Multi-objective optimization of population partitioning problem under interval uncertainty

Abstract

This paper addresses a bi-objective mixed integer optimization model under uncertainty for population partitioning problem. The objective functions are to minimize the number of communications between partitions and to balance their population. The main constraints are defined for creating contiguous and compact partitions as well as assigning uniquely each basic unit to one partition. To deal with the uncertainty of parameters, a robust programming method is proposed that causes the uncertainty parameters lie between the interval of best-case (the deterministic mode) and worst-case (the highest uncertainty level for all parameters). As the suggested method is NP-Hard, three meta-heuristic algorithms NSGAII, PESA, and SPEA are developed and, to evaluate the efficiency of the algorithms, 10 small-size examples, 10 medium-size examples and, 10 large-size examples are generated and solved. According to computational results, the SPEA has the best performance. The method is examined for a real-world application, as a case study in Iran.