Solving closed-loop supply chain problems using game theoretic particle swarm optimisation

In this paper, we propose a closed-loop supply chain network configuration model and a solution methodology that aim to address several research gaps in the literature. The proposed solution methodology employs a novel metaheuristic algorithm, along with the popular gradient descent search method, to aid location-allocation and pricing-inventory decisions in a two-stage process. In the first stage, we use an improved version of the particle swarm optimisation (PSO) algorithm, which we call improved PSO (IPSO), to solve the location-allocation problem (LAP). The IPSO algorithm is developed by introducing mutation to avoid premature convergence and embedding an evolutionary game-based procedure known as replicator dynamics to increase the rate of convergence. The results obtained through the application of IPSO are used as input in the second stage to solve the inventory-pricing problem. In this stage, we use the gradient descent search method to determine the selling price of new products and the buy-back price of returned products, as well as inventory cycle times for both product types. Numerical evaluations undertaken using problem instances of different scales confirm that the proposed IPSO algorithm performs better than the comparable traditional PSO, simulated annealing (SA) and genetic algorithm (GA) methods.     

Optimisation of a multi-objective two-dimensional strip packing problem based on evolutionary algorithms

This paper considers a real-world two-dimensional strip packing problem involving specific machinery constraints and actual cutting production industry requirements. To adapt the problem to a wider range of machinery characteristics, the design objective considers the minimisation of material length and the total number of cuts for guillotinable-type patterns. The number of cuts required for the cutting process is crucial for the life of the industrial machines and is an important aspect in determining the cost and efficiency of the cutting operation. In this paper we propose the application of evolutionary algorithms to address the multi-objective problem, for which numerous approaches to its single-objective formulation exist, but for which multi-objective approaches are almost non-existent. The multi-objective evolutionary algorithms applied provide a set of solutions offering a range of trade-offs between the two objectives from which clients can choose according to their needs. By considering both the length and number of cuts, they derive solutions with wastage levels similar to most previous approximations which just seek to optimise the overall length.     

Solving constrained optimization problems with a hybrid particle swarm optimization algorithm

This article presents a particle swarm optimization algorithm for solving general constrained optimization problems. The proposed approach introduces different methods to update the particle's information, as well as the use of a double population and a special shake mechanism designed to avoid premature convergence. It also incorporates a simple constraint-handling technique. Twenty-four constrained optimization problems commonly adopted in the evolutionary optimization literature, as well as some structural optimization problems are adopted to validate the proposed approach. The results obtained by the proposed approach are compared with respect to those generated by algorithms representative of the state of the art in the area.     

Automatic clustering for generalised cell formation using a hybrid particle swarm optimisation

This paper considers the cell formation (CF) problem in which parts have alternative process routings and the number of machine cells is not known a priori. Very few studies address these two practical issues at the same time. This paper proposes an automatic clustering approach based on a hybrid particle swarm optimisation (PSO) algorithm that can automatically evolve the number and cluster centres of machine cells for a generalised CF problem. In the proposed approach, a solution representation, comprising an integer number and a set of real numbers, is adopted to encode the number of cells and machine cluster centres, respectively. Besides, a discrete PSO algorithm is utilised to search for the number of machine cells, and a continuous PSO algorithm is employed to perform machine clustering. Effectiveness of the proposed approach has been demonstrated for test problems selected from the literature and those generated in this study. The experimental results indicate that the proposed approach is capable of solving the generalised machine CF problem without predetermination of the number of cells.     

A new multi-objective particle swarm optimizer using empirical movement and diversified search strategies

Most real-world optimization problems involve the optimization task of more than a single objective function and, therefore, require a great amount of computational effort as the solution procedure is designed to anchor multiple compromised optimal solutions. Abundant multi-objective evolutionary algorithms (MOEAs) for multi-objective optimization have appeared in the literature over the past two decades. In this article, a new proposal by means of particle swarm optimization is addressed for solving multi-objective optimization problems. The proposed algorithm is constructed based on the concept of Pareto dominance, taking both the diversified search and empirical movement strategies into account. The proposed particle swarm MOEA with these two strategies is thus dubbed the empirical-movement diversified-search multi-objective particle swarm optimizer (EMDS-MOPSO). Its performance is assessed in terms of a suite of standard benchmark functions taken from the literature and compared to other four state-of-the-art MOEAs. The computational results demonstrate that the proposed algorithm shows great promise in solving multi-objective optimization problems.     

