Maximizing production rate and workload smoothing in assembly lines using particle swarm optimization

Particle swarm optimization (PSO) one of the latest developed population heuristics has rarely been applied in production and operations management (POM) optimization problems. A possible reason for this absence is that, PSO was introduced as global optimizer over continuous spaces, while a large set of POM problems are of combinatorial nature with discrete decision variables. PSO evolves floating-point vectors (called particles) and thus, its application to POM problems whose solutions are usually presented by permutations of integers is not straightforward. This paper presents a novel method based on PSO for the simple assembly line balancing problem (SALBP), a well-known NP-hard POM problem. Two criteria are simultaneously considered for optimization: to maximize the production rate of the line (equivalently to minimize the cycle time), and to maximize the workload smoothing (i.e. to distribute the workload evenly as possible to the workstations of the assembly line). Emphasis is given on seeking a set of diverse Pareto optimal solutions for the bi-criteria SALBP. Extensive experiments carried out on multiple test-beds problems taken from the open literature are reported and discussed. Comparisons between the proposed PSO algorithm and two existing multi-objective population heuristics show a quite promising higher performance for the proposed approach.     

Particle swarm optimization with cocktail decoding method for hybrid flow shop scheduling problems with multiprocessor tasks

This paper addresses the problem of multiprocessor task-scheduling in a hybrid flow shop (HFS) problem to minimize the makespan. Due to the complex nature of an HFS problem, it is decomposed into the following two sequential decision problems: determining the job permutation in stage 1, followed by a decoding method to assign jobs into each machine in subsequent stages when designing a heuristic algorithm. The decoding method plays a pivotal role for improving the solution quality of any algorithm for the HFS problem. However, the majority of existing algorithms ignores the problem and is only concerned with the first decision problem. This study emphasizes the importance of the decoding method via a small test, and searches for a number of solid decoding methods that can be incorporated into the cocktail decoding method. Then, this study develops a particle swarm optimization (PSO) algorithm that can be combined with the cocktail decoding method. In the PSO, a variety of job sequences are generated using the PSO procedure in stage 1, and the cocktail decoding method is used to assign the jobs to machines in sequential stages. Moreover, a modified lower bound is introduced. Computational results show that the proposed lower bound is competitive, and with the help of the cocktail decoding method, the proposed PSO, and even the adoption of a standard PSO framework, significantly outperforms the majority of existing algorithms in terms of quality of solutions, especially for large problems.     

A Pareto approach to multi-objective flexible job-shop scheduling problem using particle swarm optimization and local search

The job-shop scheduling problem is one of the most arduous combinatorial optimization problems. Flexible job-shop problem is an extension of the job-shop problem that allows an operation to be processed by any machine from a given set along different routes. This paper present a new approach based on a hybridization of the particle swarm and local search algorithm to solve the multi-objective flexible job-shop scheduling problem. The particle swarm optimization is a highly efficient and a new evolutionary computation technique inspired by birds’ flight and communication behaviors. The multi-objective particle swarm algorithm is applied to the flexible job-shop scheduling problem based on priority. Also the presented approach will be evaluated for their efficiency against the results reported for similar algorithms (weighted summation of objectives and Pareto approaches). The results indicate that the proposed algorithm satisfactorily captures the multi-objective flexible job-shop problem and competes well with similar approaches.     

