Multi-objective Permutation Flow-shop Scheduling Problem Research Articles

A Multiobjective Optimization of PCB Prototyping Assembly With OFA Based on the Similarity of Intuitionistic Fuzzy Sets

Shop scheduling is a significant factor affecting the ability of manufacturers of printed circuit board (PCB) prototyping assemblies to remain profitable and meet the needs of customers. This scheduling is complicated and involves various factors; thus, the shop scheduling problem of a PCB prototyping assembly is regarded as a multiobjective permutation flow shop scheduling problem (MOPFSP). A mathematical model with four objective functions is built based on the characteristics of a PCB prototyping assembly shop. In this article an aggregation-based approach is designed to aggregate multiple objective function values into the similarity of intuitionistic fuzzy sets (sIFSs). This approach is adopted as a fitness function assignment strategy and is combined with the optimal foraging algorithm (OFA) to build a multiobjective evolutionary algorithm: the OFA based on sIFSs (OFA-sIFSs). To verify the performance of OFA-sIFSs, six congress on evolutionary computation benchmark test functions, ten MOPFSP benchmark instances and a practical problem for a PCB prototyping assembly are solved by OFA-sIFSs and three state-of-the-art algorithms. Three types of similarity measures are evaluated. During the process of testing, four performance metrics, statistical analysis, and business software are employed. The results of this study suggest that OFA-sIFSs can be used to solve the MOPFSP and have better performances compared with the other three algorithms.

Multiobjective decomposition-based Mallows Models estimation of distribution algorithm. A case of study for permutation flowshop scheduling problem

Estimation of distribution algorithms (EDAs) have become a reliable alternative to solve a broad range of single and multi-objective optimization problems. Recently, distance-based exponential models, such as Mallows Model (MM) and Generalized Mallows Model (GMM), have demonstrated their validity in the context of EDAs to deal with permutation-based optimization problems. The aim of this paper is two-fold. First, we introduce a novel general multi-objective decomposition-based EDA using Kernels of Mallows models (MEDA/D-MK framework) for solving multi-objective permutation-based optimization problems. Second, in order to demonstrate the validity of the MEDA/D-MK, we have applied it to solve the multi-objective permutation flowshop scheduling problem (MoPFSP) minimizing the total flow time and the makespan. The permutation flowshop scheduling problem is one of the most studied problems of this kind due to its fields of application and algorithmic challenge. The results of our experiments show that MEDA/D-MK outperforms an improved MOEA/D variant specific tailored for minimizing makespan and total flowtime. Furthermore, our approach achieves competitive results compared to the best-known approximated Pareto fronts reported in the literature for the benchmark considered.

A discrete differential evolution algorithm for multi-objective permutation flowshop scheduling

The more practical and interesting versions of the permutation flowshop scheduling problem (PFSP) have a variety of objective criteria to be optimized simultaneously. Multi-objective PFSP is also a relevant combinatorial multi-objective optimization problem. In this paper we propose a multi-objecti ve evolutionary algorithm for PFSP by extending the previously proposed discrete differential evolution (DE) scheme for single-objective PFSP. This is the first application of the algebraic-based discrete DE to multi-objective problems. The algorithm is extended by adopting a variety of crossover and multi-objective selection operators. Among these, the multi-objective α-selection is a novelty of this work and can be decoupled from DE and used also in other evolutionary algorithms. The other crossover and selection operators have been taken from the existing literature and, where required, have been adapted to the problem at hand. An experimental evaluation has been conducted on all the three bi-objective PFSPs among the makespan, total flowtime and total tardiness criteria. The results show that the proposed approach is competitive with respect to the state-of-the-art algorithms.

Multi-Objective Memetic Search Algorithm for Multi-Objective Permutation Flow Shop Scheduling Problem

The multiobjective permutation flowshop scheduling problem (MOPFSSP) is one of the most popular machine scheduling problems with extensive engineering relevance of manufacturing systems. There have been many attempts at solving MOPFSSP using heuristic and meta-heuristic methods, such as evolutionary algorithm. In this paper, a novel multiobjective memetic search algorithm (MMSA), is proposed to solve the MOPFSSP with makespan and total flowtime. First, a problem-specific Nawaz–Enscore–Hoam heuristic is used to initialize the population to enhance the quality of the initial solution. Second, a global search embedded with a perturbation operation is used to improve the solution of the entire population. Then, a single insert-based local search is used to improve each individual and then a further local search strategy is used to find the better solution for the non-improved individual in the single insert-based local search. The performance of our proposed algorithm is validated and compared with the four state-of-the-art algorithms on a number of benchmark problem. The experimental results show that the proposed MMSA provides better solutions than several state-of-the-art algorithms.

An effective hybrid DE-based algorithm for multi-objective flow shop scheduling with limited buffers

This paper proposes an effective hybrid algorithm based on differential evolution (DE), namely HDE, to solve multi-objective permutation flow shop scheduling problem (MPFSSP) with limited buffers between consecutive machines, which is a typical NP-hard combinatorial optimization problem with strong engineering background. Firstly, to make DE suitable for solving scheduling problems, a largest-order-value (LOV) rule is presented to convert the continuous values of individuals in DE to job permutations. Secondly, after the DE-based exploration, an efficient local search, which is designed based on the landscape of MPFSSP with limited buffers, is applied to emphasize exploitation. Thus, not only does the HDE apply the parallel evolution mechanism of DE to perform effective exploration (global search) in the whole solution space, but it also adopts problem-dependent local search to perform thorough exploitation (local search) in the promising sub-regions. In addition, the concept of Pareto dominance is used to handle the updating of solutions in sense of multi-objective optimization. Moreover, the convergence property of HDE is analyzed by using the theory of finite Markov chain. Finally, simulations and comparisons based on benchmarks demonstrate the effectiveness and efficiency of the proposed HDE.