A particle swarm optimisation for the no-wait flow shop problem with due date constraints

This paper considers the no-wait flow shop scheduling problem with due date constraints. In the no-wait flow shop problem, waiting time is not allowed between successive operations of jobs. Moreover, a due date is associated with the completion of each job. The considered objective function is makespan. This problem is proved to be strongly NP-Hard. In this paper, a particle swarm optimisation (PSO) is developed to deal with the problem. Moreover, the effect of some dispatching rules for generating initial solutions are studied. A Taguchi-based design of experience approach has been followed to determine the effect of the different values of the parameters on the performance of the algorithm. To evaluate the performance of the proposed PSO, a large number of benchmark problems are selected from the literature and solved with different due date and penalty settings. Computational results confirm that the proposed PSO is efficient and competitive; the developed framework is able to improve many of the best-known solutions of the test problems available in the literature.     

Maximising manufacturing system efficiency for multi-characteristic linear assembly by using particle swarm optimisation in batch selective assembly

Quality of an assembly is mainly based on the quality of mating parts. Due to random variation in sources such as materials, machines, operators and measurements, even those mating parts manufactured by the same process vary in their dimensions. When mating parts are assembled linearly, the resulting variation will be the sum of the mating part tolerances. Many assemblies are not able to meet the assembly specification in the available assembly methods. This will decrease the manufacturing system efficiency. Batch selective assembly is helpful to keep the assembly requirement and also to increase the manufacturing system efficiency. In traditional selective assembly, the mating part population is partitioned to form selective groups, and the parts of corresponding selective groups are assembled interchangeably. After the invention of advanced dimension measuring devices and the computer, today batch selective assembly plays a vital role in the manufacturing system. In batch selective assembly, all dimensions of a batch of mating parts are measured and stored in a computer. Instead of forming selective groups, each and every part is assigned to its best matching part. In this work, a particle swarm optimisation based algorithm is proposed by applying the batch selective assembly methodology to a multi-characteristic assembly environment, to maximise the assembly efficiency and thereby maximising the manufacturing system efficiency. The proposed algorithm is tested with a set of experimental problem data sets and is found to outperform the traditional selective assembly and sequential assembly methods, in producing solutions with higher manufacturing system efficiency.     

A modified particle swarm optimisation algorithm to solve the part feeding problem at assembly lines

The Assembly Line Part Feeding Problem (ALPFP) is a complex combinatorial optimisation problem concerned with the delivery of the required parts to the assembly workstations in the right quantities at the right time. Solving the ALPFP includes simultaneously solving two sub-problems, namely tour scheduling and tow-train loading. In this article, we first define the problem and formulate it as a multi-objective mixed-integer linear programming model. Then, we carry out a complexity analysis, proving the ALPFP to be NP-complete. A modified particle swarm optimisation (MPSO) algorithm incorporating mutation as part of the position updating scheme is subsequently proposed. The MPSO is capable of finding very good solutions with small time requirements. Computational results are reported, demonstrating the efficiency and effectiveness of the proposed MPSO.     

A hybrid particle swarm based method for process planning optimisation

A process planning (PP) problem is defined as to determine a set of operation-methods (machine, tool, and set-up configuration) that can convert the given stock to the designed part. Essentially, the PP problem involves the simultaneous decision making of two tasks: operation-method selection and sequencing. This is a combinatorial optimisation problem and it is difficult to find the best solution in a reasonable amount of time. In this article, an optimisation approach based on particle swarm optimisation (PSO) is proposed to solve the PP problem. Due to the characteristic of discrete process planning solution space and the continuous nature of the original PSO, a novel solution representation scheme is introduced for the application of PSO in solving the PP problem. Moreover, two kinds of local search algorithms are incorporated and interweaved with PSO evolution to improve the best solution in each generation. The numerical experiments and analysis have demonstrated that the proposed algorithm is capable of gaining a good quality solution in an efficient way.     

Optimisation of integrated process planning and scheduling using a particle swarm optimisation approach

Traditionally, process planning and scheduling are two independent essential functions in a job shop manufacturing environment. In this paper, a unified representation model for integrated process planning and scheduling (IPPS) has been developed. Based on this model, a modern evolutionary algorithm, i.e. the particle swarm optimisation (PSO) algorithm has been employed to optimise the IPPS problem. To explore the search space comprehensively, and to avoid being trapped into local optima, the PSO algorithm has been enhanced with new operators to improve its performance and different criteria, such as makespan, total job tardiness and balanced level of machine utilisation, have been used to evaluate the job performance. To improve the flexibility and agility, a re-planning method has been developed to address the conditions of machine breakdown and new order arrival. Case studies have been used to a verify the performance and efficiency of the modified PSO algorithm under different criteria. A comparison has been made between the result of the modified PSO algorithm and those of the genetic algorithm (GA) and the simulated annealing (SA) algorithm respectively, and different characteristics of the three algorithms are indicated. Case studies show that the developed PSO can generate satisfactory results in optimising the IPPS problem.     