Metaheuristics for drilling operation scheduling in Taiwan PCB industries

Among all types of production environment, identical parallel machines are frequently used to increase the manufacturing capacity of the drilling operation in Taiwan printed circuit board (PCB) industries. Additionally, multiple but conflicting objectives are usually considered when a manager plans the production scheduling. Compared to the single objective problem, the multiple-objective version no longer looks for an individual optimal solution, but a Pareto front consisting of a set of non-dominated solutions will be needed and established. The manager then can select one of the alternatives from the set. This research aims at employing a variable neighborhood search (VNS) algorithm and a multiple ant colony optimization (MACO) algorithm to solve the identical parallel-machine scheduling problem with two conflicting objectives: makespan and total tardiness. In VNS, two neighborhoods are defined—insert a job to a different position or swap two jobs in the sequence. To save the computational expense, one of the neighborhoods is randomly selected for the target solution which is also arbitrarily chosen from the current Pareto front. In MACO, a two-phase construction procedure where three colonies are employed in each phase is proposed. These two algorithms are tested on a set of real data collected from a leading PCB factory in Taiwan and their performances are compared. The computational results show that VNS outperforms all competing algorithms—SPGA, MOGA, NSGA-II, SPEA-II, and MACO in terms of solution quality and computational time.     

Particle swarm optimization: A study of particle displacement for solving continuous and combinatorial optimization problems

This article addresses the particle swarm optimization (PSO) method. It is a recent proposed algorithm by Kennedy and Eberhart [1995. Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks (Perth, Australia), vol. IV, IEEE Service Center, Piscataway, NJ, pp. 1942–1948]. This optimization method is motivated by social behaviour of organisms such as bird flocking and fish schooling. PSO algorithm is not only a tool for optimization, but also a tool for representing socio-cognition of human and artificial agents, based on principles of social behaviour. Some scientists suggest that knowledge is optimized by social interaction and thinking is not only private but also interpersonal. PSO as an optimization tool, provides a population-based search procedure in which individuals called particles change their position (state) with time. In a PSO system, particles fly in a multidimensional search space. During flight, each particle adjusts its position according to its own experience, and according to the experience of neighbours, making use of the best position encountered by itself and its neighbours. In this paper, we propose firstly, an extension of the PSO system that integrates a new displacement of the particles (the balance between the intensification process and the diversification process) and we highlight a relation between the coefficients of update of each dimension velocity between the classical PSO algorithm and the extension. Secondly, we propose an adaptation of this extension of PSO algorithm to solve combinatorial optimization problem with precedence constraints in general and resource-constrained project scheduling problem in particular. The numerical experiments are done on the main continuous functions and on the resource-constrained project scheduling problem (RCPSP) instances provided by the psplib. The results obtained are encouraging and push us into accepting than both PSO algorithm and extensions proposed based on the new particles displacement are a promising direction for research.     

Hybrid particle swarm optimization with mutation for optimizing industrial product lines: An application to a mixed solution space considering both discrete and continuous design variables

This article presents an artificial intelligence-based solution to the problem of product line optimization. More specifically, we apply a new hybrid particle swarm optimization (PSO) approach to design an optimal industrial product line. PSO is a biologically-inspired optimization framework derived from natural intelligence that exploits simple analogues of collective behavior found in nature, such as bird flocking and fish schooling. All existing product line optimization algorithms in the literature have been so far applied to consumer markets and product attributes that range across some discrete values. Our hybrid PSO algorithm searches for an optimal product line in a large design space which consists of both discrete and continuous design variables. The incorporation of a mutation operator to the standard PSO algorithm significantly improves its performance and enables our mechanism to outperform the state of the art Genetic Algorithm in a simulated study with artificial datasets pertaining to industrial cranes. The proposed approach deals with the problem of handling variables that can take any value from a continuous range and utilizes design variables associated with both product attributes and value-added services. The application of the proposed artificial intelligence framework yields important implications for strategic customer relationship and production management in business-to-business markets.     

粒子群算法和灰狼算法的融合

为了解决传统粒子群算法(PSO)容易“早熟”、陷入局部最优以及灰狼算法(GWO)收敛速度慢的问题。首先，采用GWO算法的个体极值更新策略来实现个体包围式向最优值趋近，融入PSO算法的速度更新策略来实现群体向最优值的趋近，并且在原始粒子群算法基础上加入线性惯性权重递减来提高算法的收敛速度，从而提出了一种基于灰狼算法和改进的粒子群算法(IPSO)的融合优化算法(GW-IPSO);其次，通过6个经典算例进行仿真试验，将融合算法与PSO算法、IPSD算法、灰狼和粒子群结合算法(GW-PSO)进行对比；最后，应用融合算法对二级直线倒立摆的控制器设计进行参数寻优。结果表明：针对6个标准测试函数，混合算法的30次试验结果平均值更接近最优值，且标准差几乎都是最小的；应用在倒立摆控制问题上，系统在5 s左右进入稳定状态。融合后的GW-IPSO算法能够在一定程度上避免早熟和陷入局部极值的问题发生，并且能够很好地应用于控制器设计过程中参数寻优问题。     

