Competitive island - based cooperative coevolution for efficient optimization of large - scale fully - separable continuous functions

In this paper, we investigate the performance of introducing competition in cooperative coevolutionary algorithms to solve large-scale fully-separable continuous optimization problems. It may seem that solving large-scale fully-separable functions is trivial by means of problem decomposition. In principle, due to lack of variable interaction in fully-separable problems, any decomposition is viable. However, the decomposition strategy has shown to have a significant impact on the performance of cooperative coevolution on such functions. Finding an optimal decomposition strategy for solving fully-separable functions is laborious and requires extensive empirical studies. In this paper, we use a competitive two-island cooperative coevolution in which two decomposition strategies compete and collaborate to solve a fully-separable problem. Each problem decomposition has features that may be beneficial at different stages of optimization. Therefore, competition and collaboration of such decomposition strategies may eliminate the need for finding an optimal decomposition. The experimental results in this paper suggest that com- petition and collaboration of suboptimal decomposition strategies of a fully-separable problem can generate better solutions than the standard cooperative coevolution with standalone decomposition strategies. We also show that a decomposition strategy that implements competition against itself can also improve the overall optimization performance

On the relationship of degree of separability with depth of evolution in decomposition for cooperative coevolution

Problem decomposition determines how subcomponents are created that have a vital role in the performance of cooperative coevolution. Cooperative coevolution naturally appeals to fully separable problems that have low interaction amongst subcomponents. The interaction amongst subcomponents is defined by the degree of separability. Typically, in cooperative coevolution, each subcomponent is implemented as a sub-population that is evolved in a round-robin fashion for a specified depth of evolution. This paper examines the relationship between the depth of evolution and degree of separability for different types of global optimisation problems. The results show that the depth of evolution is an important attribute that affects the performance of cooperative coevolution and can be used to ascertain the nature of the problem in terms of the degree of separability

Multi - island competitive cooperative coevolution for real parameter global optimization

Problem decomposition is an important attribute of cooperative coevolution that depends on the nature of the problems in terms of separability which is defined by the level of interaction amongst decision variables. Recent work in cooperative coevolution featured competition and collaboration of problem decomposition methods that was implemented as islands in a method known as competitive island cooperative coevolution (CICC). In this paper, a multi-island competitive cooperative coevolution algorithm (MICCC) is proposed in which several different problem decomposition strategies are given a chance to compete, collaborate and motivate other islands while converging to a common solution. The performance of MICCC is evaluated on eight different benchmark functions and are compared with CICC where only two islands were utilized. The results from the experimental analysis show that competition and collaboration of several different island can yield solutions with a quality better than the two-island competition algorithm (CICC) on most complex multi-modal problems

Contribution based multi-island competitive cooperative coevolution

Competition in cooperative coevolution (CC) has demonstrated success in solving global optimization problems. In a recent study, a multi-island competitive cooperative coevolution (MIC3) algorithm was introduced that featured competition and collaboration of several different problem decomposition strategies implemented as independent islands. It was shown that MIC3converges to high quality solutions without the need to find an optimal decomposition. MIC3splits the computational budget in terms of the number of function evaluations, equally amongst all the islands and evolves them in a round-robin fashion. This overlooks the difference in contributions of different islands towards improving the overall objective function value. Therefore, a considerable amount of function evaluations is wasted on the low-contributing islands as their problem decomposition strategies may not appeal to the problem at the given stage of the evolutionary process. This paper proposes contribution-based MIC3 algorithms (MIC4) that quantifies the contributions of each island and allocates the computational budget accordingly. The experimental analysis reveals that the proposed method outperforms its counterpart

Cooperative Coevolution for Non-Separable Large-Scale Black-Box Optimization: Convergence Analyses and Distributed Accelerations

Given the ubiquity of non-separable optimization problems in real worlds, in this paper we analyze and extend the large-scale version of the well-known cooperative coevolution (CC), a divide-and-conquer optimization framework, on non-separable functions. First, we reveal empirical reasons of why decomposition-based methods are preferred or not in practice on some non-separable large-scale problems, which have not been clearly pointed out in many previous CC papers. Then, we formalize CC to a continuous game model via simplification, but without losing its essential property. Different from previous evolutionary game theory for CC, our new model provides a much simpler but useful viewpoint to analyze its convergence, since only the pure Nash equilibrium concept is needed and more general fitness landscapes can be explicitly considered. Based on convergence analyses, we propose a hierarchical decomposition strategy for better generalization, as for any decomposition there is a risk of getting trapped into a suboptimal Nash equilibrium. Finally, we use powerful distributed computing to accelerate it under the multi-level learning framework, which combines the fine-tuning ability from decomposition with the invariance property of CMA-ES. Experiments on a set of high-dimensional functions validate both its search performance and scalability (w.r.t. CPU cores) on a clustering computing platform with 400 CPU cores

Efficient Resource Allocation in Cooperative Co-Evolution for Large-Scale Global Optimization

Cooperative co-evolution (CC) is an explicit means of problem decomposition in multipopulation evolutionary algorithms for solving large-scale optimization problems. For CC, subpopulations representing subcomponents of a large-scale optimization problem co-evolve, and are likely to have different contributions to the improvement of the best overall solution to the problem. Hence, it makes sense that more computational resources should be allocated to the subpopulations with greater contributions. In this paper, we study how to allocate computational resources in this context and subsequently propose a new CC framework named CCFR to efficiently allocate computational resources among the subpopulations according to their dynamic contributions to the improvement of the objective value of the best overall solution. Our experimental results suggest that CCFR can make efficient use of computational resources and is a highly competitive CCFR for solving large-scale optimization problems