Taicir Loukil

Solving multi-objective production scheduling problems using metaheuristics

Abstract Most of research in production scheduling is concerned with the optimization of a single criterion. However the analysis of the performance of a schedule often involves more than one aspect and therefore requires a multi-objective treatment. In this paper we first present ( Section 1 ) the general context of multi-objective production scheduling, analyze briefly the different possible approaches and define the aim of this study i.e. to design a general method able to approximate the set of all the efficient schedules for a large set of scheduling models. Then we introduce ( Section 2 ) the models we want to treat––one machine, parallel machines and permutation flow shops––and the corresponding notations. The method used––called multi-objective simulated annealing––is described in Section 3 . Section 4 is devoted to extensive numerical experiments and their analysis. Conclusions and further directions of research are discussed in the last section.

Differential evolution for solving multi-mode resource-constrained project scheduling problems

In this paper we consider the resource-constrained project scheduling problem with multiple execution modes for each activity and minimization of the makespan. To solve this problem, we propose a differential evolution (DE) algorithm. We focus on the performance of this algorithm to solve the problem within small time per activity. Finally, we present the results of our thorough computational study. Results obtained on six classes of test problems and comparison with other algorithms from the literature show that our algorithm gives better solutions.

A multi-objective production scheduling case study solved by simulated annealing

Abstract During several decades, research in production scheduling mainly concerns a single criterion to optimize. However, the analysis of the performance of a schedule often involves more than one aspect and therefore requires multi-objective analysis. Such situation appears in the real case study considered here. This paper deals with a production scheduling problem in a flexible (or hybrid) job-shop with particular constraints: batch production; existence of two steps: production of several sub-products followed by the assembly of the final product; possible overlaps for the processing periods of two successive operations of a same job. At the end of the production step, different objectives should be considered simultaneously, among the makespan, the mean completion time, the maximal tardiness, the mean tardiness. The research is based on a real case study, concerning a Tunisian firm. We propose a multi-objective simulated annealing approach to tackle this problem and to propose to the manager an approximation of the set of efficient schedules. Several numerical results are reported.

The Pareto fitness genetic algorithm: Test function study

Evolutionary algorithms have shown some success in solving multiobjective optimization problems. The methods of fitness assignment are mainly based on the information about the dominance relation between individuals. We propose a Pareto fitness genetic algorithm (PFGA) in which we introduce a modified ranking procedure and a promising way of sharing; a new fitness function based on the rank of the individual and its density value is designed. This is considered as our main contribution. The performance of our algorithm is evaluated on six multiobjective benchmarks with different Pareto front features. Computational results (quality of the approximation of the Pareto optimal set and the number of fitness function evaluations) proving its efficiency are reported.

A genetic algorithm for robust hybrid flow shop scheduling

Most of scheduling methods consider a deterministic environment for which the data of the problem are known. Nevertheless, in reality, several kinds of uncertainties should be considered, and robust scheduling allows uncertainty to be taken into account. In this article, we consider a scheduling problem under uncertainty. Our case study is a hybrid flow shop scheduling problem, and the processing time of each job for each machine at each stage is the source of uncertainty. To solve this problem, we developed a genetic algorithm. A robust bi-objective evaluation function was defined to obtain a robust, effective solution that is only slightly sensitive to data uncertainty. This bi-objective function minimises simultaneously the makespan of the initial scenario, and the deviation between the makespan of all the disrupted scenarios and the makespan of the initial scenario. We validated our approach with a simulation in order to evaluate the quality of the robustness faced with uncertainty. The computational results show that our algorithm can generate a trade off for effectiveness and robustness for various degrees of uncertainty.

Multiple crossover genetic algorithm for the multiobjective traveling salesman problem

Abstract Many crossover operators have been proposed and adapted to different combinatorial optimization problems. In particular, many permutation based crossovers are well designed for the traveling salesman problem (TSP) which is among the most-studied combinatorial optimization problems. However, there is no evidence that one crossover operator is superior to another operator. This is specially true for multiobjective optimization. The performance of any genetic algorithm generally varies accordingto the crossover and mutation operators used. We propose to include mutiple crossover and mutation operators with a dynamic selection scheme into a multiobjective genetic algorithm in order to choose the best crossover operator to be used at any given time. The objective is to find a good approximation of the Pareto set. Experimental results on different benchmark data show synergy effects amongdifferen t used crossovers and prove the efficiency of the proposed approach.

Solving multi-criteria scheduling flow shop problem through compromise programming and satisfaction functions

The multi-criteria scheduling problem is one of the main research subjects in the field of multiple objectives programming. Several procedures have been developed to deal with this type of problem where some conflicting criteria have to be optimized simultaneously. The aim of our paper is to propose an aggregation procedure that integrates three different criteria to find the best sequence in a flow shop production environment. The compromise programming model and the concept of satisfaction functions will be utilized to integrate explicitly the managers preferences according to the deviations between the achievement and the aspiration levels of the following criteria: Makespan, total flow time and total tardiness.

Scheduling hybrid flow shop problem with non-fixed availability constraints

In this study, we deal with a k-stage hybrid flow shop scheduling problem under availability constraints (HFSPAC). In such a problem, machines are not continuously available due to preventive maintenance tasks. Our study aims to provide a good approximate solution to this specific problem with the makespan minimisation as the performance measure. Few studies exist in the literature dealing with the HFSPAC. We consider in this paper two variants to tackle this problem. In the first, the starting times of maintenance tasks are fixed, whereas in the second variant, maintenance must be performed on given time windows. In this last case, a theoretical analysis is elaborated based on the machine idle time to decide which action to perform between left-shifting or right-shifting the maintenance task in the window. Due to the NP-hardness of the HFSPAC, an approximate approach, based on a genetic algorithm (GA), is proposed to minimise the makespan. Computational experiments are performed on randomly generated instances to show the efficiency of the proposed variant (flexibility of the starting times of the maintenance tasks) in terms of makespan minimisation. Moreover, a correlation function computation is proposed to statistically analyse these experiments. [Received 7 November 2008; Revised 30 May 2009; Accepted 6 December 2009]

Lexicographic optimization of a permutation flow shop scheduling problem with time lag constraints

This paper considers the permutation flow shop scheduling problem with minimal and maximal time lags. Time lags are defined as intervals of time that must exist between every pair of consecutive operations of a job. The objective is to hierarchically minimize two criteria, the primary criterion is the minimization of the number of tardy jobs and the secondary one minimizes the makespan. We propose a mixed integer mathematical programming formulation which can be solved with the subroutine CPLEX. We also propose several versions of simulated annealing algorithm to heuristically solve the problem. Computational experiments to compare the proposed procedures are presented and discussed.

Minimizing the Number of Tardy Jobs in a Permutation Flowshop Scheduling Problem with Setup Times and Time Lags Constraints

This paper studies the permutation flowshop scheduling problem with sequence dependent setup times and time lags constraints minimizing the number of tardy jobs. Dependent setup times are defined as the work to prepare the machines between two successive jobs. Time lags are defined as intervals of time that must exist between every couple of successive operations of the same job. Two mathematical programming formulations are proposed for the considered problem. A simulated annealing algorithm is also developed to solve the problem. Computational experiments are presented and discussed.