Choquet integral for criteria aggregation in the flexible job-shop scheduling problems

Most complex scheduling problems are combinatorial problems and difficult to solve. That is why, several methods focus on the optimization according to a single criterion such as makespan, workloads of machines, waiting times, etc. In this paper, the Choquet integral is introduced as a general tool for dealing with multiple criteria decision making and used in optimization flexible job-shop scheduling problems. The considered optimization problem is based of the Genetic Algorithm (GA) used as objective function the Choquet integral for criteria aggregation. Then lower bounds are defined for each criterion. Presented examples illustrate theoretical considerations and show the efficiency of the proposed approach.