Novel Discrete Particle Swarm Optimization Based on Huge Value Penalty for Solving Engineering Problem

For the purpose of solving the engineering constrained discrete optimization problem, a novel discrete particle swarm optimization(DPSO) is proposed. The proposed novel DPSO is based on the idea of normal particle swarm optimization(PSO), but deals with the variables as discrete type, the discrete optimum solution is found through updating the location of discrete variable. To avoid long calculation time and improve the efficiency of algorithm, scheme of constraint level and huge value penalty are proposed to deal with the constraints, the stratagem of reproducing the new particles and best keeping model of particle are employed to increase the diversity of particles. The validity of the proposed DPSO is examined by benchmark numerical examples, the results show that the novel DPSO has great advantages over current algorithm. The optimum designs of the 100-1 500 mm bellows under 0.25 MPa are fulfilled by DPSO. Comparing the optimization results with the bellows in-service, optimization results by discrete penalty particle swarm optimization(DPPSO) and theory solution, the comparison result shows that the global discrete optima of bellows are obtained by proposed DPSO, and confirms that the proposed novel DPSO and schemes can be used to solve the engineering constrained discrete problem successfully.     

考虑批量装配的柔性作业车间调度问题研究

柔性作业车间调度是生产调度领域中的一个重要组合优化问题,由于取消了工序与加工设备的唯一性对应关系,因而相较于作业车间调度问题,具有更高的复杂度。针对该问题在批量装配方面的不足,考虑将批量因素与装配环节同时集成到柔性作业车间调度问题当中。以成品件的完工时间为优化目标,对该批量装配柔性作业车间调度问题进行了数学建模。针对该模型,提出一种多层编码结构的粒子群算法,并对该算法的各个模块进行了设计。最后,以实例验证了该数学模型的正确性及算法的有效性。     

交货期惩罚下柔性车间调度多目标Pareto优化研究

针对传统作业车间调度问题的局限性,结合实际生产过程的特点和约束条件,建立路径柔性的作业车间调度仿真模型。采用连续空间蚁群算法,对柔性车间作业进行多变量、多约束下的调度布局优化设计,在考虑各个机器提前/拖期完工的惩罚值,所有机器上的总负荷、成品合格率和最大设备利用率等性能指标更加合理情况下,为每次迭代产生的邻域解集作为Pareto非支配排序,防止算法操作过程中劣解的产生,提高求解效率。并与自适应免疫算法和交换序列混合粒子群法的优化结果进行对比,该算法可有效改善基本蚁群算法的停滞现象和全局寻优能力差的缺点。目前,该方法已在某机械公司进行示范,在提高加工效率、降低生产成本、减少协作费等方面效果显著。     

APPLYING PARTICLE SWARM OPTIMIZATION TO JOB-SHOPSCHEDULING PROBLEM

A new heuristic algorithm is proposed for the problem of finding the minimum makespan in the job-shop scheduling problem. The new algorithm is based on the principles of particle swarm optimization (PSO). PSO employs a collaborative population-based search, which is inspired by the social behavior of bird flocking. It combines local search (by self experience) and global search (by neighboring experience), possessing high search efficiency. Simulated annealing (SA) employs certain probability to avoid becoming trapped in a local optimum and the search process can be controlled by the cooling schedule. By reasonably combining these two different search algorithms, a general, fast and easily implemented hybrid optimization algorithm, named HPSO, is developed. The effectiveness and efficiency of the proposed PSO-based algorithm are demonstrated by applying it to some benchmark job-shop scheduling problems and comparing results with other algorithms in literature. Comparing results indicate that PSO-based a     

A discrete PSO for two-stage assembly scheduling problem

In this paper, a discrete particle swarm optimization (PSO) algorithm called DPSO is proposed to solve the two-stage assembly scheduling problem with respect to bicriteria of makespan and mean completion time where setup times are treated as separate from processing times. In DPSO, the particle velocity representation is redefined, and particle movement is modified accordingly. In order to refrain from the shortcoming of premature convergence, individual intensity is defined, which is used to control adaptive mutation of the particle, and mutation mode is decided by the individual fitness. Furthermore, a randomized exchange neighborhood search is introduced to enhance the local search ability of the particle and increase the convergence speed. Finally, the proposed algorithm is tested on different scale problems and compared with the proposed efficient algorithms in the literature recently. The results show that DPSO is an effective and efficient for assembly scheduling problem.     