Metaheuristic-based simulation optimization approach to network revenue management with an improved self-adjusting bid price function

Making accurate accept/reject decisions on dynamically arriving customer requests for different combinations of resources is a challenging task under uncertainty of competitors' pricing strategies. Because customer demand may be affected by a competitor's pricing action, changes in customer interarrival times should also be considered in capacity control procedures. In this article, a simulation model is developed for a bid price–based capacity control problem of an airline network revenue management system by considering the uncertain nature of booking cancellations and competitors' pricing strategy. An improved bid price function is proposed by considering competitors' different pricing scenarios that occur with different probabilities and their effects on the customers' demands. The classical deterministic linear program (DLP) is reformulated to determine the initial base bid prices that are utilized as control parameters in the proposed self-adjusting bid price function. Furthermore, a simulation optimization approach is applied in order to determine the appropriate values of the coefficients in the bid price function. Different evolutionary computation techniques such as differential evolution (DE), particle swarm optimization (PSO), and seeker optimization algorithm (SOA), are utilized to determine these coefficients along with comparisons. The computational experiments show that promising results can be obtained by making use of the proposed metaheuristic-based simulation optimization approach.     

Inventory control in a two-level supply chain with risk pooling effect

We consider an inventory control problem in a supply chain consisting of a single supplier, with a central distribution center (CDC) and multiple regional warehouses, and multiple retailers. We focus on the problem of selecting warehouses to be used among a set of candidate warehouses, assigning each retailer to one of the selected warehouses and determining replenishment plans for the warehouses and the retailers. For the problem with the objective of minimizing the sum of warehouse operation costs, inventory holding costs at the warehouses and the retailers, and transportation costs from the CDC to warehouses as well as from warehouses to retailers, we present a non-linear mixed integer programming model and develop a heuristic algorithm based on Lagrangian relaxation and subgradient optimization methods. A series of computational experiments on randomly generated test problems shows that the heuristic algorithm gives relatively good solutions in a reasonable computation time.     

A genetic algorithm based heuristic for two machine no-wait flowshop scheduling problems with class setup times that minimizes maximum lateness

Machine scheduling problem has been extensively studied by researchers for many decades in view of its numerous applications on solving practical problems. Due to the complexity of this class of scheduling problems, various approximation solution approaches have been presented in the literature. In this paper, we present a genetic algorithm (GA) based heuristic approach to solve the problem of two machine no-wait flowshop scheduling problems that the setup time on the machines is class dependent, and the objective is to minimize the maximum lateness of the jobs processed. This class of machine scheduling problems has many practical applications in manufacturing industry, such as metal refinery operations, food processing industry and chemical products production processes, in which no interruption between subsequent processes is allowed and the products can be grouped into families. Extensive computation experiments have been conducted to evaluate the effectiveness of the proposed algorithm. Results show the proposed methodology is suitable to be adopted for the development of an efficient scheduling plan for this class of problems in real life application.     

