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$$k$$-balanced center location problem: a new multi-objective facility location problem. (English) Zbl 1458.90426
Summary: Balancing workload among a set of facility centers is one of the practical objectives in location problems. In this paper, we introduce a multi-objective optimization facility location problem which considers two goals: minimizing the maximum distance between each client and its closest center, and maximizing workload balance among the centers. To achieve the second goal, we define two objectives, minimizing the maximum number of clients allocated to each center, and minimizing the difference between the maximum and minimum number of clients allocated to each center. We prove the hardness of finding even one Pareto optimal solution in the resulted multi-objective problem. Also, we propose a simple iterative algorithm based on the Voronoi diagram to solve the problem. We show the efficiency of the proposed algorithm using test problems and compare the results with a robust multi-objective evolutionary algorithm.
##### MSC:
 90B80 Discrete location and assignment 90C29 Multi-objective and goal programming 90C59 Approximation methods and heuristics in mathematical programming 68Q25 Analysis of algorithms and problem complexity