Population based-heuristic for solving the assignment problems with two objectives

The paper presents a population-based heuristic for computing approximations of the efficient solution set for the assignment problem with two objectives. The heuristic is based on the intensive use of three operators-a local search, a crossover and a path-relinking-performed on a population composed only of elite solutions. The initial population is a subset of supported solutions, where each solution is one optimal assignment for an appropriate weighted sum of two objectives. Genetic information is derived from the elite solutions, providing a useful genetic heritage to be exploited by crossover operators. An upper bound set, defined in the objective space, provides one acceptable limit for performing a local search. Results of extensive numerical experiments have shown that the heuristic is able to quickly find a very good approximation of the efficient frontier, and outperforms all previously published results. In addition, this heuristic has two main advantages. It is based on simple easy-to-implement principles, and it does not need a parameter tuning phase.