A Priori Optimization
نویسندگان
چکیده
Consider a complete graph G = (V,E), in which each node is present with probability pi. We are interested in solving combinatorial optimization problems on subsets of nodes present with a certain probability. We introduce the idea of a priori optimization as a strategy competitive to the strategy of re-optimization, under which the combinatorial optimization problem is solved optimally for every one of its instances. We consider four problems: the traveling salesman problem (TSP), the minimum spanning tree problem, the vehicle routing problem and the traveling salesman facility location problem. We discuss the applicability of a priori optimization strategies in several areas and show that if the nodes are randomly distributed in the plane the a priori and re-optimization strategies are very close in terms of performance. We characterize the complexity of a priori optimization and address the question of approximating the optimal a priori solutions with polynomial time heuristics with provable worst-case guarantees. Finally, we use the TSP as an example of finding practical solutions based on ideas of local optimality. AMS(MOS) Subject Classification. 05C45, 90C27, 60C05, 05-04
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ورودعنوان ژورنال:
- Operations Research
دوره 38 شماره
صفحات -
تاریخ انتشار 1990