A New Method for Optimizing a Function Over the Efficient Set

In this paper, we present a new deterministic method to optimize a linear function over the efficient set of a multiple objective integer linear problem, it is called the 2-phase algorithm. This algorithm is based on two phases : the first uses the student copula to determine the pilot objective and the second optimises it to obtain the optimal solution. To check the algorithm’s performance, we compare it with two benchmark algorithms from the literature. A detailed didactic example is given to illustrate the different steps. The algorithm is implemented on Machine and interesting results are obtained and discussed.