An assembly sequence planning approach with a discrete particle swarm optimization algorithm

In this paper, a discrete particle swarm optimization (DPSO) algorithm is proposed to solve the assembly sequence planning (ASP) problem. To make the DPSO algorithm effective for solving ASP, some key technologies including a special coding method of the position and velocity of particles and corresponding operators for updating the position and velocity of particles are proposed and defined. The evolution performance of the DPSO algorithm with different setting of control parameters is investigated, and the performance of the proposed DPSO algorithm to solve ASP is verified through a case study.     

基于粒子群优化和模拟退火的混合调度算法

提出了一种离散粒子群调度算法，采用基于工序的编码方式及相应的位置和速度更新方法，使具有连续本质的粒子群算法直接适用于调度问题。针对粒子群算法容易陷入局部最优的缺陷，将其与模拟退火算法结合，得到了粒子群-模拟退火算法、改进的粒子群算法、粒子群-模拟退火交替算法以及粒子群-模拟退火协同算法等4种混合调度算法。仿真结果表明，混合算法均具有较高的求解质量。     

Solving a multi-objective job shop scheduling problem with sequence-dependent setup times by a Pareto archive PSO combined with genetic operators and VNS

In this paper, we present a combination of particle swarm optimization (PSO) and genetic operators for a multi-objective job shop scheduling problem that minimizes the mean weighted completion time and the sum of the weighted tardiness/earliness costs, simultaneously. At first, we propose a new integer linear programming for the given problem. Then, we redefine and modify PSO by introducing genetic operators, such as crossover and mutation operators, to update particles and improve particles by variable neighborhood search. Furthermore, we consider sequence-dependent setup times. We then design a Pareto archive PSO, where the global best position selection is combined with the crowding measure-based archive updating method. To prove the efficiency of our proposed PSO, a number of test problems are solved. Its reliability based on some comparison metrics is compared with a prominent multi-objective genetic algorithm (MOGA), namely non-dominated sorting genetic algorithm II (NSGA-II). The computational results show that the proposed PSO outperforms the above MOGA, especially for large-sized problems.     

基于Pareto优化的离散自由搜索算法求解多目标柔性作业车间调度问题

针对多目标柔性作业车间调度问题搜索空间的离散性和求解算法的收敛性,提出一种基于Pareto优化的离散自由搜索算法来求解多目标柔性作业车间调度问题。在建立基于Markov链数学模型的基础上,证明了算法以概率1收敛;引入首达最优解期望时间来分析算法收敛速度,并分析了算法时间复杂度。采用基于工序排序和机器分配的个体表达方式,在多目标柔性作业车间离散域,利用自由搜索算法在邻域小步幅精确搜索和在全局空间大步幅勘测进行寻优;通过自由搜索算法自适应赋予个体各异辨别能力和Pareto优化概念来比较个体优劣性,不仅保留优化个体,而且使个体寻优方向沿多目标柔性作业车间调度问题Pareto前沿逼近。通过对搜索过程中产生的伪调度方案进行可行性判定,以确保调度方案可行。采用10×10FJSP和8×8FJSP问题的实例进行寻优测试,验证了所提算法的可行性和有效性。     

Research on job-shop scheduling optimization method with limited resources

Job-shop scheduling is an important subject in the fields of production management and combinatorial optimization. It is also an urgent problem to be solved in actual production. It is usually difficult to achieve the optimal solution with classical methods, due to a high computational complexity (NP-Hard). According to the nature of job-shop scheduling, a solution based on a particle swarm optimiser (PSO) is presented in this paper. In addition to establishing a job-shop scheduling model based on PSO, we have researched the coding and optimized operation of PSO. We have also considered more suitable methods of coding and operation for job-shop scheduling as well as the target function and calculation of the proper figure. The software system of job-shop scheduling is developed according to the PSO algorithm. Test simulations illustrate that the PSO algorithm is a suitable and effective approach for solving the job-shop scheduling problem.     

