Minimum Manhattan Distance Approach to Multiple Criteria Decision Making in Multiobjective Optimization Problems

A minimum Manhattan distance (MMD) approach to multiple criteria decision making in multiobjective optimization problems (MOPs) is proposed. The approach selects the final solution corresponding with a vector that has the MMD from a normalized ideal vector. This procedure is equivalent to the knee s...

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Veröffentlicht in:	IEEE transactions on evolutionary computation Jg. 20; H. 6; S. 972 - 985
Hauptverfasser:	Wei-Yu Chiu, Yen, Gary G., Teng-Kuei Juan
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York IEEE 01.12.2016 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Decision making Divide and conquer (D&C) approach Electronic mail Evolutionary algorithms Evolutionary computation knee solutions Linear programming minimum Manhattan distance (MMD) approach multicriteria decision making (MCDM) multiobjective evolutionary algorithms (MOEAs) multiobjective optimization problems (MOPs) multiple attribute decision making (MADM) multiple criteria decision making (MCDM) Multiple criterion Optimization Pareto optimization Visualization
ISSN:	1089-778X, 1941-0026
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Abstract	A minimum Manhattan distance (MMD) approach to multiple criteria decision making in multiobjective optimization problems (MOPs) is proposed. The approach selects the final solution corresponding with a vector that has the MMD from a normalized ideal vector. This procedure is equivalent to the knee selection described by a divide and conquer approach that involves iterations of pairwise comparisons. Being able to systematically assign weighting coefficients to multiple criteria, the MMD approach is equivalent to a weighted-sum (WS) approach. Because of the equivalence, the MMD approach possesses rich geometric interpretations that are considered essential in the field of evolutionary computation. The MMD approach is elegant because all evaluations can be performed by efficient matrix calculations without iterations of comparisons. While the WS approach may encounter an indeterminate situation in which a few solutions yield almost the same WS, the MMD approach is able to determine the final solution discriminately. Since existing multiobjective evolutionary algorithms aim for a posteriori decision making, i.e., determining the final solution after a set of Pareto optimal solutions is available, the proposed MMD approach can be combined with them to form a powerful solution method of solving MOPs. Furthermore, the approach enables scalable definitions of the knee and knee solutions.
AbstractList	A minimum Manhattan distance (MMD) approach to multiple criteria decision making in multiobjective optimization problems (MOPs) is proposed. The approach selects the final solution corresponding with a vector that has the MMD from a normalized ideal vector. This procedure is equivalent to the knee selection described by a divide and conquer approach that involves iterations of pairwise comparisons. Being able to systematically assign weighting coefficients to multiple criteria, the MMD approach is equivalent to a weighted-sum (WS) approach. Because of the equivalence, the MMD approach possesses rich geometric interpretations that are considered essential in the field of evolutionary computation. The MMD approach is elegant because all evaluations can be performed by efficient matrix calculations without iterations of comparisons. While the WS approach may encounter an indeterminate situation in which a few solutions yield almost the same WS, the MMD approach is able to determine the final solution discriminately. Since existing multiobjective evolutionary algorithms aim for a posteriori decision making, i.e., determining the final solution after a set of Pareto optimal solutions is available, the proposed MMD approach can be combined with them to form a powerful solution method of solving MOPs. Furthermore, the approach enables scalable definitions of the knee and knee solutions.
Author	Yen, Gary G. Wei-Yu Chiu Teng-Kuei Juan
Author_xml	– sequence: 1 surname: Wei-Yu Chiu fullname: Wei-Yu Chiu email: chiuweiyu@gmail.com organization: Dept. of Electr. Eng., Yuan Ze Univ., Taoyuan, Taiwan – sequence: 2 givenname: Gary G. surname: Yen fullname: Yen, Gary G. email: gyen@okstate.edu organization: Sch. of Electr. & Comput. Eng., Oklahoma State Univ., Stillwater, OK, USA – sequence: 3 surname: Teng-Kuei Juan fullname: Teng-Kuei Juan email: s1034650@mail.yzu.edu.tw organization: Dept. of Electr. Eng., Yuan Ze Univ., Taoyuan, Taiwan
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SubjectTerms	Decision making Divide and conquer (D&C) approach Electronic mail Evolutionary algorithms Evolutionary computation knee solutions Linear programming minimum Manhattan distance (MMD) approach multicriteria decision making (MCDM) multiobjective evolutionary algorithms (MOEAs) multiobjective optimization problems (MOPs) multiple attribute decision making (MADM) multiple criteria decision making (MCDM) Multiple criterion Optimization Pareto optimization Visualization
Title	Minimum Manhattan Distance Approach to Multiple Criteria Decision Making in Multiobjective Optimization Problems
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