By Frédéric Gardi
This ebook covers neighborhood look for combinatorial optimization and its extension to mixed-variable optimization. even though now not but understood from the theoretical standpoint, neighborhood seek is the paradigm of selection for tackling large-scale real-life optimization difficulties. cutting-edge end-users call for interactivity with selection help structures. For optimization software program, this implies acquiring good-quality solutions �Read more...
summary: This e-book covers neighborhood look for combinatorial optimization and its extension to mixed-variable optimization. even though now not but understood from the theoretical standpoint, neighborhood seek is the paradigm of selection for tackling large-scale real-life optimization difficulties. state-of-the-art end-users call for interactivity with determination aid platforms. For optimization software program, this suggests acquiring good-quality recommendations quick. speedy iterative development tools, like neighborhood seek, are fitted to enjoyable such wishes. the following the authors express neighborhood seek in a brand new gentle, particularly offering a brand new relations
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Additional info for Mathematical Programming Solver Based on Local Search
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Berthold [BER 06] provides an extensive survey of primal heuristics for MIP. Among them, we can cite large neighborhood search [FOC 03, SHA 98] used in CP, as well as local branching [FIS 03, FIS 08] or relaxed induced neighborhood search [DAN 05] in mixed-integer Local Search for 0–1 Nonlinear Programming 33 programming. Nevertheless, all these works consist of integrating high-level local search ingredients into the tree search paradigm, whereas the actual power of local search relies on fast incremental computations made possible by small modifications of the incumbent solution.
Our approach follows the methodology described above: a fast exploration of several small but rich neighborhoods. Our search strategy is simply a standard first-improvement descent. The main conclusion drawn from our victory is that sophisticated metaheuristics are useless in solving car sequencing problems. More generally, it demonstrates that algorithmic aspects, often neglected in favor of trendy “meta” aspects, remain the key ingredients for designing and engineering high-performance local search heuristics.
All the strategies are detailed in [EST 08]. The bottleneck of each iteration of the local search in terms of time complexity is clearly the evaluation of the move that is attempted. Fortunately, almost all moves reveal some invariants that can be exploited using special data structures to evaluate the impact of a move on the cost of the current solution quickly. For ratios, the crucial remark is that the number of windows which are impacted by swaps, insertions or reflections depends only on the denominator of each ratio, generally small in practice.