile EEG sensor. The results confirm that EC algorithms can effectively support feature selection to identify the best EEG features and the best channels to maximize performance over a four-quadrant emotion classification problem. These findings are significant for informing future development of EEG-based emotion classification because low-cost mobile EEG sensors with fewer electrodes are becoming popular for many new applications.

Particle Swarm Optimization: A survey of historical and recent developments with hybridization perspectives

Abstract: Particle Swarm Optimization (PSO) is a metaheuristic global optimization paradigm that has gained prominence in the last two decades due to its ease of application in unsupervised, complex multidimensional problems that cannot be solved using traditional deterministic algorithms. The canonical particle swarm optimizer is based on the flocking behavior and social co-operation of birds and fish schools and draws heavily from the evolutionary behavior of these organisms. This paper serves to provide a thorough survey of the PSO algorithm with special emphasis on the development, deployment, and improvements of its most basic as well as some of the very recent state-of-the-art implementations. Concepts and directions on choosing the inertia weight, constriction factor, cognition and social weights and perspectives on convergence, parallelization, elitism, niching and discrete optimization as well as neighborhood topologies are outlined. Hybridization attempts with other evolutionary and swarm paradigms in selected applications are covered and an up-to-date review is put forward for the interested reader.

A Recursive Decomposition Method for Large Scale Continuous Optimization

Abstract: Cooperative co-evolution (CC) is an evolutionary computation framework that can be used to solve high-dimensional optimization problems via a “divide-and-conquer” mechanism. However, the main challenge when using this framework lies in problem decomposition. That is, deciding how to allocate decision variables to a particular subproblem, especially interacting decision variables. Existing decomposition methods are typically computationally expensive. In this paper, we propose a new decomposition method, which we call recursive differential grouping (RDG), by considering the interaction between decision variables based on nonlinearity detection. RDG recursively examines the interaction between a selected decision variable and the remaining variables, placing all interacting decision variables into the same subproblem. We use analytical methods to show that RDG can be used to efficiently decompose a problem, without explicitly examining all pairwise variable interactions. We evaluated the efficacy of the RDG method using large scale benchmark optimization problems. Numerical simulation experiments showed that RDG greatly improved the efficiency of problem decomposition in terms of time complexity. Significantly, when RDG was embedded in a CC framework, the optimization results were better than results from seven other decomposition methods.

Optimization using lion algorithm: a biological inspiration from lion’s social behavior

Abstract: Nature-inspired optimization algorithms, especially evolutionary computation-based and swarm intelligence-based algorithms are being used to solve a variety of optimization problems. Motivated by the obligation of having optimization algorithms, a novel optimization algorithm based on a lion’s unique social behavior had been presented in our previous work. Territorial defense and territorial takeover were the two most popular lion’s social behaviors. This paper takes the algorithm forward on rigorous and diverse performance tests to demonstrate the versatility of the algorithm. Four different test suites are presented in this paper. The first two test suites are benchmark optimization problems. The first suite had comparison with published results of evolutionary and few renowned optimization algorithms, while the second suite leads to a comparative study with state-of-the-art optimization algorithms. The test suite 3 takes the large-scale optimization problems, whereas test suite 4 considers benchmark engineering problems. The performance statistics demonstrate that the lion algorithm is equivalent to certain optimization algorithms, while outperforming majority of the optimization algorithms. The results also demonstrate the trade-off maintainability of the lion algorithm over the traditional algorithms.

Evolutionary Computation for Community Detection in Networks: A Review

Abstract: In today’s world, the interconnections among objects in many domains are often modeled as networks, with nodes representing the objects and edges the existing relationships among them. A key feature of complex networks is the tendency of entities to group together to form communities. The detection of communities has been receiving a great deal of interest by researchers. In fact, the knowledge of how objects organize allows a better understanding of a network, and gives a deeper insight of interesting characteristics, that could not be caught if considering the network as a whole. In the last decade, evolutionary computation techniques have given a significant contribution in this context. The aim of this paper is to present the approaches based on evolutionary computation to uncover community structure. Especially, the representation schemes with the genetic operators apt for them are described, and the most popular fitness functions employed by the methods are discussed. The survey covers the most recent proposals optimizing either a single objective or multiple objectives for different types of network models, such as signed, dynamic, and multidimensional.