A simulated annealing algorithm to find approximate Pareto optimal solutions for the multi-objective facility layout problem

In this article, we consider the facility layout problem which combines the objective of minimization of the total material handling cost and the maximization of total closeness rating scores. Multi-objective optimization is the way to consider the two objectives at the same time. A simulated annealing (SA) algorithm is proposed to find the non-dominated solution (Pareto optimal) set approximately for the multi-objective facility layout problem we tackle. The Pareto optimal sets generated by the proposed algorithm was compared with the solutions of the previous algorithms for multi-objective facility layout problem. The results showed that the approximate Pareto optimal sets we have found include almost all the previously obtained results and many more approximate Pareto optimal solutions.     

A hybrid discrete particle swarm optimization algorithm for the no-wait flow shop scheduling problem with makespan criterion

This paper proposes a novel hybrid discrete particle swarm optimization (HDPSO) algorithm to solve the no-wait flow shop scheduling problems with the criterion to minimize the maximum completion time (makespan). Firstly, a simple approach is presented in the paper to calculate the makespan of a job permutation. Secondly, a speed-up method is proposed to evaluate the similar insert neighborhood solution. Thirdly, a discrete particle swarm optimization (DPSO) algorithm based on permutation representation and a local search algorithm based on the insert neighborhood are fused to enhance the searching ability and to balance the exploration and exploitation. Then, computational simulation results based on the well-known benchmarks and statistical performance comparisons are provided. It is concluded that the proposed HDPSO algorithm is superior to both the single DPSO algorithm and the existing hybrid particle swarm optimization (HPSO) algorithm from literature in terms of searching quality, robustness and efficiency.     

柔性作业车间调度问题的两级遗传算法

研究不同性能指标柔性作业车间调度问题的优化.针对柔性作业车间调度问题的特点,设计基于工序编码和基于机器分配编码的两种交叉和变异算子,并提出一种双层子代产生模式的改进遗传算法应用于该调度问题,以使子代更好地继承父代的优良特征.使用实例测试改进的遗传算法,并与其他遗传算法的测试结果进行比较,所提出算法的有效性得到证实.     

Scheduling flowshops with condition-based maintenance constraint to minimize expected makespan

Flexible job-shop scheduling problem (FJSP) is an extended traditional job-shop scheduling problem, which more approximates to practical scheduling problems. This paper presents a multi-objective genetic algorithm (MOGA) based on immune and entropy principle to solve the multi-objective FJSP. In this improved MOGA, the fitness scheme based on Pareto-optimality is applied, and the immune and entropy principle is used to keep the diversity of individuals and overcome the problem of premature convergence. Efficient crossover and mutation operators are proposed to adapt to the special chromosome structure. The proposed algorithm is evaluated on some representative instances, and the comparison with other approaches in the latest papers validates the effectiveness of the proposed algorithm.     

Pareto archived simulated annealing for job shop scheduling with multiple objectives

In this paper, the job shop scheduling problem is studied with the objectives of minimizing the makespan and the mean flow time of jobs. The simultaneous consideration of these objectives is the multi-objective optimization problem under study. A metaheuristic procedure based on the simulated annealing algorithm called Pareto archived simulated annealing (PASA) is proposed to discover non-dominated solution sets for the job shop scheduling problems. The seed solution is generated randomly. A new perturbation mechanism called segment-random insertion (SRI) scheme is used to generate a set of neighbourhood solutions to the current solution. The PASA searches for the non-dominated set of solutions based on the Pareto dominance or through the implementation of a simple probability function. The performance of the proposed algorithm is evaluated by solving benchmark job shop scheduling problem instances provided by the OR-library. The results obtained are evaluated in terms of the number of non-dominated schedules generated by the algorithm and the proximity of the obtained non-dominated front to the Pareto front.     

