Scaling Up Dynamic Optimization Problems: A Divide-and-Conquer Approach

Abstract

Scalability is a crucial aspect of designing efficient algorithms. Despite their prevalence, large-scale dynamic optimization problems are not well-studied in the literature. This paper is concerned with designing benchmarks and frameworks for the study of large-scale dynamic optimization problems. We start by a formal analysis of the moving peaks benchmark and show its nonseparable nature irrespective of its number of peaks. We then propose a composite moving peaks benchmark suite with exploitable modularity covering a wide range of scalable partially separable functions suitable for the study of largescale dynamic optimization problems. The benchmark exhibits modularity, heterogeneity, and imbalance features to resemble real-world problems. To deal with the intricacies of large-scale dynamic optimization problems, we propose a decompositionbased coevolutionary framework which breaks a large-scale dynamic optimization problem into a set of lower dimensional components. A novel aspect of the framework is its efficient bilevel resource allocation mechanism which controls the budget assignment to components and the populations responsible for tracking multiple moving optima. Based on a comprehensive empirical study on a wide range of large-scale dynamic optimization problems with up to 200 dimensions, we show the crucial role of problem decomposition and resource allocation in dealing with these problems. The experimental results clearly show the superiority of the proposed framework over three other approaches in solving large-scale dynamic optimization problems.

A Novel Evolutionary Algorithm for Dynamic Constrained Multiobjective Optimization Problems

“…Considering that scalability plays a crucial role in designing an efficient algorithm [55], in the future we will study the scalable dynamic constrained many-objective optimization algorithms and design the benchmark problems that are close to real-world applications and can easily be extended to three or more objective functions. In many real-world applications, changing the production solution introduces additional cost [64].…”

A Three-Level Recursive Differential Grouping Method for Large-Scale Continuous Optimization

“…In the future, we will extend the three-level recursive differential grouping decomposition method into large-scale multi-objective optimization problems [34], large-scale dynamic optimization problems [35], and large-scale bilevel optimization problems [36]. From 2013 to 2014, he was a Post-Doctoral Fellow with the Department of Electrical Engineering, Yeungnam University, Gyeongsan, South Korea.…”

Adaptive Control of Subpopulations in Evolutionary Dynamic Optimization

“…The activity status of a sub-population is determined based on a threshold a . If all dimensions of the diversity vector of a sub-population fall below a , it will be deactivated until the end of the current environment [19]. Consequently, no computation resource is allocated to the inactivated sub-populations.…”

“…However, this method has some shortcomings which are consequences of the uniform distribution of computational resource among all sub-populations over time. Other existing computational resource allocation methods can be categorized into two groups of hibernating [15], [17]- [19] and progress based [20]- [22] approaches. In the hibernating methods, the Round Robin scheme is used but the sub-populations that have converged/stagnated would be removed from the Round Robin list.…”