A multi-objective particle swarm for a flow shop scheduling problem

Flow shop problems as a typical manufacturing challenge have gained wide attention in academic fields. In this paper, we consider a bi-criteria permutation flow shop scheduling problem, where weighted mean completion time and weighted mean tardiness are to be minimized simultaneously. Since a flow shop scheduling problem has been proved to be NP-hard in strong sense, an effective multi-objective particle swarm (MOPS), exploiting a new concept of the Ideal Point and a new approach to specify the superior particle's position vector in the swarm, is designed and used for finding locally Pareto-optimal frontier of the problem. To prove the efficiency of the proposed algorithm, various test problems are solved and the reliability of the proposed algorithm, based on some comparison metrics, is compared with a distinguished multi-objective genetic algorithm, i.e. SPEA-II. The computational results show that the proposed MOPS performs better than the genetic algorithm, especially for the large-sized problems.     

The permutation flow shop problem with just in time production considerations

This research presents a variation to the permutation flow shop problem where Just In Time (JIT) production requirements are taken into account. The model developed in this research employs dual objectives. In addition to the traditional objective of minimizing the production makespan, minimization of Miltenburg's material usage rate is also incorporated. In this model, multiple units of any product are permitted in the production sequence. However, the minimization of material usage rates attempts to prevent batch scheduling of products and allows unit flow of products as required in demand flow manufacturing. A solution method is proposed for determining an optimal production sequence via an efficient frontier approach and Simulated Annealing (SA). Test problems and specific performance criteria are used to assess the solutions generated by the proposed method. Experimental results presented in this paper show that the use of the efficient frontier and SA provide solutions that approach the optimal solution for the performance measures used in this research.     

Approximation schemes for two-machine flow shop scheduling with two agents

In this paper we consider two-machine flow shop scheduling with two agents. Two models are investigated. One is the weighted-sum optimization model and the other is the constrained optimization model. For the former, we show that it is weakly NP-hard and propose a fully polynomial time approximation scheme. For the latter, we also show the problem is weakly NP-hard. With violating the constraint a factor of ?? a fully polynomial time approximation scheme is provided.     

A two-machine no-wait flow shop problem with two competing agents

Journal of Combinatorial Optimization - In this paper, we study the two-machine no-wait flow shop scheduling problem with two competing agents. The objective is to minimize the overall completion...     

Lot scheduling problems of multiple items in the shop with both receiving and delivery just in time

Abstract. This paper deals with lot scheduling problems of multiple items processed in the shop with either a single machine or heterogeneous machines, under the condition that parts to be processed must arrive at the production line at the right times in the right quantities, and that completed parts must be delivered at their due date. Each of the problems is divided into subproblems of lot sizing and scheduling the resulting lots. Solution procedures solving the subproblems are separately optimal. However, since one of the subproblems is not independent of the other, the proposed algorithms adopting these procedures are to be considered heuristic. An iterative procedure is provided to improve solutions. The performance measure used is that of minimizing the total actual flow time considering both receiving just in time and delivery just in time. Numerical examples are presented to show the implementation of the algorithms.     

Multi-objective permutation flow shop scheduling problem: Literature review,classification and current trends

The flow shop scheduling problem is finding a sequence given n jobs with same order at m machines according to certain performance measure(s). The job can be processed on at most one machine; meanwhile one machine can process at most one job. The most common objective for this problem is makespan. However, many real-world scheduling problems are multi-objective by nature. Over the years there have been several approaches used to deal with the multi-objective flow shop scheduling problems (MOFSP). Hence, in this study, we provide a brief literature review of the contributions to MOFSP and identify areas of opportunity for future research.     

A heuristic to minimize total flow time in permutation flow shop

In this paper, we address an n-job, m-machine permutation flow shop scheduling problem for the objective of minimizing the total flow time. We propose a modification of the best-known method of Framinan and Leisten [An efficient constructive heuristic for flowtime minimization in permutation flow shops. Omega 2003;31:311–7] for this problem. We show, through computational experimentation, that this modification significantly improves its performance while not affecting its time-complexity.     

一种求解双目标flow shop排序问题的进化算法

提出一种求解双目标flow shop排序的递进多目标进化算法.算法采用改进的精英复制策略,在实现精英保留的前提下降低了计算复杂性;通过递进进化模式增加群体多样性,改善了算法收敛性;通过群体进化过程中对非劣解集进行竞争型可变邻域启发式搜索,增强了算法局部搜索性能.采用新算法和参照算法NSGA-II对31个标准双目标flow shop算例进行优化.研究结果表明,新算法在所有算例的求解中均获得了优于NSGA-II的非劣解集,验证了算法的有效性.     

Asymptotically optimal policy for stochastic job shop scheduling problem to minimize makespan

This paper studies the large-scale stochastic job shop scheduling problem with general number of similar jobs, where the processing times of the same step are independently drawn from a known probability distribution, and the objective is to minimize the makespan. For the stochastic problem, we introduce the fluid relaxation of its deterministic counterpart, and define a fluid schedule for the fluid relaxation. By tracking the fluid schedule, a policy is proposed for the stochastic job shop scheduling problem. The expected value of the gap between the solution produced by the policy and the optimal solution is proved to be O(1), which indicates the policy is asymptotically optimal in expectation.     

