Local search for mixed-integer nonlinear optimization: methodology and applications

Local search [1] is a practical solution approach for tackling large-scale discrete optimization problems, particularly whose arising in real-life applications. The authors have designed a methodology [5] for designing and engineering high-performance local-search heuristics in such contexts. This methodology has been shown to be successful for solving various industrial problems; several of these applications have been awarded on the occasion of OR competitions (1er Junior/Senior Prize at ROADEF 2005 Challenge [4], 2nd Senior Prize at ROADEF 2007 Challenge [5]). Recently, this methodology was extended to deal with mixed-integer optimization problems (linear as well as nonlinear). Note that local search is rarely used for solving mixed-integer optimization problems. A classical way to address these problems in practice is to use decomposition approaches (empirical or mathematical). Here we present the main ingredients of our methodology and its application for solving three industrial problems with high economic stakes (but short running times): rich inventory routing [2], resource scheduling for mass transportation [8], nuclear maintenance planning [6]. This methodology seems to be suited for tackling large-scale unit commitment problems arising in energy management, especially in operational contexts (daily or hourly use, very short running times, on-line replanification). The first particularity of our local search is to be pure and direct. Indeed, no decomposition is done; the problem is tackled frontally. The search space explored by our algorithm is close to the original solution space. In particular, the combinatorial and continuous parts of the problem are treated together: com-binatorial and continuous decisions can be simultaneously modified by a move during the search. By avoiding decompositions or reductions, no solution is lost and the probability to find good-quality ones is increased. Then, no hybridization is done: no particular metaheuristic is used, no tree-search technique is used. In this way, we avoid complex parameter tuning and simplify the architecture of the resulting software. Then, the second specificity of our local search is to be highly randomized, in order to avoid bias while exploring the search space. Such a diver