Continuous Dynamic Constrained Optimization With Ensemble of Locating and Tracking Feasible Regions Strategies

Abstract

Dynamic Constrained Optimization Problems (DCOPs) are difficult to solve because both the objective function and constraints can vary with time. Although DCOPs have drawn attention in recent years, little work has been performed to solve DCOPs with multiple dynamic feasible regions from the perspective of locating and tracking multiple feasible regions in parallel. Moreover, few benchmarks have been proposed to simulate the dynamics of multiple disconnected feasible regions. In this paper, first, the idea of tracking multiple feasible regions, originally proposed by Nguyen and Yao, is enhanced by specifically adopting multiple sub-populations. To this end, the Dynamic Species-based Particle Swam Optimization (i.e., DSPSO), a representative multi-population algorithm, is adopted. Second, an ensemble of locating and tracking feasible regions strategies is proposed to handle different types of dynamics in constraints. Third, two benchmarks are designed to simulate the DCOPs with dynamic constraints. The first benchmark, including two variants of G24 (called G24v and G24w), could control the size of feasible regions. The second benchmark, named Moving Feasible Regions Benchmark (MFRB), is highly configurable. The global optimum of MFRB is calculated mathematically for experimental comparisons. Experimental results on G24, G24v, G24w and MFRB show that the DSPSO with the ensemble of strategies performs significantly better than the original DSPSO and other typical algorithms.

A survey of swarm intelligence for dynamic optimization: Algorithms and applications

“…Other performance measurements were proposed exclusively to evaluate the ability of the algorithms to track and locate feasible regions such as: feasible time ratio, optimal region tracking measure, local search cover, number of evaluations for constraints. In addition, existing measurements were modified for dynamic constrained optimization problems such as: the peak cover to count the number of only feasible regions in each period and the offline error to consider the best error as normal but if there is no feasible solution; then the current worst possible value is considered [56].…”

“…Bu et al [56] applied a variation of the SPSO with an ensemble of strategies to locate and track feasible regions. The strategies include: a gradient-based repair, an adaptive local search, constraint handling, memory and prediction strategy.…”

On the Use of Diversity Mechanisms in Dynamic Constrained Continuous Optimization

“…Our algorithms were tested on two benchmarks for DCOPs [12,21], which contains 22 problems in total. The first 18 test cases are from [21] that captures different characteristics of DCOPs like multiple disconnected feasible regions, gradually moving feasible regions and global optimum switching between different feasible regions.…”

“…The first 18 test cases are from [21] that captures different characteristics of DCOPs like multiple disconnected feasible regions, gradually moving feasible regions and global optimum switching between different feasible regions. The last 4 test cases are from [12] in which Bu used a parameter in the original test cases in [21] that controls the size and the number of disconnected feasible regions. In the experiments, medium severity is chosen for the objective function (k = 0.5) and the constraints (S = 20).…”

A Comparison of Constraint Handling Techniques for Dynamic Constrained Optimization Problems

“…One of the of the most important aspects of solving DCOPs is using an effective constraint handling technique to deal with the dynamic constraints in order to guide the search to those regions with feasible solutions and quickly adapt if constraints are changing. In the specialized literature about DCOPs, the constraint handling techniques that have been applied include penalty function [4], repair methods [1,5,6] and feasibility rules [7].…”