Analysis of closed loop supply chain using genetic algorithm and particle swarm optimisation

This paper describes a relational database system for semi-generative process planning for sheet metal parts that emulates expert system capabilities. The system integrates a feature-based relational database for the parts, a forward chaining rule-based strategy for machine selection, both global and feature-specific execution of the rules and a graph theoretic cost optimization model for optimal process plan selection. This system, which is currently being developed for a sheet metal fabrication company, suggests that, using the experience of shopfloor personnel, an efficient integration of feature-based process planning and expert system strategies can be accomplished.     

Two-staged guillotine cut,two-dimensional bin packing optimisation with flexible bin size for steel mother plate design

This paper looks into the steel mother plate design problem. A slab, which is an intermediate work in process, is subsequently rolled into a mother plate with the specific dimensions of thickness, length, and width. The mother plate is then cut into customer order plates. As a slab is rolled into a mother plate through a series of horizontal and vertical rolling processes, different-sized mother plates can be generated from a single-slab type. This flexibility allows for the size of a mother plate to be determined according to the order plates assigned to it. Furthermore, when the order plates are cut from a mother plate, a guillotine cut is required to reduce the production cost. The steel mother plate design problem involves the placing of order plates on the mother plates in a guillotine cut pattern and determining the sizes of the mother plates with the objective of minimising the number of slabs; thus it may be considered as a two-staged guillotine cut, two-dimensional bin packing problem with flexible bin size. This paper introduces the problem, presents several mathematical models, and proposes an iterative two-phase heuristic method consisting of several algorithms to solve the problem. Computational results for the benchmark problems show the effectiveness of the proposed method.     

A discrete particle swarm optimisation for operation sequencing in CAPP

Operation sequencing is one of crucial tasks for process planning in a CAPP system. In this study, a novel discrete particle swarm optimisation (DPSO) named feasible sequence oriented DPSO (FSDPSO) is proposed to solve the operation sequencing problems in CAPP. To identify the process plan with lowest machining cost efficiently, the FSDPSO only searches the feasible operation sequences (FOSs) satisfying precedence constraints. In the FSDPSO, a particle represents a FOS as a permutation directly and the crossover-based updating mechanism is developed to evolve the particles in discrete feasible solution space. Furthermore, the fragment mutation for altering FOS and the uniform and greedy mutations for changing machine, cutting tool and tool access direction for each operation, along with the adaptive mutation probability, are adopted to improve exploration ability. Case studies are used to verify the performance of the FSDPSO. For case studies, the Taguchi method is used to determine the key parameters of the FSDPSO. A comparison has been made between the result of the proposed FSDPSO and those of three existing PSOs, an existing genetic algorithm and two ant colony algorithms. The comparative results show higher performance of the FSDPSO with respect to solution quality for operation sequencing.     

Machining fixture layout optimisation under dynamic conditions based on evolutionary techniques

Optimisation of fixture layout is critical to reduce geometric and form error of the workpiece during the machining process. In this paper the optimal placement of fixture elements (locator and clamp locations) under dynamic conditions is investigated using evolutionary techniques. The application of the newly developed particle swarm optimisation (PSO) algorithm and widely used genetic algorithm (GA) is presented to minimise elastic deformation of the workpiece considering its dynamic response. To improve the performances of GA and PSO, an improved GA (IGA) obtained by basic GA (GA) with sharing and adaptive mutation and an improved PSO (IPSO) obtained by basic PSO (PSO) incorporated into adaptive mutation are developed. ANSYS parametric design language (APDL) of finite element analysis is employed to compute the objective function for a given fixture layout. Three layout optimisation cases derived from the high speed slot milling case are used to test the effectiveness of the GA, IGA, PSO and IPSO based approaches. The comparisons of computational results show that IPSO seems superior to GA, IGA and PSO approaches with respect to the trade-off between global optimisation capability and convergence speed for the presented type problems.     

Multi-objective particle swarm optimisation based integrated production inventory routing planning for efficient perishable food logistics operations

Sustainable and efficient food supply chain has become an essential component of one’s life. The model proposed in this paper is deeply linked to people's quality of life as a result of which there is a large incentive to fulfil customer demands through it. This proposed model can enhance food quality by making the best possible food quality accessible to customers, construct a sustainable logistics system considering its environmental impact and ensure the customer demand to be fulfilled as fast as possible. In this paper, an extended model is examined that builds a unified planning problem for efficient food logistics operations where four important objectives are viewed: minimising the total expense of the system, maximising the average food quality along with the minimisation of the amount of CO₂ emissions in transportation along with production and total weighted delivery lead time minimisation. A four objective mixed integer linear programming model for intelligent food logistics system is developed in the paper. The optimisation of the formulated mathematical model is proposed using a modified multi-objective particle swarm optimisation algorithm with multiple social structures: MO-GLNPSO (Multi-Objective Global Local Near-Neighbour Particle Swarm Optimisation). Computational results of a case study on a given dataset as well as on multiple small, medium and large-scale datasets followed by sensitivity analysis show the potency and effectiveness of the introduced method. Lastly, there has been a scope for future study displayed which would lead to the further progress of these types of models.     

