Using multi-objective evolutionary algorithms for single-objective constrained and unconstrained optimization

Segura, Carlos; Coello, Carlos A. Coello; Miranda, Gara; León, Coromoto

doi:10.1007/s10479-015-2017-z

Cited by 68 publications

(34 citation statements)

References 153 publications

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“…The idea of applying multi-objective optimisation to COPs has attracted much interest over last two decades [2]- [4]. In late 1990s, Surry and Radcliff [5] proposed constrained optimisation with multi-objective genetic algorithms.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Let Ω * denote the set of optimal feasible solution(s). There exist a variety of evolutionary algorithms (EAs) for solving COPs, which employ different constraint handling Manuscript methods, such as the penalty function, repairing infeasible solutions and multi-objective optimisation [1]- [4]. A multiobjective method works by transforming a COP into a multiobjective optimisation problem without inequality and equality constraints and then, solving it by a multi-objective EAs.…”

Section: Introductionmentioning

confidence: 99%

“…A multiobjective method works by transforming a COP into a multiobjective optimisation problem without inequality and equality constraints and then, solving it by a multi-objective EAs. Perhaps the most popular implementation is to minimise the original objective function and the degree of constraint violation simultaneously [4]- [6].…”

Section: Introductionmentioning

confidence: 99%

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Helper and Equivalent Objectives: Efficient Approach for Constrained Optimization

Shang

2022

IEEE Trans. Cybern.

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Numerous multi-objective evolutionary algorithms have been designed for constrained optimisation in last two decades. This method is to transform a constrained optimisation problem into a multi-objective optimisation problem, then solve it by an evolutionary algorithm. In this paper, we propose a new multi-objective method for constrained optimisation, which is to convert a constrained optimisation problem into a problem with helper and equivalent objectives. An equivalent objective means that its optimal solution set is the same as that to the constrained problem but a helper objective not. Then this multiobjective optimisation problem is decomposed into a group of sub-problems using the weighted sum approach. Weights are dynamically adjusted so that each subproblem eventually tends to a problem with an equivalent objective. We theoretically analyse the computation time of the helper and equivalent objective method on a hard problem called "wide gap". The "wide gap" problem means that an algorithm needs exponential time to cross between two fitness levels. We prove that using helper and equivalent objectives may shorten the time of crossing the "wide gap". We conduct a case study for validating our method. An algorithm with helper and equivalent objectives is implemented. Experimental results show that its overall performance is ranked first when compared with other eight state-of-art evolutionary algorithms. The case study proves the efficiency of the helper and equivalent objective method for constrained optimisation.

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Section: Literature Reviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Helper and Equivalent Objectives: Efficient Approach for Constrained Optimization

Shang

2022

IEEE Trans. Cybern.

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“…Diversity has been recognized as an important indicator for good performance, although mainly applied to the static scenarios of offline adaptation: The authors of [37] provide an extensive survey of various methods to enforce diversity in genetic algorithms. These fall into the categories of external methods controlling the evolutionary process "from the outside" [18], [38] and methods integrating diversity as an additional objective into the genetic algorithm, using the concepts of multi-objective genetic optimization [39], [40]. Following the biological inspiration, the aptitude of genetic algorithms to an online setting with a changing environment has been thoroughly analyzed [41], [42].…”

Section: Related Workmentioning

confidence: 99%

Preparing for the Unexpected: Diversity Improves Planning Resilience in Evolutionary Algorithms

Gabor

Belzner

Phan

et al. 2018

2018 IEEE International Conference on Autonomic Computing (ICAC)

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As automatic optimization techniques find their way into industrial applications, the behavior of many complex systems is determined by some form of planner picking the right actions to optimize a given objective function. In many cases, the mapping of plans to objective reward may change due to unforeseen events or circumstances in the real world. In those cases, the planner usually needs some additional effort to adjust to the changed situation and reach its previous level of performance. Whenever we still need to continue polling the planner even during re-planning, it oftentimes exhibits severely lacking performance. In order to improve the planner's resilience to unforeseen change, we argue that maintaining a certain level of diversity amongst the considered plans at all times should be added to the planner's objective. Effectively, we encourage the planner to keep alternative plans to its currently best solution.As an example case, we implement a diversity-aware genetic algorithm using two different metrics for diversity (differing in their generality) and show that the blow in performance due to unexpected change can be severely lessened in the average case. We also analyze the parameter settings necessary for these techniques in order to gain an intuition how they can be incorporated into larger frameworks or process models for software and systems engineering.

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“…There exist a variety of evolutionary algorithms (EAs) for solving COPs, which employ different constraint handling techniques, such as the penalty function method, feasibility rule, repair method and multiobjective optimization [1,2,3]. This paper focuses on the multi-objective optimization method [4], which is to convert a COP into a multi-objective optimization problem without any constraint. The advantage of using this method is no need to handle constraints in a special way, because constraints themselves are converted into objectives and a COP will be solved by MOEAs.…”

Section: Introductionmentioning

confidence: 99%

Multiobjective differential evolution enhanced with principle component analysis for constrained optimization

Huang

et al. 2019

Swarm and Evolutionary Computation

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Multiobjective evolutionary algorithms (MOEAs) have been successfully applied to a number of constrained optimization problems. Many of them adopt mutation and crossover operators from differential evolution. However, these operators do not explicitly utilise features of fitness landscapes. To improve the performance of algorithms, this paper aims at designing a search operator adapting to fitness landscapes. Through an observation, we find that principle component analysis (PCA) can be used to characterise fitness landscapes. Based on this finding, a new search operator, called PCA-projection, is proposed. In order to verify the effectiveness of PCA-projection, we design two algorithms enhanced with PCA-projection for solving constrained optimization problems, called PMODE and HECO-PDE, respectively. Experiments have been conducted on the IEEE CEC 2017 competition benchmark suite in constrained optimisation. PMODE and HECO-PDE are compared with the algorithms from the IEEE CEC 2018 competition and another recent MOEA for constrained optimisation. Experimental results show that an algorithm enhanced with PCA-projection performs better than its corresponding opponent without this operator. Furthermore, HECO-PDE is ranked first on all dimensions according to the competition rules. This study reveals that decomposition-based MOEAs, such as HECO-PDE, are competitive with best single-objective and multiobjective evolutionary algorithms for constrained optimisation, but MOEAs based on non-dominance, such as PMODE, may not.

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Using multi-objective evolutionary algorithms for single-objective constrained and unconstrained optimization

Cited by 68 publications

References 153 publications

Helper and Equivalent Objectives: Efficient Approach for Constrained Optimization

Helper and Equivalent Objectives: Efficient Approach for Constrained Optimization

Preparing for the Unexpected: Diversity Improves Planning Resilience in Evolutionary Algorithms

Multiobjective differential evolution enhanced with principle component analysis for constrained optimization

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