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Stacker Crane Problem
In combinatorial optimization, the stacker crane problem is an optimization problem closely related to the traveling salesperson problem. Its input consists of a collection of ordered pairs of points in a metric space, and the goal is to connect these points into a cycle of minimum total length that includes all of the pairs, oriented consistently with each other. It models problems of scheduling the pickup and delivery of individual loads of cargo, by a stacker crane, construction crane or (in drayage) a truck, in a simplified form without constraints on the timing of these deliveries. It was introduced by , with an equivalent formulation in terms of mixed graphs with directed edges modeling the input pairs and undirected edges modeling their distances. Frederickson et al. credit its formulation to a personal communication of Daniel J. Rosenkrantz. The stacker crane problem can be viewed as a generalization of the traveling salesperson problem in metric spaces: any instance of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Optimization
Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set. Typical combinatorial optimization problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsack problem. In many such problems, such as the ones previously mentioned, exhaustive search is not tractable, and so specialized algorithms that quickly rule out large parts of the search space or approximation algorithms must be resorted to instead. Combinatorial optimization is related to operations research, algorithm theory, and computational complexity theory. It has important applications in several fields, including artificial intelligence, machine learning, auction theory, software engineering, VLSI, applied mathematics and theoretical computer science. Applications Basic applications of combina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Traveling Salesperson Problem
In the Computational complexity theory, theory of computational complexity, the travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hardness, NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research. The Traveling purchaser problem, travelling purchaser problem, the vehicle routing problem and the ring star problem are three generalizations of TSP. The decision version of the TSP (where given a length ''L'', the task is to decide whether the graph has a tour whose length is at most ''L'') belongs to the class of NP-completeness, NP-complete problems. Thus, it is possible that the Best, worst and average case, worst-case Time complexity, running time for any algorithm for the TSP increases Time complexity#Superpolynomial time, su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
