The first cooperative co-evolutionary algorithm (CCEA) was proposed by Potter and De Jong in 1994 and since then many CCEAs have been proposed and successfully applied to solving various complex optimization problems. In applying CCEAs, the complex optimization problem is decomposed into multiple subproblems, and each subproblem is solved with a separate subpopulation, evolved by an individual evolutionary algorithm (EA). Through cooperative co-evolution of multiple EA subpopulations, a complete problem solution is acquired by assembling the representative members from each subpopulation. The underlying divide-and-conquer and collaboration mechanisms enable CCEAs to tackle complex optimization problems efficiently, and hence CCEAs have been attracting wide attention in the EA community. This paper presents a comprehensive survey of these CCEAs, covering problem decomposition, collaborator selection, individual fitness evaluation, subproblem resource allocation, implementations, benchmark test problems, control parameters, theoretical analyses, and applications. The unsolved challenges and potential directions for their solutions are discussed.

A Survey on Cooperative Co-Evolutionary Algorithms

We present a hybrid metaheuristic optimization algorithm for solving economic dispatch problems in power systems. The proposed algorithm, based on bat algorithm, combines chaotic map and random black hole model together. Chaotic map is used to prevent premature convergence, and the random black hole model is helpful not only in avoiding premature convergence, but also in increasing the global search ability, enlarging exploitation area and accelerating convergence speed. The pseudocode and related parameters of the proposed algorithm are also given in this paper. Different from other related works, the costs of conventional thermal generators and random wind power are both included in the cost function because of the increasing penetration of wind power. The proposed algorithm has no requirement on the convexity or continuous differentiability of the cost function, although the effect on fuel cost, caused by the underestimation and overestimation of wind power, is included. This makes it feasible to take more practical nonlinear constraints into account, such as prohibited operating zones and ramp rate limits. Three test cases are given to illustrate the effectiveness of the proposed method.

A Hybrid Bat Algorithm for Economic Dispatch With Random Wind Power

Evolutionary multitasking is an emergent topic in evolutionary computation area. Recently, a well-known evolutionary multitasking method, the multi-factorial evolutionary algorithm (MFEA), has been proposed and applied to concurrently solve two or three problems. In MFEA, individuals of different tasks are recombined in a predefined random mating probability. As the number of tasks increases, such recombination of different tasks becomes very frequent, thereby detracting the search from any specific problems and limiting the MFEA's capability to solve many-tasking problems. This study proposes a general framework, called the evolution of biocoenosis through symbiosis (EBS), for evolutionary algorithms to deal with the many-tasking problems. The EBS has two main features: the selection of candidates from concatenate offspring and the adaptive control of information exchange among tasks. The concatenate offspring represent a set of offspring used for all tasks. Moreover, this study presents a test suite of many-tasking problems (MaTPs), modified from the CEC 2014 benchmark problems. The Spearman correlation is adopted to analyze the effect of the shifts of optima on the MaTPs. Experimental results show that the effectiveness of EBS is superior to that of single task optimization and MFEA on the four MaTPs. The results also validate that EBS is capable of exploiting the synergy of fitness landscapes.

Evolutionary many-tasking based on biocoenosis through symbiosis: A framework and benchmark problems

In this paper we use a divide-and-conquer approach to tackle large-scale optimization problems with overlapping components. Decomposition for an overlapping problem is challenging as its components depend on one another. The existing decomposition methods typically assign all the linked decision variables into one group, thus cannot reduce the original problem size. To address this issue we modify the Recursive Differential Grouping (RDG) method to decompose overlapping problems, by breaking the linkage at variables shared by multiple components. To evaluate the efficacy of our method, we extend two existing overlapping benchmark problems considering various level of overlap. Experimental results show that our method can greatly improve the search ability of an optimization algorithm via divide-and-conquer, and outperforms RDG, random decomposition as well as other state-of-the-art methods. We further evaluate our method using the CEC’2013 benchmark problems and show that our method is very competitive when equipped with a component optimizer.