Evolutionary Many-Objective Optimization: A Comparative Study of the State-of-the-Art

Abstract: With the increasing attention paid to many-objective optimization in the evolutionary multi-objective optimization community, various approaches have been proposed to solve many-objective problems. However, existing experimental comparative studies are usually restricted to a few methods. Few studies have encompassed most of the recently proposed state-of-the-art approaches and made an experimental comparison. To this end, this paper offers a systematic comparison of 13 algorithms covering various categories to solve many-objective problems. The experimental comparison is conducted on three groups of test functions by using two performance metrics and a visual observation in the decision space. The experimental results demonstrate that different approaches have different search abilities. None of the test approaches outperform the others on all types of problems. However, some of the approaches are competitive on a large number of test problems. Moreover, inconsistent results from the hypervolume and the inverted generational distance metrics are revealed in this paper. Based on these comparative results, researchers can obtain useful suggestions for choosing appropriate algorithms for different problems.

Coevolutionary Multiobjective Evolutionary Algorithms: Survey of the State-of-the-Art

Abstract: In the last 20 years, evolutionary algorithms (EAs) have shown to be an effective method to solve multiobjective optimization problems (MOPs). Due to their population-based nature, multiobjective EAs (MOEAs) are able to generate a set of tradeoff solutions (called nondominated solutions) in a single algorithmic execution instead of having to perform a series of independent executions, as normally done with mathematical programming techniques. Additionally, MOEAs can be successfully applied to problems with difficult features such as multifrontality, discontinuity and disjoint feasible regions, among others. On the other hand, coevolutionary algorithms (CAs) are extensions of traditional EAs which have become subject of numerous studies in the last few years, particularly for dealing with large-scale global optimization problems. CAs have also been applied to the solution of MOPs, motivating the development of new algorithmic and analytical formulations that have advanced the state-of-the-art in CAs research, while simultaneously opening a new research path within MOEAs. This paper presents a critical review of the most representative coevolutionary MOEAs (CMOEAs) that have been reported in the specialized literature. This survey includes a taxonomy of approaches together with a brief description of their main features. In the final part of this paper, we also identify what we believe to be promising areas of future research in the field of CMOEAs.

Real-parameter unconstrained optimization based on enhanced fitness-adaptive differential evolution algorithm with novel mutation

Abstract: This paper presents enhanced fitness-adaptive differential evolution algorithm with novel mutation (EFADE) for solving global numerical optimization problems over continuous space. A new triangular mutation operator is introduced. It is based on the convex combination vector of the triplet defined by the three randomly chosen vectors and the difference vectors between the best, better and the worst individuals among the three randomly selected vectors. Triangular mutation operator helps the search for better balance between the global exploration ability and the local exploitation tendency as well as enhancing the convergence rate of the algorithm through the optimization process. Besides, two novel, effective adaptation schemes are used to update the control parameters to appropriate values without either extra parameters or prior knowledge of the characteristics of the optimization problem. In order to verify and analyze the performance of EFADE, numerical experiments on a set of 28 test problems from the CEC2013 benchmark for 10, 30 and 50 dimensions, including a comparison with 12 recent DE-based algorithms and six recent evolutionary algorithms, are executed. Experimental results indicate that in terms of robustness, stability and quality of the solution obtained, EFADE is significantly better than, or at least comparable to state-of-the-art approaches with outstanding performance.

Standard Steady State Genetic Algorithms Can Hillclimb Faster Than Mutation-Only Evolutionary Algorithms

Abstract: Explaining to what extent the real power of genetic algorithms (GAs) lies in the ability of crossover to recombine individuals into higher quality solutions is an important problem in evolutionary computation. In this paper we show how the interplay between mutation and crossover can make GAs hillclimb faster than their mutation-only counterparts. We devise a Markov chain framework that allows to rigorously prove an upper bound on the runtime of standard steady state GAs to hillclimb the OneMax function. The bound establishes that the steady-state GAs are 25% faster than all standard bit mutation-only evolutionary algorithms with static mutation rate up to lower order terms for moderate population sizes. The analysis also suggests that larger populations may be faster than populations of size 2. We present a lower bound for a greedy (2 + 1) GA that matches the upper bound for populations larger than 2, rigorously proving that two individuals cannot outperform larger population sizes under greedy selection and greedy crossover up to lower order terms. In complementary experiments the best population size is greater than 2 and the greedy GAs are faster than standard ones, further suggesting that the derived lower bound also holds for the standard steady state (2 + 1) GA.

