Multi-objective Permutation Flow Shop Scheduling Research Articles

Multi-Objective Optimization Flow Shop Scheduling Problem Solving the Makespan and Total Flow Time with Sequence Independent Setup Time

In this paper, a multi-objective permutation flow shop scheduling problem with sequence independent setup time is studied. The bi-objective function that we consider is a linear combination of the makespan and total flow time with a weighted factor for each criterion. We propose a set of exact and approximate methods to minimize the makespan and total flow time in our flow shop optimization problem case. Hence, our main goal is to find the sequence of jobs that minimizes the two criteria of makespan and total flow time. The purpose is to solve this problem, with a mixed integer linear programming model (MILP) and a collection of efficient metaheuristics for different sizes of instances. Moreover, three metaheuristics are used: the Genetic Algorithm (GA), the Iterative Local Search (ILS) algorithm and the Iterated Greedy (IG) algorithm. The three last algorithms GA, ILS and IG are suggested in two ways for exploring the neighborhood. In order to test the efficacy of our resolution approach, different series of instances containing n jobs and m machines are generated randomly ranging from small to relatively large instances. The examination of the suggested simulations allowed us to remark that, for large and medium-scale instances, IG based on the exploration of the neighborhood records the best performances in terms of comparison with the other metaheuristics.

An energy-efficient multi-objective permutation flow shop scheduling problem using an improved hybrid cuckoo search algorithm

The flow shop scheduling problem has been widely studied in recent years, but the research on multi-objective flow shop scheduling with green indicators is still relatively limited. It is urgent to strengthen the research on effective methods to solve such interesting problems. To consider the economic and environmental factors simultaneously, the paper investigates the multi-objective permutation flow shop scheduling problems (MOPFSP) which minimizes the makespan and total carbon emissions. Since MOPFSP is proved to be a NP-hard problem for more than two machines. A hybrid cuckoo search algorithm (HCSA) is proposed to solve the problems. Firstly, a largest-order-value method is proposed to enhance the performance of HCS algorithm in the solution space of MOPFSP. Then, an adaptive factor of step size is designed to control the search scopes in the evolution phases. Finally, a multi-neighborhood local search rule is addressed in order to find the optimal sub-regions obtained by the HCSA. Numerical experiments show that HCSA can solve MOPFSP efficiently.

Using Non-dominated Sorting Particle Swarm Optimization Algorithm II for Bi-objective Flow Shop Scheduling Problems

A hybrid particulate swarm optimization (hybrid) combination of an optimization algorithm of the particle swarm and a variable neighborhood search algorithm is proposed for the multi-objective permutation flow shop scheduling problem (PFSP) with the smallest cumulative completion time and the smallest total flow time. Algorithm for hybrid particulate swarm optimization (HPSO) is applied to maintain a fair combination of centralized search with decentralized search. The Nawaz-Enscore-Ham )NEH) heuristic algorithm in this hybrid algorithm is used to initialize populations in order to improve the efficiency of the initial solution. The method design is based on ascending order (ranked-order-value, ROV), applying the continuous PSO algorithm to the PFSP, introducing the external archive set storage Pareto solution, and using a hybrid strategy that combines strong dominance and aggregation distance to ensure the distribution of the solution set. We adopted the Sigma method and the roulette method, based on the aggregation distance, to select the global optimal solution. A variable neighborhood search algorithm was proposed to further search the Pareto solution in the external set. The suggested hybrid algorithm was used to solve the Taillard test set and equate the test results with the SPEA2 algorithm to check the scheduling algorithm’s efficacy.

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.

A novel fuzzy model for multi-objective permutation flow shop scheduling problem with fuzzy processing time

This article proposes a novel fuzzy model for solving fuzzy multi-objective permutation flow shop scheduling problem with fuzzy processing time. Specifically, two fuzzy objectives, that is, the fuz...

