Generating Pareto Surface for Multi Objective Integer Programming Problems with Stochastic Objective Coefficients
Stochastic multi objective programming problems commonly arise in complex systems such as portfolio analysis, medium- to long-term capacity planning and design applications under uncertainty. The identification of the candidate solution set is a main step in many applications which depends on the na...
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| Vydáno v: | Procedia computer science Ročník 6; s. 46 - 51 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
2011
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| ISSN: | 1877-0509, 1877-0509 |
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| Abstract | Stochastic multi objective programming problems commonly arise in complex systems such as portfolio analysis, medium- to long-term capacity planning and design applications under uncertainty. The identification of the candidate solution set is a main step in many applications which depends on the nature of uncertainty. This study presents a method to generate Pareto surface for multi-objective integer programs with stochastic coefficients in the objective functions based on minimum expectation and variance criteria. The objective function coefficients are represented through random discrete distributions. The methodology follows a two-phase approach where, in the first phase, the stochastic multiple objectives are converted into deterministic equivalents based on the minimum expectation and variance efficiency concepts. The second phase solves the deterministic multi objective problem, using a Pareto generation methodology which aims at generating the whole Pareto surface of multi objective integer programming problems. We present results of experimental study of applying the proposed method to an assignment problem with three objective functions. |
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| AbstractList | Stochastic multi objective programming problems commonly arise in complex systems such as portfolio analysis, medium- to long-term capacity planning and design applications under uncertainty. The identification of the candidate solution set is a main step in many applications which depends on the nature of uncertainty. This study presents a method to generate Pareto surface for multi-objective integer programs with stochastic coefficients in the objective functions based on minimum expectation and variance criteria. The objective function coefficients are represented through random discrete distributions. The methodology follows a two-phase approach where, in the first phase, the stochastic multiple objectives are converted into deterministic equivalents based on the minimum expectation and variance efficiency concepts. The second phase solves the deterministic multi objective problem, using a Pareto generation methodology which aims at generating the whole Pareto surface of multi objective integer programming problems. We present results of experimental study of applying the proposed method to an assignment problem with three objective functions. |
| Author | Turgut, Ozgu Murat, Alper E. |
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| CitedBy_id | crossref_primary_10_1016_j_ijpe_2018_05_025 crossref_primary_10_3390_pr9111871 |
| Cites_doi | 10.1016/j.amc.2009.12.065 10.1016/j.ejor.2008.10.023 10.1016/j.ejor.2005.10.021 10.1016/S0377-2217(03)00371-0 10.1007/s10732-008-9071-5 10.1016/0377-2217(86)90160-8 10.1016/j.ejor.2007.09.039 10.1007/s10732-008-9090-2 10.1007/s11067-007-9025-8 10.1057/jors.2008.106 10.1016/S0377-2217(02)00859-7 |
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| Keywords | Pareto surface stochastic visualization Multi objective optimization |
| Language | English |
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| Title | Generating Pareto Surface for Multi Objective Integer Programming Problems with Stochastic Objective Coefficients |
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