A branch-and-bound based heuristic algorithm for convex multi-objective MINLPs

•Convex multiobjective mixed integer nonlinear programming problem.•General branch-and-bound based heuristic algorithm enhanced with a refinement procedure.•Tests on hydro unit commitment and scheduling.•Tests on convex bi-objective mixed integer nonlinear knapsack problem. We study convex multi-obj...

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Vydáno v:European journal of operational research Ročník 260; číslo 3; s. 920 - 933
Hlavní autoři: Cacchiani, Valentina, D’Ambrosio, Claudia
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.08.2017
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ISSN:0377-2217, 1872-6860
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Abstract •Convex multiobjective mixed integer nonlinear programming problem.•General branch-and-bound based heuristic algorithm enhanced with a refinement procedure.•Tests on hydro unit commitment and scheduling.•Tests on convex bi-objective mixed integer nonlinear knapsack problem. We study convex multi-objective Mixed Integer Non-Linear Programming problems (MINLPs), which are characterized by multiple objective functions and non linearities, features that appear in real-world applications. To derive a good approximated set of non-dominated points for convex multi-objective MINLPs, we propose a heuristic based on a branch-and-bound algorithm. It starts with a set of feasible points, obtained, at the root node of the enumeration tree, by iteratively solving, with an ε-constraint method, a single objective model that incorporates the other objective functions as constraints. Lower bounds are derived by optimally solving Non-Linear Programming problems (NLPs). Each leaf node of the enumeration tree corresponds to a convex multi-objective NLP, which is solved heuristically by varying the weights in a weighted sum approach. In order to improve the obtained points and remove dominated ones, a tailored refinement procedure is designed. Although the proposed method makes no assumptions on the number of objective functions nor on the type of the variables, we test it on bi-objective mixed binary problems. In particular, as a proof-of-concept, we tested the proposed heuristic algorithm on instances of a real-world application concerning power generation, and instances of the convex biobjective Non-Linear Knapsack Problem. We compared the obtained results with those derived by well-known scalarization methods, showing the effectiveness of the proposed method.
AbstractList •Convex multiobjective mixed integer nonlinear programming problem.•General branch-and-bound based heuristic algorithm enhanced with a refinement procedure.•Tests on hydro unit commitment and scheduling.•Tests on convex bi-objective mixed integer nonlinear knapsack problem. We study convex multi-objective Mixed Integer Non-Linear Programming problems (MINLPs), which are characterized by multiple objective functions and non linearities, features that appear in real-world applications. To derive a good approximated set of non-dominated points for convex multi-objective MINLPs, we propose a heuristic based on a branch-and-bound algorithm. It starts with a set of feasible points, obtained, at the root node of the enumeration tree, by iteratively solving, with an ε-constraint method, a single objective model that incorporates the other objective functions as constraints. Lower bounds are derived by optimally solving Non-Linear Programming problems (NLPs). Each leaf node of the enumeration tree corresponds to a convex multi-objective NLP, which is solved heuristically by varying the weights in a weighted sum approach. In order to improve the obtained points and remove dominated ones, a tailored refinement procedure is designed. Although the proposed method makes no assumptions on the number of objective functions nor on the type of the variables, we test it on bi-objective mixed binary problems. In particular, as a proof-of-concept, we tested the proposed heuristic algorithm on instances of a real-world application concerning power generation, and instances of the convex biobjective Non-Linear Knapsack Problem. We compared the obtained results with those derived by well-known scalarization methods, showing the effectiveness of the proposed method.
Author Cacchiani, Valentina
D’Ambrosio, Claudia
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  organization: LIX CNRS (UMR7161), École Polytechnique, Palaiseau Cedex 91128, France
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Issue 3
Keywords Convex Mixed Integer Non-Linear Programming
Multi-objective
Heuristic algorithm
Hydro unit commitment
Knapsack problem
Language English
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SSID ssj0001515
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Snippet •Convex multiobjective mixed integer nonlinear programming problem.•General branch-and-bound based heuristic algorithm enhanced with a refinement...
SourceID crossref
elsevier
SourceType Enrichment Source
Index Database
Publisher
StartPage 920
SubjectTerms Convex Mixed Integer Non-Linear Programming
Heuristic algorithm
Hydro unit commitment
Knapsack problem
Multi-objective
Title A branch-and-bound based heuristic algorithm for convex multi-objective MINLPs
URI https://dx.doi.org/10.1016/j.ejor.2016.10.015
Volume 260
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