Local Search for Mixed-Integer Nonlinear Optimization: A Methodology and an Application

Abstract

A methodology is presented for tackling mixed-integer nonlinear optimization problems by local search, in particular large-scale real-life problems. This methodology is illustrated through the local-search heuristic implemented for solving an energy management problem posed by the EDF company in the context of the ROADEF/EURO Challenge 2010, an international competition of applied optimization. Our local-search approach is pure and direct: the problem is tackled frontally, without decomposition nor hybridization. In this way, both combinatorial and continuous decisions can be modified by a move during the search. Then, our work focuses on the diversification by the moves and on the performance of the incremental evaluation machinery. Exploring millions of feasible solutions within one hour of running time, the resulting local search allows us to obtain among the best results of the competition, in which 44 teams from 25 countries were engaged.