Analysis of inverted PBI and comparison with other scalarizing functions in decomposition based MOEAs

MOEA/D is one of the promising evolutionary approaches for solving multi and many-objective optimization problems. MOEA/D decomposes a multi-objective optimization problem into a number of single objective optimization problems. Each single objective optimization problem is defined by a scalarizing...

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Veröffentlicht in:Journal of heuristics Jg. 21; H. 6; S. 819 - 849
1. Verfasser: Sato, Hiroyuki
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.12.2015
Springer Nature B.V
Schlagworte:
Analysis
Artificial Intelligence
Calculus of Variations and Optimal Control; Optimization
Decomposition
Genetic algorithms
Heuristic
Management Science
Mathematics
Mathematics and Statistics
Operations Research
Operations Research/Decision Theory
Optimization
Optimization techniques
Pareto optimum
Population
Studies
MOEA/D
Evolutionary multi-objective optimization
Scalarizing functions
ISSN:1381-1231, 1572-9397
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Zusammenfassung:MOEA/D is one of the promising evolutionary approaches for solving multi and many-objective optimization problems. MOEA/D decomposes a multi-objective optimization problem into a number of single objective optimization problems. Each single objective optimization problem is defined by a scalarizing function using a weight vector. In MOEA/D, there are several scalarizing approaches such as weighted Tchebycheff, reciprocal weighted Tchebycheff, weighted sum (WS) and penalty-based boundary intersection (PBI). Each scalarizing function has a characteristic effect on the search performance of MOEA/D and provides a scenario of multi-objective solution search. To improve the availability of MOEA/D framework for solving various kinds of problems, it is important to provide a new scalarizing function which has different characteristics from the conventional scalarizing functions. In particular, the conventional scalarizing approaches face a difficulty to approximate a widely spread Pareto front in some problems. To approximate the entire Pareto front by improving the spread of solutions in the objective space and enhance the search performance of MOEA/D in multi and many-objective optimization problems, in this work we propose the inverted PBI scalarizing approach which is an extension of the conventional PBI and WS. In this work, we analyze differences between inverted PBI and other scalarizing functions, and compare the search performances of NSGA-III and five MOEA/Ds using weighted Tchebycheff, reciprocal weighted Tchebycheff, WS, PBI and inverted PBI in many-objective knapsack problems and WFG4 problems with 2–8 objectives. As results, we show that the inverted PBI based MOEA/D achieves higher search performance than other algorithms in problems with many-objectives and the difficulty to approximate a widely spread Pareto front in the objective space. Also, we show the robustness of the inverted PBI on Pareto front geometry by using problems with four representative concave, linear, convex and discontinuous Pareto fronts.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1381-1231
1572-9397
DOI:10.1007/s10732-015-9301-6