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 |
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| Jazyk: | angličtina |
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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. |
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| 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 |
| Author_xml | – sequence: 1 givenname: Valentina orcidid: 0000-0002-6269-7136 surname: Cacchiani fullname: Cacchiani, Valentina email: valentina.cacchiani@unibo.it organization: DEI, University of Bologna, Viale Risorgimento 2, Bologna I-40136, Italy – sequence: 2 givenname: Claudia surname: D’Ambrosio fullname: D’Ambrosio, Claudia email: dambrosio@lix.polytechnique.fr organization: LIX CNRS (UMR7161), École Polytechnique, Palaiseau Cedex 91128, France |
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| Keywords | Convex Mixed Integer Non-Linear Programming Multi-objective Heuristic algorithm Hydro unit commitment Knapsack problem |
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