Multi-objective Flow-shop Problem Research Articles

A Multi Objective Evolutionary Algorithm based on Decomposition for a Flow Shop Scheduling Problem in the Context of Industry 4.0

Under the novel paradigm of Industry 4.0, missing operations have arisen as a result of the increasingly customization of the industrial products in which customers have an extended control over the characteristics of the final products. As a result, this has completely modified the scheduling and planning management of jobs in modern factories. As a contribution in this area, this article presents a multi objective evolutionary approach based on decomposition for efficiently addressing the multi objective flow shop problem with missing operations, a relevant problem in modern industry. Tests performed over a representative set of instances show the competitiveness of the proposed approach when compared with other baseline metaheuristics.

An Effective Heuristic Method to Minimize Makespan and Flow Time in a Flow Shop Problem

In this paper, it is presented a heuristic method for solving the multi-objective flow shop problem. The work carried out considers the simultaneous optimization of the makespan and the flow time; both objectives are essential in measuring the production system's performance since they aim to reduce the completion time of jobs, increase the efficiency of resources, and reduce waiting time in queue. The proposed method is an adaptation of multi-objective Newton's method, which is applied to problems with functions of continuous variables. In this adaptation, the method seeks to improve a sequence of jobs through local searches recursively. The computational experiments show the potential of the proposed method to solve medium-sized and large instances compared with other existing literature methods.

Modelling and scheduling multi-objective flow shop problems with interfering jobs

This paper studies multi-objective flow shop scheduling problems with interfering jobs. That is, there are two sets of jobs and each of which has its own objective. Some jobs are scheduled so as to minimize makespan while the others are to minimize total tardiness. In this case, the problem was mathematically modeled by a mixed integer linear program. Then, a novel biogeography-based optimization was developed to solve the problem. To evaluate the algorithm, its performance was compared with three well-known algorithms in the literature. The results of the present study show that the proposed algorithm outperforms the other tested algorithms.

A hybrid differential evolution for general multi-objective flow shop problem with a modified learning effect

In this article, a modification of multi-objective differential evolution based on simulated annealing is proposed to solve a general tri-objective non-permutation flow shop problem. The flow shop system considers the release dates, machine breakdowns, past-sequence-dependent setup times and learning effect for all the jobs. The algorithm proposed to tackle such a model combines the robustness of differential evolution with the rapid convergence and conditional diversification of simulated annealing. For small and medium low-sized problems, the solutions found by the proposed algorithm are compared with the exact solutions, achieved by augmented ε-constraint method. Due to the high complexity of the model, for medium high and large-sized problems, the algorithm is tested against the imperialist competitive algorithm and the multi-objective differential evolution scheduling. Comparisons of the results show a good balance between intensification and diversification in the proposed algorithm.

Augmented ε-constraint method in multi-objective flowshop problem with past sequence set-up times and a modified learning effect

This article addresses a general tri-objective non-permutation flowshop problem to minimise the makespan, the sum of flow time and maximum tardiness simultaneously. In order to enhance the applicability of the model, some practical assumptions are included. These are release dates, past sequence-dependent set-up times, a truncated generalisation of Dejong’s learning effect and predetermined machine availability constraints. First, the problem is formulated as a mixed-integer linear programming model. Second, the true Pareto front is achieved with augmented ε-constraint method for small-sized problems. Third, due to the high complexity of the model and the impractical computational times of larger instances, a heuristic algorithm based on the ε-constraint method is also proposed. Finally, the algorithms are tested to gauge their effectiveness, and the results are compared with other methods.

Refined ranking relations for selection of solutions in multi objective metaheuristics

Abstract Two methods for ranking of solutions of multi objective optimization problems are proposed in this paper. The methods can be used, e.g. by metaheuristics to select good solutions from a set of non dominated solutions. They are suitable for population based metaheuristics to limit the size of the population. It is shown theoretically that the ranking methods possess some interesting properties for such applications. In particular, it is shown that both methods form a total preorder and are both refinements of the Pareto dominance relation. An experimental investigation for a multi objective flow shop problem shows that the use of the new ranking methods in a Population-based Ant Colony Optimization algorithm and in a genetic algorithm leads to good results when compared to other methods.

Hypervolume-based multi-objective local search

This paper presents a multi-objective local search, where the selection is realized according to the hypervolume contribution of solutions. The HBMOLS algorithm proposed is inspired from the IBEA algorithm, an indicator-based multi-objective evolutionary algorithm proposed by Zitzler and Kunzli in 2004, where the opti- mization goal is defined in terms of a binary indicator defining the selection operator. In this paper, we use the indicator optimization principle, and we apply it to an iterated local search algorithm, using hypervolume contri- bution indicator as selection mechanism. The methodology proposed here has been defined in order to be easily adaptable and to be as parameter-independent as possible. We carry out a range of experiments on the multi-objective flow shop problem and the multi-objective quadratic assignment problem, using the hypervolume contribution selection as well as two different binary indicators which were initially proposed in the IBEA algorithm. Experi- mental results indicate that the HBMOLS algorithm is highly effective in comparison with the algorithms based on binary indicators.

K-PPM: A new exact method to solve multi-objective combinatorial optimization problems

In this paper we propose an exact method able to solve multi-objective combinatorial optimization problems. This method is an extension, for any number of objectives, of the 2-Parallel Partitioning Method (2-PPM) we previously proposed. Like 2-PPM, this method is based on splitting of the search space into several areas, leading to elementary searches. The efficiency of the proposed method is evaluated using a multi-objective flow-shop problem.

A Review and Evaluation of Multiobjective Algorithms for the Flowshop Scheduling Problem

This paper contains a complete and updated review of the literature for multiobjective flowshop problems, which are among the most studied environments in the scheduling research area. No previous comprehensive reviews exist in the literature. Papers about lexicographical, goal programming, objective weighting, and Pareto approaches have been reviewed. Exact, heuristic, and metaheuristic methods have been surveyed. Furthermore, a complete computational evaluation is also carried out. A total of 23 different algorithms including both flowshop-specific methods as well as general multiobjective optimization approaches have been tested under three different two-criteria combinations with a comprehensive benchmark. All methods have been studied under recent state-of-the-art quality measures. Parametric and nonparametric statistical testing is profusely employed to support the observed performance of the compared methods. As a result, we have identified the best-performing methods from the literature, which along with the review, constitutes a reference work for further research.

A comparison of neighborhood search techniques for multi-objective combinatorial problems

In this paper we compare the performance of simulated annealing and tabu search when both are applied to a large, complex multi-objective flow-shop problem. Repeated descent, an older neighborhood search technique, is used as a basis for comparison. The best parameters needed for the methods and their subsequent performance are compared on two further levels: as the total number of perturbations allowed increases and as the number of objectives increases. It is shown that, as the number of objectives (and thus the complexity of the problem) increases, simulated annealing (which epitomizes randomized search methods) becomes more attractive than tabu search (which epitomizes deterministic search methods). In addition, the relative value of simulated annealing is greater when only a small number of perturbations are allowed. Reasons are offered for these phenomena. These experiments identify the need for appropriate measures of complexity of a combinatorial problem. Two such measures are described, and it is shown that these can lead us to revise our a priori notions about the complexity of multi-objective combinatorial problems. In particular, the complexity of a combinatorial problem may be strongly influenced by the type of objectives as well as their number.