Multiobjective Discrete Artificial Bee Colony Algorithm for Multiobjective Permutation Flow Shop Scheduling Problem With Sequence Dependent Setup Times

The multiobjective permutation flow shop scheduling problem with sequence dependent setup times has been an object of investigations for decades. This widely studied problem from the scheduling theory links the sophisticated solution algorithms with the moderate real world applications. This paper presents a novel multiobjective discrete artificial bee colony algorithm based decomposition, called MODABC/D , to solve the sequence dependent setup times multiobjective permutation flowshop scheduling problem with the objective to minimize makespan and total flowtime. First, in order to make the standard artificial bee colony algorithm to solve the scheduling problem, a discrete artificial bee colony algorithm is proposed to solve the problem based on the perturbation operation. Then, a problem-specific solution builder heuristic is used to initialize the population to enhance the quality of the initial solution. Finally, a further local search method are comprised of a single local search procedures based on the insertion neighborhood structures to find the better solution for the nonimproved individual. The performance of the proposed algorithms is tested on the well-known benchmark suite of Taillard. The highly effective performance of the multiobjective discrete artificial bee colony algorithm-based decomposition is compared against the state of art algorithms from the existing literature in terms of both coverage value and hypervolume indicator.

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.

A Pareto block-based estimation and distribution algorithm for multi-objective permutation flow shop scheduling problem

Multi-objective flow shop scheduling plays a key role in real-life scheduling problem which attract the researcher attention. The primary concern is to find the best sequence for flow shop scheduling problem. Estimation of Distribution Algorithms (EDAs) has gained sufficient attention from the researchers and it provides prominent results as an alternate of traditional evolutionary algorithms. In this paper, we propose the pareto optimal block-based EDA using bivariate model for multi-objective flow shop scheduling problem. We apply a bivariate probabilistic model to generate block which have the better diversity. We employ the non-dominated sorting technique to filter the solutions. To check the performance of proposed approach, we test it on the benchmark problems available in OR-library and then we compare it with non-dominated sorting genetic algorithm-II (NSGA-II). Computational results show that pareto optimal BBEDA provides better result and better convergence than NSGA-II.

NNMA: An effective memetic algorithm for solving multiobjective permutation flow shop scheduling problems

The permutation flow shop scheduling problem is addressed in this paper. Two objectives, minimization of makespan and total flow time, are considered. We propose a memetic algorithm, called NNMA, by integrating a general multiobjective evolutionary algorithm (NSGA-II) with a problem-specific heuristic (NEH). We take NEH as a local improving procedure in NNMA and propose several adaptations including the acceptance criterion and job-insertion ordering to deal with multiple objectives and to improve its performance. We test the performance of NNMA using 90 public problem instances with different problem scales, and compare its performance with 23 algorithms. The experimental results show that our NNMA provides close performance for 30 small-scale instances and better performance for 50 medium- and large-scale instances. Furthermore, more than 70% of the net set of non-dominated solutions is updated by NNMA for these 50 instances.

A novel differential evolution algorithm for bi-criteria no-wait flow shop scheduling problems

This paper presents a novel discrete differential evolution (DDE) algorithm for solving the no-wait flow shop scheduling problems with makespan and maximum tardiness criteria. First, the individuals in the DDE algorithm are represented as discrete job permutations, and new mutation and crossover operators are developed based on this representation. Second, an elaborate one-to-one selection operator is designed by taking into account the domination status of a trial individual with its counterpart target individual as well as an archive set of the non-dominated solutions found so far. Third, a simple but effective local search algorithm is developed to incorporate into the DDE algorithm to stress the balance between global exploration and local exploitation. In addition, to improve the efficiency of the scheduling algorithm, several speed-up methods are devised to evaluate a job permutation and its whole insert neighborhood as well as to decide the domination status of a solution with the archive set. Computational simulation results based on the well-known benchmarks and statistical performance comparisons are provided. It is shown that the proposed DDE algorithm is superior to a recently published hybrid differential evolution (HDE) algorithm [Qian B, Wang L, Huang DX, Wang WL, Wang X. An effective hybrid DE-based algorithm for multi-objective flow shop scheduling with limited buffers. Computers & Operations Research 2009;36(1):209–33] and the well-known multi-objective genetic local search algorithm (IMMOGLS2) [Ishibuchi H, Yoshida I, Murata T. Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling. IEEE Transactions on Evolutionary Computation 2003;7(2):204–23] in terms of searching quality, diversity level, robustness and efficiency. Moreover, the effectiveness of incorporating the local search into the DDE algorithm is also investigated.

