Objective Reduction in Many-Objective Optimization: Linear and Nonlinear Algorithms

The difficulties faced by existing multiobjective evolutionary algorithms (MOEAs) in handling many-objective problems relate to the inefficiency of selection operators, high computational cost, and difficulty in visualization of objective space. While many approaches aim to counter these difficultie...

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Vydáno v:	IEEE transactions on evolutionary computation Ročník 17; číslo 1; s. 77 - 99
Hlavní autoři:	Saxena, D. K., Duro, J. A., Tiwari, A., Deb, K., Qingfu Zhang
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.02.2013 Institute of Electrical and Electronics Engineers
Témata:	Algorithm design and analysis Algorithmics. Computability. Computer arithmetics Applied sciences Computational efficiency Computer science; control theory; systems Data processing. List processing. Character string processing Decision making Decision theory. Utility theory Evolutionary multiobjective optimization Exact sciences and technology many-objective optimization Mathematical programming maximum variance unfolding and kernels Memory organisation. Data processing Operational research and scientific management Operational research. Management science Optical fibers Optimization principal component analysis Redundancy Search problems Software Theoretical computing Fidelity Visualization Costs Error estimation Evolutionary algorithm Variability Multiobjective programming Non linear programming Optimization Relevance maximum variance unfolding and kernels Dependence Robustness Productivity Sensitivity analysis Dominating set Pareto optimum Preservation Decision making Redundancy Critical parameter Dominance Linear programming many-objective optimization Standards Dimension reduction Quality control Algorithm analysis Principal component analysis Evolutionary multiobjective optimization
ISSN:	1089-778X, 1941-0026
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Popis
Shrnutí:	The difficulties faced by existing multiobjective evolutionary algorithms (MOEAs) in handling many-objective problems relate to the inefficiency of selection operators, high computational cost, and difficulty in visualization of objective space. While many approaches aim to counter these difficulties by increasing the fidelity of the standard selection operators, the objective reduction approach attempts to eliminate objectives that are not essential to describe the Pareto-optimal front (POF). If the number of essential objectives is found to be two or three, the problem could be solved by the existing MOEAs. It implies that objective reduction could make an otherwise unsolvable (many-objective) problem solvable. Even when the essential objectives are four or more, the reduced representation of the problem will have favorable impact on the search efficiency, computational cost, and decision-making. Hence, development of generic and robust objective reduction approaches becomes important. This paper presents a principal component analysis and maximum variance unfolding based framework for linear and nonlinear objective reduction algorithms, respectively. The major contribution of this paper includes: 1) the enhancements in the core components of the framework for higher robustness in terms of applicability to a range of problems with disparate degree of redundancy; mechanisms to handle input data that poorly approximates the true POF; and dependence on fewer parameters to minimize the variability in performance; 2) proposition of an error measure to assess the quality of results; 3) sensitivity analysis of the proposed algorithms for the critical parameter involved, and the characteristics of the input data; and 4) study of the performance of the proposed algorithms vis-à-vis dominance relation preservation based algorithms, on a wide range of test problems (scaled up to 50 objectives) and two real-world problems.
ISSN:	1089-778X 1941-0026
DOI:	10.1109/TEVC.2012.2185847