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Decomposition for Large-scale Optimization Problems with Overlapping Components

The weight-adapted convolution neural network (WACNN) is proposed to extract discriminative expression representations for recognizing facial expression. It aims to make good use of the convolution neural network’s (CNN’s) potential performance in avoiding local optima and speeding up convergence by the hybrid genetic algorithm (HGA) with optimal initial population, in such a way that it realizes deep and global emotion understanding in human–robot interaction. Moreover, the idea of novelty search is introduced to solve the deception problem in the HGA, which can expend the search space to help genetic algorithm jump out of local optimum and optimize large-scale parameters. In the proposal, the facial expression image preprocessing is conducted first, then the low-level expression features are extracted by using a principal component analysis. Finally, the high-level expression semantic features are extracted and recognized by WACNN which is optimized by HGA. In order to evaluate the effectiveness of WACNN, experiments on JAFFE, CK+, and static facial expressions in the wild 2.0 databases are carried out by using ${k}$ -fold cross validation, and experimental results show the recognition accuracies of the proposal are superior to that of the state-of-the-art, such as local directional ternary pattern and weighted mixture deep neural network (DNN), which aim to extract discriminative and are the DNN-based methods. Moreover, recognition accuracies of the proposal are also higher than the deep CNN without HGA, which indicates that the proposal has better global optimization ability. Meanwhile, preliminary application experiments are also carried out by using the proposed algorithm on the emotional social robot system, where nine volunteers and two-wheeled robots experience the scenario of emotion understanding. Application results indicate that the wheeled robots can recognize basic expressions, such as happy, surprise, and so on.

Weight-Adapted Convolution Neural Network for Facial Expression Recognition in Human–Robot Interaction

Factored evolutionary algorithms (FEAs) are a new class of evolutionary search-based optimization algorithms that have successfully been applied to various problems, such as training neural networks and performing abductive inference in graphical models. An FEA is unique in that it factors the objective function by creating overlapping subpopulations that optimize over a subset of variables of the function. In this paper, we give a formal definition of FEA algorithms and present empirical results related to their performance. One consideration in using an FEA is determining the appropriate factor architecture, which determines the set of variables each factor will optimize. For this reason, we present the results of experiments comparing the performance of different factor architectures on several standard applications for evolutionary algorithms. Additionally, we show that FEA’s performance is not restricted by the underlying optimization algorithm by creating FEA versions of hill climbing, particle swarm optimization, genetic algorithm, and differential evolution and comparing their performance to their single-population and cooperative coevolutionary counterparts.

Factored Evolutionary Algorithms

Particle Swarm Optimization (PSO) has been shown to perform very well on a wide range of optimization problems. One of the drawbacks to PSO is that the base algorithm assumes continuous variables. In this paper, we present a version of PSO that is able to optimize over discrete variables. This new PSO algorithm, which we call Integer and Categorical PSO (ICPSO), incorporates ideas from Estimation of Distribution Algorithms (EDAs) in that particles represent probability distributions rather than solution values, and the PSO update modifies the probability distributions. In this paper, we describe our new algorithm and compare its performance against other discrete PSO algorithms. In our experiments, we demonstrate that our algorithm outperforms comparable methods on both discrete benchmark functions and NK landscapes, a mathematical framework that generates tunable fitness landscapes for evaluating EAs.

A New Discrete Particle Swarm Optimization Algorithm

In this work, we present an extension to the recently developed Integer and Categorical Particle Swarm Optimization (ICPSO), which we refer to as Markovian ICPSO (MICPSO). MICPSO uses a Markov network to represent a particle's position, thus allowing each particle to incorporate information about dependencies between solution variables. In this work, we compare MICPSO to ICPSO, Integer PSO (IPSO), an Estimation of Distribution Algorithm called Markovianity-Based Optimization Algorithm (MOA), and a hillclimber on a set of benchmark vertex coloring problems. We find that MICPSO significantly outperforms all alternatives on all problems tested.

MICPSO: A method for incorporating dependencies into discrete particle swarm optimization

The use of phase-type distributions is an established method for extending the representational power of continuous time Bayesian networks beyond exponentially-distributed state transitions. In this paper, we propose a method for learning phase-type distributions from known parametric distributions. We find that by using particle swarm optimization to minimize a modified KL-divergence value, we are able to efficiently obtain good phase-type approximations for a variety of parametric distributions. Our experiments show that particle swarm optimization outperforms genetic algorithms and hill climbing with simulated annealing. In addition, we investigate the trade-off between accuracy and complexity with respect to the number of phases in the phase-type distribution. Finally, we propose and evaluate an extension that uses informed starting locations during optimization, which we found to improve convergence rates when compared to random initialization.

Rollie Goodman

Papers

Factored Evolutionary Algorithms

A New Discrete Particle Swarm Optimization Algorithm

MICPSO: A method for incorporating dependencies into discrete particle swarm optimization

A Swarm-Based Approach to Learning Phase-Type Distributions for Continuous Time Bayesian Networks