Level-Based Analysis of Genetic Algorithms and Other Search Processes

Abstract: Understanding how the time complexity of evolutionary algorithms (EAs) depend on their parameter settings and characteristics of fitness landscapes is a fundamental problem in evolutionary computation. Most rigorous results were derived using a handful of key analytic techniques, including drift analysis. However, since few of these techniques apply effortlessly to population-based EAs, most time complexity results concern simple EAs, such as the (1+1) EA. We present the level-based theorem , a new technique tailored to population-based processes. It applies to any nonelitist process where offspring are sampled independently from a distribution depending only on the current population. Given conditions on this distribution, our technique provides upper bounds on the expected time until the process reaches a target state. The technique is demonstrated on pseudo-Boolean functions, the sorting problem, and approximation of optimal solutions in combinatorial optimization. The conditions of the theorem are often straightforward to verify, even for genetic algorithms and estimation of distribution algorithms which were considered highly nontrivial to analyze. The proofs for the example applications are available in the supplementary materials. Finally, we prove that the theorem is nearly optimal for the processes considered. Given the information the theorem requires about the process, a much tighter bound cannot be proved.

A Decomposition-Based Many-Objective Evolutionary Algorithm With Two Types of Adjustments for Direction Vectors

Abstract: Decomposition-based multiobjective evolutionary algorithm has shown its advantage in addressing many-objective optimization problem (MaOP). To further improve its convergence on MaOPs and its diversity for MaOPs with irregular Pareto fronts (PFs, e.g., degenerate and disconnected ones), we proposed a decomposition-based many-objective evolutionary algorithm with two types of adjustments for the direction vectors (MaOEA/D-2ADV). At the very beginning, search is only conducted along the boundary direction vectors to achieve fast convergence, followed by the increase of the number of the direction vectors for approximating a more complete PF. After that, a Pareto-dominance-based mechanism is used to detect the effectiveness of each direction vector and the positions of ineffective direction vectors are adjusted to better fit the shape of irregular PFs. The extensive experimental studies have been conducted to validate the efficiency of MaOEA/D-2ADV on many-objective optimization benchmark problems. The effects of each component in MaOEA/D-2ADV are also investigated in detail.

Long Short Term Memory Hyperparameter Optimization for a Neural Network Based Emotion Recognition Framework

Abstract: Recently, emotion recognition using low-cost wearable sensors based on electroencephalogram and blood volume pulse has received much attention Long short-term memory (LSTM) networks, a special type of recurrent neural networks, have been applied successfully to emotion classification However, the performance of these sequence classifiers depends heavily on their hyperparameter values, and it is important to adopt an efficient method to ensure the optimal values To address this problem, we propose a new framework to automatically optimize LSTM hyperparameters using differential evolution (DE) This is the first systematic study of hyperparameter optimization in the context of emotion classification In this paper, we evaluate and compare the proposed framework with other state-of-the-art hyperparameter optimization methods (particle swarm optimization, simulated annealing, random search, and tree of Parzen estimators) using a new dataset collected from wearable sensors Experimental results demonstrate that optimizing LSTM hyperparameters significantly improve the recognition rate of four-quadrant dimensional emotions with a 14% increase in accuracy The best model based on the optimized LSTM classifier using the DE algorithm achieved 7768% accuracy The results also showed that evolutionary computation algorithms, particularly DE, are competitive for ensuring optimized LSTM hyperparameter values Although DE algorithm is computationally expensive, it is less complex and offers higher diversity in finding optimal solutions

Evolutionary Multiobjective Optimization-Based Multimodal Optimization: Fitness Landscape Approximation and Peak Detection

Abstract: Recently, by taking advantage of evolutionary multiobjective optimization techniques in diversity preservation, the means of multiobjectivization has attracted increasing interest in the studies of multimodal optimization (MMO). While most existing work of multiobjectivization aims to find all optimal solutions simultaneously, in this paper, we propose to approximate multimodal fitness landscapes via multiobjectivization, thus providing an estimation of potential optimal areas. To begin with, an MMO problem is transformed into a multiobjective optimization problem (MOP) by adding an adaptive diversity indicator as the second optimization objective, and an approximate fitness landscape is obtained via optimization of the transformed MOP using a multiobjective evolutionary algorithm. Then, on the basis of the approximate fitness landscape, an adaptive peak detection method is proposed to find peaks where optimal solutions may exist. Finally, local search is performed inside the detected peaks on the approximate fitness landscape. To assess the performance of the proposed algorithm, extensive experiments are conducted on 20 multimodal test functions, in comparison with three state-of-the-art algorithms for MMO. Experimental results demonstrate that the proposed algorithm not only shows promising performance in benchmark comparisons, but also has good potential in assisting preference-based decision-making in MMO.

