Solving the Lexicographic Multi-Objective Mixed-Integer Linear Programming Problem using branch-and-bound and grossone methodology

Marco Cococcioni,Alessandro Cudazzo,Massimo Pappalardo,Yaroslav D. Sergeyev

Communications in Nonlinear Science and Numerical Simulation（2020）

引用 46|浏览20

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摘要

•Lexicographic Multi-Objective Mixed Integer Linear Programming problem (LMILP) is studied.•The Grossone methodology using numerical infinities and infinitesimals is applied to LMILP.•A Grossone-based Branch-and-Bound in combination with Grossone-based simplex is proposed.•Theoretical conditions for the correctness of the proposed methodology are established.•Experiments show that the new methods are able to solve LMILPs with up to 200 objectives.

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关键词

Multi-objective optimization,Lexicographic optimization,Mixed-integer linear programming,Numerical infinitesimals,Grossone methodology

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