A multi-objective robust optimization model for multi-product multi-site aggregate production planning in a supply chain under uncertainty

Manufacturers need to satisfy consumer demands in order to compete in the real world. This requires the efficient operation of a supply chain planning. In this research we consider a supply chain including multiple suppliers, multiple manufacturers and multiple customers, addressing a multi-site, multi-period, multi-product aggregate production planning (APP) problem under uncertainty. First a new robust multi-objective mixed integer nonlinear programming model is proposed to deal with APP considering two conflicting objectives simultaneously, as well as the uncertain nature of the supply chain. Cost parameters of the supply chain and demand fluctuations are subject to uncertainty. Then the problem transformed into a multi-objective linear one. The first objective function aims to minimize total losses of supply chain including production cost, hiring, firing and training cost, raw material and end product inventory holding cost, transportation and shortage cost. The second objective function considers customer satisfaction through minimizing sum of the maximum amount of shortages among the customers’ zones in all periods. Working levels, workers productivity, overtime, subcontracting, storage capacity and lead time are also considered. Finally, the proposed model is solved as a single-objective mixed integer programming model applying the LP-metrics method. The practicability of the proposed model is demonstrated through its application in solving an APP problem in an industrial case study. The results indicate that the proposed model can provide a promising approach to fulfill an efficient production planning in a supply chain.     

A coevolutionary algorithm for the flexible delivery and pickup problem with time windows

This paper addresses a flexible delivery and pickup problem with time windows (FDPPTW) and formulates the problem into a mixed binary integer programming model in order to minimize the number of vehicles and to minimize the total traveling distance. This problem is shown to be NP-hard. In this study, therefore, a coevolutionary algorithm incorporated with a variant of the cheapest insertion method is developed to speed up the solution procedure. The FDPPTW scheme overcomes the shortcomings of the existing schemes for the delivery and pickup problems. By testing with some revised Solomon's benchmark problems, the computational results have shown the efficiency and the effectiveness of the developed algorithm.     

混合邻域结构的粒子群算法

为了克服标准粒子群算法的早熟、停滞进化或易于陷入局部最优的现象,提出了一种混合模型(简称NSPO)。NSPO将一个粒子映射到无标度网络的多个网络节点上,借助网络结构获得该粒子的邻域拓扑。对粒子的更新,NSPO既考虑种群的最优,又考虑邻域的最优。在3个具有不同难度特点的测试函数上,将NSPO与标准粒子群算法进行了比较。实验结果表明:对于全局最优和梯度信息明显的函数,NSPO具有非常优越的表现;对于具有诸多局部最优的函数,NSPO逃逸局部最优的能力要强于标准粒子群算法;对于具有误导性梯度信息的函数,NSPO偶尔表现优异。     

Stochastic optimization for transshipment problems with positive replenishment lead times

Transshipments, monitored movements of material at the same echelon of a supply chain, represent an effective pooling mechanism. Earlier papers dealing with transshipments either do not incorporate replenishment lead times into their analysis, or only provide a heuristic algorithm where optimality cannot be guaranteed beyond settings with two locations. This paper uses infinitesimal perturbation analysis by combining with a stochastic approximation method to examine the multi-location transshipment problem with positive replenishment lead times. It demonstrates the computation of optimal base stock quantities through sample path optimization. From a methodological perspective, this paper deploys a duality-based gradient computation method to improve computational efficiency. From an application perspective, it solves transshipment problems with non-negligible replenishment lead times. A numerical study illustrates the performance of the proposed approach.     

Hybrid flow shop scheduling with parallel batching

In this research the problem of parallel batch scheduling in a hybrid flow shop environment with minimizing C_max is studied. In parallel batching it is assumed that machines in some stages are able to process a number of operations simultaneously. Since the problem is NP-hard, three heuristic algorithms are developed to give near optimal solutions. Since this problem has not been studied previously, therefore, a lower bound is developed for evaluating the performance of the proposed heuristics. Several test problems have been solved using these heuristics and results compared. To further enhance the solution quality, a three dimensional genetic algorithm (3DGA) is also developed. Several test problems have been solved using 3DGA and the results indicate its superiority to the other heuristics.     