Unequal-area stochastic facility layout problems: solutions using improved covariance matrix adaptation evolution strategy,particle swarm optimisation,and genetic algorithm

Determining the locations of departments or machines in a shop floor is classified as a facility layout problem. This article studies unequal-area stochastic facility layout problems where the shapes of departments are fixed during the iteration of an algorithm and the product demands are stochastic with a known variance and expected value. These problems are non-deterministic polynomial-time hard and very complex, thus meta-heuristic algorithms and evolution strategies are needed to solve them. In this paper, an improved covariance matrix adaptation evolution strategy (CMA ES) was developed and its results were compared with those of two improved meta-heuristic algorithms (i.e. improved particle swarm optimisation [PSO] and genetic algorithm [GA]). In the three proposed algorithms, the swapping method and two local search techniques which altered the positions of departments were used to avoid local optima and to improve the quality of solutions for the problems. A real case and two problem instances were introduced to test the proposed algorithms. The results showed that the proposed CMA ES has found better layouts in contrast to the proposed PSO and GA.     

Cross-docking truck scheduling with product unloading/loading constraints based on an improved particle swarm optimisation algorithm

Cross-docking is a very useful logistics technique that can substantially reduce distribution costs and improve customer satisfaction. A key problem in its success is truck scheduling, namely, decision on assignment and docking sequence of inbound/outbound trucks to receiving/shipping dock doors. This paper focuses on the problem with the requirement of unloading/loading products in a given order, which is very common in many industries, but is less concerned by existing researches. An integer programming model is established to minimise the makespan. An improved particle swarm optimisation (ωc-PSO) algorithm is proposed for solving it. In the algorithm, a cosine decreasing strategy of inertia weight is designed to dynamically balance global and local search. A repair strategy is put forward for continuous search in the feasible solution space and a crossover strategy is presented to prevent the algorithm from falling into local optimum. After algorithm parameters are tuned using Taguchi method, computational experiments are conducted on different problem scales to evaluate ωc-PSO against genetic algorithm, basic PSO and GLNPSO. The results show that ωc-PSO outperforms other three algorithms, especially when the number of dock doors, trucks and product types is great. Statistical tests show that the performance difference is statistically significant.     

Parallel asynchronous particle swarm optimization

The high computational cost of complex engineering optimization problems has motivated the development of parallel optimization algorithms. A recent example is the parallel particle swarm optimization (PSO) algorithm, which is valuable due to its global search capabilities. Unfortunately, because existing parallel implementations are synchronous (PSPSO), they do not make efficient use of computational resources when a load imbalance exists. In this study, we introduce a parallel asynchronous PSO (PAPSO) algorithm to enhance computational efficiency. The performance of the PAPSO algorithm was compared to that of a PSPSO algorithm in homogeneous and heterogeneous computing environments for small- to medium-scale analytical test problems and a medium-scale biomechanical test problem. For all problems, the robustness and convergence rate of PAPSO were comparable to those of PSPSO. However, the parallel performance of PAPSO was significantly better than that of PSPSO for heterogeneous computing environments or heterogeneous computational tasks. For example, PAPSO was 3.5 times faster than was PSPSO for the biomechanical test problem executed on a heterogeneous cluster with 20 processors. Overall, PAPSO exhibits excellent parallel performance when a large number of processors (more than about 15) is utilized and either (1) heterogeneity exists in the computational task or environment, or (2) the computation-to-communication time ratio is relatively small.     

A batching-move iterated local search algorithm for the bin packing problem with generalized precedence constraints

In this paper, we propose a generalisation of the bin packing problem, obtained by adding precedences between items that can assume heterogeneous non-negative integer values. Such generalisation also models the well-known Simple Assembly Line Balancing Problem of type I. To solve the problem, we propose a simple and effective iterated local search algorithm that integrates in an innovative way of constructive procedures and neighbourhood structures to guide the search to local optimal solutions. Moreover, we apply some preprocessing procedures and adapt classical lower bounds from the literature. Extensive computational experiments on benchmark instances suggest that the developed algorithm is able to generate good quality solutions in a reasonable computational time.