A comparative study of constraint-handling techniques in evolutionary constrained multiobjective optimization

Multi-objective optimization is increasingly used in engineering to design new systems and to identify design tradeoffs. Yet, design problems often have objective functions and constraints that are expensive and highly non-linear. Combinations of these features lead to poor convergence and diversity loss with common algorithms that have not been specifically designed for constrained optimization. Constrained benchmark problems exist, but they do not necessarily represent the challenges of engineering problems. In this paper, a framework to design electro-mechanical actuators, called MODAct, is presented and 20 constrained multi-objective optimization test problems are derived from the framework with a specific focus on constraints. The full source code is made available to ease its use. The effects of the constraints are analyzed through their impact on the Pareto front as well as on the convergence performance. A constraint landscape analysis approach is followed and extended with three new metrics to characterize the search and objective spaces. The features of MODAct are compared to existing test suites to highlight the differences. In addition, a convergence analysis using NSGA-II, NSGA-III and C-TAEA on MODAct and existing test suites suggests that the design problems are indeed difficult due to the constraints. In particular, the number of simultaneously violated constraints in newly generated solutions seems key in understanding the convergence challenges. Thus, MODAct offers an efficient framework to analyze and handle constraints in future optimization algorithm design.

show abstract

“…More recent variants of this framework have been proposed (e.g. NCTP [18]), but the shortcomings mentioned previously remain.…”

Section: Related Work a Constrained Multi-objective Optimizationmentioning

confidence: 99%

Realistic Constrained Multiobjective Optimization Benchmark Problems From Design

Picard

Schiffmann

2021

IEEE Trans. Evol. Computat.

View full text Add to dashboard Cite

show abstract

“…Test problems play a crucial role in judging whether an algorithm is a candidate for solving MOPs [3]- [4]. Currently, test instances for DMOPs [3]- [5], [63] and CMOPs [6], [31], [48] have been proposed. However, these test problems do not consider dynamism and constraints simultaneously.…”

Section: Proposed Test Problemsmentioning

confidence: 99%

“…Designing test problems with trigonometric functions can easily reflect these characteristics arising in real-world problems by adjusting the corresponding parameters. Based on the above discussions and benchmarks designed in [4], [6], and [48], this study proposes the following instance generator.…”

Section: Proposed Test Problemsmentioning

confidence: 99%

A Novel Evolutionary Algorithm for Dynamic Constrained Multiobjective Optimization Problems

Chen

Ding

Yang

et al. 2020

IEEE Trans. Evol. Computat.

Self Cite

View full text Add to dashboard Cite

Abstract-To promote research on dynamic constrained multiobjective optimization, we first propose a group of generic test problems with challenging characteristics, including different modes of the true Pareto front (e.g., convexity-concavity and connectedness-disconnectedness) and the changing feasible region. Subsequently, motivated by the challenges presented by dynamism and constraints, we design a dynamic constrained multiobjective optimization algorithm with a nondominated solution selection operator, a mating selection strategy, a population selection operator, a change detection method, and a change response strategy. The designed nondominated solution selection operator can obtain a nondominated population with diversity when the environment changes. The mating selection strategy and population selection operator can adaptively handle infeasible solutions. If a change is detected, the proposed change response strategy reuses some portion of the old solutions in combination with randomly generated solutions to reinitialize the population, and a steady-state update method is designed to improve the retained previous solutions. Experimental results show that the proposed test problems can be used to clearly distinguish the performance of algorithms, and that the proposed algorithm is very competitive for solving dynamic constrained multiobjective optimization problems in comparison with state-of-the-art algorithms. Index Terms-Dynamic constrained multiobjective optimization, test problems, population selection, change response I. INTRODUCTION ANY real-world optimization problems, particularly online optimization problems or optimal control problems, involve multiple objectives and constraints that may change over time throughout the optimization [1]; such problems can be called dynamic constrained multiobjective optimization problems (DCMOPs). Without loss of generality,

show abstract

“…Normally, there should be four combinations altogether, i.e., Deb's feasibility-based rule and ε constrained method in the first and second phase, named D-E, D-D, E-E, E-D respectively. In [11], the first three combinations are compared, and this paper will further study the fourth combination (C 2 oDE-ED), i.e., ε constrained method in the first phase and Deb's feasibilitybased rule in the second phase.…”

Section: General Model For Comparisonmentioning

confidence: 99%

“…Mezura-Montes et al [10] proposed a simple combination of two DE variants (i.e., DE/rand/1/bin and DE/best/1/bin) based on the empirical analysis of four DE variants. Li et al [11] suggested more experimental comparisons on different constraint-handling techniques are needed. They compared three representative constrainthandling techniques (i.e., Constrained-domination Principle, Self-adaptive Penalty, and Adaptive Tradeoff Model), and the search algorithm is nondominated sorting genetic algorithm II (NSGA II).…”

Section: Introductionmentioning

confidence: 99%

On the Cooperation Between Evolutionary Algorithms and Constraint Handling Techniques: A Further Empirical Study

2020

View full text Add to dashboard Cite

Cooperation between Evolutionary Algorithms (EAs) and Constraint Handling Techniques (CHTs) plays an important role in Constrained Optimization Evolutionary Algorithms (COEAs). A constrained composite differential evolution (C 2 oDE) sets a good example on the cooperation. This paper tries to further study the inner mechanism, i.e., the effect of different methods on generating and selecting solutions. In the solution generating part, a new method, which adopts stochastic ranking in selecting the best individual in the DE mutation operators, is proposed. In the solution selecting part, a new constraint handling technique combination is added. The experiments on benchmark functions from IEEE CEC2006 verify the effect. During the experiment, it is found that a new cooperation manner performs better than C 2 oDE, which reflects the importance of cooperation. INDEX TERMS constrained optimization, constraint handling techniques, differential evolution, cooperation manner.

show abstract

A comparative study of constraint-handling techniques in evolutionary constrained multiobjective optimization

Cited by 46 publications

References 22 publications

Realistic Constrained Multiobjective Optimization Benchmark Problems From Design

Realistic Constrained Multiobjective Optimization Benchmark Problems From Design

A Novel Evolutionary Algorithm for Dynamic Constrained Multiobjective Optimization Problems

On the Cooperation Between Evolutionary Algorithms and Constraint Handling Techniques: A Further Empirical Study

Contact Info

Product

Resources

About