Industrial and Tramp Ship Routing Problems: Closing the Gap for Real-Scale Instances
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In a recent study, Hemmati et al. (2014) proposed a class of ship routing problems and a benchmark suite based on real shipping segments, considering pickups and deliveries, cargoes selections, ship-dependent starting locations, travel times and costs, time windows, incompatibility constraints, among other features. Together, these characteristics pose considerable challenges for exact and heuristic methods, and some cases with as few as 18 cargoes remain unsolved. We propose an exact branch-and-price (B&P) algorithm and a hybrid metaheuristic. Our exact method generates elementary routes, but exploits decremental state-space relaxation to speed up column generation, heuristic strong branching, as well as advanced preprocessing and route enumeration techniques. Our metaheuristic is a sophisticated extension of the unified hybrid genetic search. It exploits a set-partitioning phase and uses problem-tailored variation operators to efficiently handle all the problem characteristics. As shown in our experimental analyses, the B&P optimally solves 239/240 instances within one hour, with up to 50 ships, 130 cargoes and therefore 260 pickups and deliveries. The hybrid metaheuristic outperforms all previous heuristics and produces near-optimal solutions within minutes. These results are noteworthy, since the largest instances of this set are comparable in size with the largest problems routinely solved by shipping companies.
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