انتگرال Choquet برای تجمیع شاخص در مشکلات برنامه ریزی تولید کارگاهی انعطاف پذیر

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.

The flexible job-shop scheduling problem (FJSP) is known in the literature as one of the hardest optimization problems [2]. In lot of cases, the combination of goals and resources has an exponentially increasing search space. Approached methods are then preferred to exact methods and have given good solutions near the optimal one. The scheduling problem of a FJSP consists of a routing sub-problem, that is, assigning each operation to a machine out of a set of capable machines and the scheduling sub-problem, which consists of sequencing the assigned operations on all machines in order to obtain a feasible schedule minimizing a predefined objective function. The FJSP mainly presents two difficulties. The first one is to assign each operation to a machine, and the second one is to schedule these operations in order to make a predefined objective minimal. In this paper, an aggregative approach is proposed for solving multi-objective optimization FJSP based on the evolutionary algorithms. This approach makes it possible to construct a set of satisfactory solutions according to the preferences of the decision-maker. The considered objective is to minimize makespan, the workload of the critical machine, the total workload of machines, the penalties of earliness/tardiness, and the production cost. Thus, in Sections 2 and 3, the ordered weighted averaging (OWA) operators and the Choquet Integral aggregative methods are defined and the proposed approach is described. The discussion about the use of the OWA operators is presented in Section 4. In Section 5, a multi-objective optimization by the genetic algorithm for solving FJSP is proposed. The two last sections are devoted to the formulation of some problems and to corresponding results.

In this paper, a new approach based on the hybridation with the Choquet integral for solving multi-objective flexible job-shop scheduling problems, is presented. Besides, approach uses Choquet integral to estimate and to classify obtained decisions. It is compared with OWA operators, knowing that this approach did not guarantee the optimality, such an approach provides solutions with good quality in a reasonable time limit. The performances of the new approach are evaluated and compared with the results obtained with the use of other methods and show the effectiveness of this approach. However, the job-shop problems are dealt with in the literature, but the FJSP remains not considered. Therefore, there is still a need to develop an effective approach for this complex problem. The proposed hybrid approach in this paper can be considered as effective mechanisms from this point of view.