Multi-objective artificial bee colony algorithm for simultaneous sequencing and balancing of mixed model assembly line

In recent years, mixed model assembly lines are gaining popularity to produce a variety of models on the single-model assembly lines. Mixed model assembly lines have two types of problems which include sequencing of different models on the line and balancing of assembly line. These two problems collectively affect the performance of assembly lines, and therefore, current research is aimed to balance the workload of different models on each station, to reduce the deviation of workload of a station from the average workload of all the stations and to minimize the total flow time of models on different stations simultaneously. A multi-objective artificial bee colony (multi-ABC) algorithm for simultaneous sequencing and balancing problem with Pareto concepts and local search mechanism is presented. Two kinds of mixed model assembly line problems are analysed. For the first and second problems, each model task time data and precedence relation data are taken from standard assembly line problems, from operation research library (ORL) and from a truck manufacturing company in China, respectively. Both problems are solved using the proposed multi-ABC algorithm on two different demand scenarios of models, and the results are compared against the results obtained from a famous algorithm in the literature, i.e. non-dominated sorting genetic algorithm (NSGA) II. Computational results of the selected problems indicate that the proposed multi-ABC algorithm outperforms NSGA II and gives better Pareto solutions for the selected problems on different demand scenarios of models.     

改进遗传算法求解柔性作业车间调度问题

分析柔性作业车间调度问题的特点,提出一种求解该问题的改进遗传算法。在考虑各个机器负荷平衡,所有机器上的总负荷和最大完工时间等性能指标更加合理情况下,设计一种全局搜索、局部搜索和随机产生相结合的初始化方法,提高种群初始解的质量,加快遗传算法的收敛速度。结合问题特点设计合理的染色体编码方式、交叉算子和变异算子,防止遗传操作过程中非法解的产生,避免染色体的修复,提高求解效率。使用文献中相同的实例测试利用初始化方法的改进遗传算法,并将计算结果与文献中其他遗传算法的测试结果进行比较,验证所提出的初始化方法的可行性和有效性。     

No-idle permutation flow shop scheduling based on a hybrid discrete particle swarm optimization algorithm

A novel hybrid discrete particle swarm optimization (HDPSO) algorithm is proposed in this paper to solve the no-idle permutation flow shop scheduling problems with the criterion to minimize the maximum completion time (makespan). Firstly, two simple approaches are presented to calculate the makespan of a job permutation. Secondly, a speed-up method is proposed to evaluate the whole insert neighborhood of a job permutation with (n?1)² neighbors in time O(mn ²), where n and m denote the number of jobs and machines, respectively. Thirdly, a discrete particle swarm optimization (DPSO) algorithm based on permutation representation and a local search algorithm based on the insert neighborhood are fused to enhance the searching ability and to balance the exploration and exploitation. Then, computational simulation results based on the well-known benchmarks and statistical performance comparisons are provided. It is concluded that the proposed HDPSO algorithm is not only superior to two recently published heuristics, the improved greedy (IG) heuristic and Kalczynski–Kamburowski (KK) heuristic, in terms of searching quality, but also superior to the single DPSO algorithm and the PSO algorithm with variable neighborhood search (PSOvns) in terms of searching quality, robustness and efficiency.     

A hybrid algorithm based on particle swarm optimization and simulated annealing for a periodic job shop scheduling problem

Generating schedules such that all operations are repeated every constant period of time is as important as generating schedules with minimum delays in all cases where a known discipline is desired or obligated by stakeholders. In this paper, a periodic job shop scheduling problem (PJSSP) based on the periodic event scheduling problem (PESP) is presented, which deviates from the cyclic scheduling. The PESP schedules a number of recurring events as such that each pair of event fulfills certain constraints during a given fixed time period. To solve such a hard PJSS problem, we propose a hybrid algorithm, namely PSO-SA, based on particle swarm optimization (PSO) and simulated annealing (SA) algorithms. To evaluate this proposed PSO-SA, we carry out some randomly constructed instances by which the related results are compared with the proposed SA and PSO algorithms as well as a branch-and-bound algorithm. In addition, we compare the results with a hybrid algorithm embedded with electromagnetic-like mechanism and SA. Moreover, three lower bounds (LBs) are studied, and the gap between the found LBs and the best found solutions are reported. The outcomes prove that the proposed hybrid algorithm is an efficient and effective tool to solve the PJSSP.