A hybrid artificial bee colony algorithm for the job shop scheduling problem

The job shop scheduling problem (JSSP) has attracted much attention in the field of both information sciences and operations research. In terms of the objective function, most existing research has been focused on the makespan criterion (i.e., minimizing the overall completion time). However, for contemporary manufacturing firms, the due date related performance is usually more important because it is crucial for maintaining a high service reputation. Therefore, in this study we aim at minimizing the total weighted tardiness in JSSP. Considering the high complexity, a novel artificial bee colony (ABC) algorithm is proposed for solving the problem. A neighborhood property of the problem is discovered, and then a tree search algorithm is devised to enhance the exploitation capability of ABC. According to extensive computational tests, the proposed approach is efficient in solving the job shop scheduling problem with total weighted tardiness criterion.     

Simultaneous dock assignment and sequencing of inbound trucks under a fixed outbound truck schedule in multi-door cross docking operations

This paper studies the simultaneous dock assignment and sequencing of inbound trucks for a multi-door cross docking operation with the objective to minimize total weighted tardiness, under a fixed outbound truck departure schedule. The problem is newly formulated and solved by six different metaheuristic algorithms, which include simulated annealing, tabu search, ant colony optimization, differential evolution, and two hybrid differential-evolution algorithms. To evaluate the total weighted tardiness associated with any given inbound-truck sequence and dock assignment, an operational policy is developed. This policy is employed by every metaheuristic algorithm in searching for the optimal dock assignment and sequence. Each metaheuristic algorithm is tested with 40 problems. The major conclusions are: (1) metaheuristic is generally an effective optimization method for the subject problem; (2) population based metaheuristic algorithms are generally more effective than projection based metaheuristic algorithms; (3) proper selection of algorithmic parameters is important and more critical for projection based metaheuristic algorithms than population based algorithms; (4) the two best algorithms are ant colony optimization and hybrid differential evolution 2; among them, ACO takes less time than hybrid 2 and thus can be declared the best among all the six metaheuristic algorithms tested.     

A hybrid heuristic algorithm adopting both Boltzmann function and mutation operator for manufacturing cell formation problems

This study proposes a hybrid heuristic algorithm employing both the Boltzmann function from simulated annealing and the mutation operator from the genetic algorithm to explore the unvisited solution region and expedite the solution searching process for the cell formation problem, so that grouping efficacy is maximized. Test problems drawn from the literature are used to test the performance of the proposed heuristic algorithm. The comparative study shows that the proposed algorithm improves the best results found in the literature for 36% of the test problems in the case when singletons solutions are allowed.     

A decision method for supplier selection in multi-service outsourcing

Although supplier selection in multi-service outsourcing is a very important decision problem, research concerning this issue is still relatively scarce. This paper proposes a decision method for selecting a pool of suppliers for the provision of different service process/product elements. It pioneers the use of collaborative utility between partner firms for supplier selection. A multi-objective model is built to select desired suppliers. This model is proved to be NP-hard, so we develop a multi-objective algorithm based on Tabu search for solving it. We then use an example to show the applicability of the proposed model and algorithm. Extensive computational experiments are also conducted to further test the performance of the proposed algorithm.     

Constraint-based ACO for a shared resource constrained scheduling problem

We consider a scheduling problem arising in the mining industry. Ore from several mining sites must be transferred to ports to be loaded on ships in a timely manner. In doing so, several constraints must be met which involve transporting the ore and deadlines. These deadlines are two-fold: there is a preferred deadline by which the ships should be loaded and there is a final deadline by which time the ships must be loaded. Corresponding to the two types of deadlines, each task is associated with a soft and hard due time. The objective is to minimize the cumulative tardiness, measured using the soft due times, across all tasks. This problem can be formulated as a resource constrained job scheduling problem where several tasks must be scheduled on multiple machines satisfying precedence and resource constraints and an objective to minimize total weighted tardiness. For this problem we present hybrids of ant colony optimization, Beam search and constraint programming. These algorithms have previously shown to be effective on similar tightly-constrained combinatorial optimization problems. We show that the hybrid involving all three algorithms provides the best solutions, particularly with respect to feasibility. We also investigate alternative estimates for guiding the Beam search component of our algorithms and show that stochastic sampling is the most effective.