An Effective PSO-Based Hybrid Algorithm for Multiobjective Permutation Flow Shop Scheduling

This paper proposes a hybrid algorithm based on particle swarm optimization (PSO) for a multiobjective permutation flow shop scheduling problem, which is a typical NP-hard combinatorial optimization problem with strong engineering backgrounds. Not only does the proposed multiobjective algorithm (named MOPSO) apply the parallel evolution mechanism of PSO characterized by individual improvement, population cooperation, and competition to effectively perform exploration but it also utilizes several adaptive local search methods to perform exploitation. First, to make PSO suitable for solving scheduling problems, a ranked-order value (ROV) rule based on a random key technique to convert the continuous position values of particles to job permutations is presented. Second, a multiobjective local search based on the Nawaz-Enscore-Ham heuristic is applied to good solutions with a specified probability to enhance the exploitation ability. Third, to enrich the searching behavior and to avoid premature convergence, a multiobjective local search based on simulated annealing with multiple different neighborhoods is designed, and an adaptive meta-Lamarckian learning strategy is employed to decide which neighborhood will be used. Due to the fusion of multiple different searching operations, good solutions approximating the real Pareto front can be obtained. In addition, MOPSO adopts a random weighted linear sum function to aggregate multiple objectives to a single one for solution evaluation and for guiding the evolution process in the multiobjective sense. Due to the randomness of weights, searching direction can be enriched, and solutions with good diversity can be obtained. Simulation results and comparisons based on a variety of instances demonstrate the effectiveness, efficiency, and robustness of the proposed hybrid algorithm.

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.

On operators and search space topology in multi-objective flow shop scheduling

Multi-objective optimization using evolutionary algorithms identifies Pareto-optimal alternatives or their close approximation by means of a sequence of successive local improvement moves. While several successful applications to combinatorial optimization problems are known, studies of underlying problem structures are still scarce. The paper presents a study of the problem structure of multi-objective permutation flow shop scheduling problems and investigates the effectiveness of local search neighborhoods within an evolutionary search framework. First, small problem instances with up to six objective functions for which the optimal alternatives are known are studied. Second, benchmark instances taken from literature are investigated. It turns out for the investigated data sets that the Pareto-optimal alternatives are found relatively concentrated in alternative space. Also, it can be shown that no single neighborhood operator is able to equally identify all Pareto-optimal alternatives. Taking this into consideration, significant improvements have been obtained by combining different neighborhood structures into a multi-operator search framework.

Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling

This paper shows how the performance of evolutionary multiobjective optimization (EMO) algorithms can be improved by hybridization with local search. The main positive effect of the hybridization is the improvement in the convergence speed to the Pareto front. On the other hand, the main negative effect is the increase in the computation time per generation. Thus, the number of generations is decreased when the available computation time is limited. As a result, the global search ability of EMO algorithms is not fully utilized. These positive and negative effects are examined by computational experiments on multiobjective permutation flowshop scheduling problems. Results of our computational experiments clearly show the importance of striking a balance between genetic search and local search. In this paper, we first modify our former multiobjective genetic local search (MOGLS) algorithm by choosing only good individuals as initial solutions for local search and assigning an appropriate local search direction to each initial solution. Next, we demonstrate the importance of striking a balance between genetic search and local search through computational experiments. Then we compare the modified MOGLS with recently developed EMO algorithms: the strength Pareto evolutionary algorithm and revised nondominated sorting genetic algorithm. Finally, we demonstrate that a local search can be easily combined with those EMO algorithms for designing multiobjective memetic algorithms.