THE SHUFFLE FROG LEAPING ALGORITHM FOR THE PRODUCTION LOCATION PROBLEM

Abstract

The production location problem is one of the most well-known discrete optimization problems. There are many options for setting this task. As a rule, all these variants of the problem of location of production belong to the class of NP-hard problems, that is, for its exact solution of such a problem, algorithms of polynomial complexity are currently unknown. So far, no effective methods have been developed for calculating the lower bounds for this problem, which make it possible to assess the achievement of the optimum. Exact algorithms for this problem are reduced to a complete enumeration of options. In this regard, the use of exact algorithms for solving the problem of production location often turns out to be inappropriate and impossible due to the large time costs. Therefore, the development and study of heuristic optimization methods is of considerable interest. One of the promising areas is the development of algorithms based on well-known metaheuristic approaches that are successfully used to solve many discrete optimization problems. In this paper, we show that one of the classes of production location problems is reduced to the problem of covering a complete graph with vertex-disjoint stars. It is proved that in this formulation the problem can be considered as an optimization problem on an oriented fragmentary structure. This allows you to create hybrid algorithms for finding suboptimal solutions to problems of this class based on a combination of well-known metaheuristics and a fragmentary algorithm. The mixed jumping frogs algorithm was chosen as a metaheuristic. It is shown that this algorithm can be used to find suboptimal solutions on a set of permutations. On the other hand, in the presence of an oriented fragmentary structure, the discrete optimization problem can be reduced to an optimization problem on a set of permutations. Thus, a simple and rather effective method for finding suboptimal solutions to the production location problem has been obtained. The method can be easily transferred to other classes of discrete optimization problems, which can be considered as problems on an oriented fragmentary structure.