A faster strongly polynomial time algorithm to solve the minimum cost tension problem

This paper presents a strongly polynomial time algorithm for the minimum cost tension problem, which runs in \(O(\max \{m^3n, m^2 \log n(m+n \log n)\})\) time, where n and m denote the number of nodes and number of arcs, respectively. Our algorithm improves upon the previous strongly polynomial time of \(O(n^4 m^3 \log n)\) due to Hadjiat and Maurras (Discret Math 165(166):377–394, 1997).     

元胞微粒群算法及其在多维背包问题中的应用

针对离散微粒群算法早熟收敛问题,基于元胞自动机的原理和离散微粒群算法,提出一种元胞微粒群算法.将元胞及其邻居引入到算法中来保持种群的多样性,利用元胞的演化规则进行局部优化,避免算法陷入局部极值.通过对典型多维背包问题的仿真实验和与其他算法的比较,表明本算法可行有效,有良好的全局优化能力.     

A heuristic approach to n/ m job shop scheduling: fuzzy dynamic scheduling algorithms

n/m shop scheduling is a ‘ NP-Hard’ problem. Using conventional heuristic algorithms ( priority rules) only, it is almost impossible to achieve an optimal solution. Research has been carried out to improve the heuristic algorithms to give a near-optimal solution. This paper advocates a fuzzy logic based, dynamic scheduling algoridim aimed at achieving this goal. The concept of new membership functions is discussed in die algorithm as a link to connect several priority rules. The constraints to determine the membership function of jobs for a particular priority rule are established, and three membership functions are developed. In order to decide the weight vector of priority rules, an aggregate performance measure is suggested. The methodology for constructing the weight vector is discussed in detail. Experiments have been carried out using a simulation technique to validate the proposed scheduling algorithm.     

Single machine group scheduling to minimize mean flow time subject to due date constraints

This paper considers a single machine group scheduling problem. All jobs are classified into groups and the jobs within a group are processed contiguously on the machine. A sequence-independent setup time is incurred between each two consecutively scheduled groups. This paper presents a solution procedure which utilizes Smith's algorithm and a proposed modified Smith's algorithm to find an optimal job sequence and an optimal group sequence which minimizes the mean flow time of jobs subject to the constraint that no jobs are tardy. The complexity of the algorithm is shown to have a polynomial running time in the number of groups and jobs.     

Two-stage proportionate flexible flow shop to minimize the makespan

We consider a two-stage flexible flow shop problem with a single machine at one stage and m identical machines at the other stage, where the processing times of each job at both stages are identical. The objective is to minimize the makespan. We describe some optimality conditions and show that the problem is NP-hard when m is fixed. Finally, we present an approximation algorithm that has a worst-case performance ratio of $\frac{5}{4}$ for m=2 and $\frac{\sqrt{1+m^{2}}+1+m}{2m}$ for m≥3.     

Designing a tabu search algorithm for the two-stage flow shop problem with secondary criterion

This paper discusses the process of desigining a tabu search-based heuristic for the two-stage flow shop problem with makespan minimization as the primary criterion and the minimization of total flow time as the secondary criterion. A factorial experiment is designed to analyse thoroughly the effects of four different factors, i.e. the initial solution, type of move, size of neighbourhood and the list size, on the performance of the tabu search-based heuristic. Using the techniques of evolution curves, and response tables and response graphs, coupled with the Taguchi method, the best combination of the factors for the tabu search-based heuristic is identified, and the effectiveness of the heuristic algorithm in finding an optimal solution is evaluated by comparing its performance with the best known heuristic to solve this problem.     

Outpatient appointment scheduling problem considering patient selection behavior: data modeling and simulation optimization

Journal of Combinatorial Optimization - In medical outpatient services, due to patients’ imbalanced selection for doctors of different levels and for different visiting periods, inefficiency...     

An adaptive multistart tabu search approach to solve the maximum clique problem

Given an undirected graph G=(V,E) with vertex set V={1,…,n} and edge set E?V×V. The maximum clique problem is to determine in G a clique (i.e., a complete subgraph) of maximum cardinality. This paper presents an effective algorithm for the maximum clique problem. The proposed multistart tabu search algorithm integrates a constrained neighborhood, a dynamic tabu tenure mechanism and a long term memory based restart strategy. Our proposed algorithm is evaluated on the whole set of 80 DIMACS challenge benchmarks and compared with five state-of-the-art algorithms. Computational results show that our proposed algorithm attains the largest known clique for 79 benchmarks.     

Using branch-and-price approach to solve the directed network design problem with relays

We present node-arc and arc-path formulations, and develop a branch-and-price approach for the directed network design problem with relays (DNDR). The DNDR problem can be used to model many network design problems in transportation, service, and telecommunication system, where relay points are necessary. The DNDR problem consists of introducing a subset of arcs and locating relays on a subset of nodes such that in the resulting network, the total cost (arc cost plus relay cost) is minimized, and there exists a directed path linking the origin and destination of each commodity, in which the distances between the origin and the first relay, any two consecutive relays, and the last relay and the destination do not exceed a predefined distance limit. With the node-arc formulation, we can directly solve small DNDR instances using mixed integer programming solver. With the arc-path formulation, we design a branch-and-price approach, which is a variant of branch-and-bound with bounds provided by solving linear programs using column generation at each node of the branch-and-bound tree. We design two methods to efficiently price out columns and present computational results on a set of 290 generated instances. Results demonstrate that our proposed branch-and-price approach is a computationally efficient procedure for solving the DNDR problem.