An Improved Crow Search Algorithm Applied to Energy Problems

Abstract: The efficient use of energy in electrical systems has become a relevant topic due to its environmental impact. Parameter identification in induction motors and capacitor allocation in distribution networks are two representative problems that have strong implications in the massive use of energy. From an optimization perspective, both problems are considered extremely complex due to their non-linearity, discontinuity, and high multi-modality. These characteristics make difficult to solve them by using standard optimization techniques. On the other hand, metaheuristic methods have been widely used as alternative optimization algorithms to solve complex engineering problems. The Crow Search Algorithm (CSA) is a recent metaheuristic method based on the intelligent group behavior of crows. Although CSA presents interesting characteristics, its search strategy presents great difficulties when it faces high multi-modal formulations. In this paper, an improved version of the CSA method is presented to solve complex optimization problems of energy. In the new algorithm, two features of the original CSA are modified: (I) the awareness probability (AP) and (II) the random perturbation. With such adaptations, the new approach preserves solution diversity and improves the convergence to difficult high multi-modal optima. In order to evaluate its performance, the proposed algorithm has been tested in a set of four optimization problems which involve induction motors and distribution networks. The results demonstrate the high performance of the proposed method when it is compared with other popular approaches.

Loser-Out Tournament-Based Fireworks Algorithm for Multimodal Function Optimization

Abstract: Real-world optimization problems are usually multimodal which require optimization algorithms to keep a balance between exploration and exploitation. Therefore, multimodal optimization is one of the main opportunities as well as one of the main challenges for evolutionary algorithms. In this paper, a loser-out tournament-based fireworks algorithm (LoTFWA) is proposed for solving multimodal optimization problems. The search manner of the conventional fireworks algorithm (FWA) is based on the cooperation of several fireworks. While in the LoTFWA, we propose competition as a new manner of interaction, in which the fireworks are compared with each other not only according to their current status but also according to their progress rate. If the fitness of a certain firework cannot catch up with the best one with its current progress rate, it is considered a loser in the competition. The losers will be eliminated and reinitialized because it is vain to continue their search processes. Reinitializing these fireworks would greatly reduce the probability of being trapped in local minima for the algorithm. Experimental results show that the proposed algorithm is very powerful in optimizing multimodal functions. It not only outperforms previous versions of the FWA, but also outperforms several famous evolutionary algorithms.

A Double-Niched Evolutionary Algorithm and Its Behavior on Polygon-Based Problems

Abstract: Multi-modal multi-objective optimization problems are commonly seen in real-world applications. However, most existing researches focus on solving multi-objective optimization problems without multi-modal property or multi-modal optimization problems with single objective. In this paper, we propose a double-niched evolutionary algorithm for multi-modal multi-objective optimization. The proposed algorithm employs a niche sharing method to diversify the solution set in both the objective and decision spaces. We examine the behaviors of the proposed algorithm and its two variants as well as three other existing evolutionary optimizers on three types of polygon-based problems. Our experimental results suggest that the proposed algorithm is able to find multiple Pareto optimal solution sets in the decision space, even if the diversity requirements in the objective and decision spaces are inconsistent or there exist local optimal areas in the decision space.

Evolution of Repertoire-Based Control for Robots With Complex Locomotor Systems

Abstract: The evolution of task-oriented control for robots with complex locomotor systems is currently out of reach for traditional evolutionary computation techniques, as the coordination of a high number of locomotion parameters in response to the robot’s sensory inputs is extremely challenging. Evolutionary techniques have therefore mainly been applied to the optimization of specific locomotion patterns, such as forward motion. In this paper, we explore the evolutionary repertoire-based control (EvoRBC) approach, which divides the synthesis of control into two steps: 1) the evolution of a repertoire of locomotion primitives using a quality diversity algorithm and 2) the evolution of a high-level arbitrator that leverages the locomotion primitives in the repertoire to solve a given task. We comprehensively study the main components of the EvoRBC approach using a four-wheel steering robot. We then conduct a set of experiments in simulation using a hexapod robot. Our results show that EvoRBC is robust to parameter variations, and for all the robots tested, it is able to evolve controllers for a maze navigation task and significantly outperforms the traditional evolutionary robotics approach.