Assessing hypermutation operators of a clonal selection algorithm for the unequal area facility layout problem

A mutation operator is critical for the performance of a clonal selection algorithm (CSA) since it diversifies the search directions and avoids early convergence to local optima. This article introduces a CSA approach for the unequal area facility layout problem (UAFLP) with flexible bay structure. A new encoding, the use of mutation types with different combinations, and different static and dynamic mutation application strategies are also proposed. In addition, a guideline in parameter optimization of the CSA is provided. An experimental study is performed on five cases of the UAFLP. It is concluded that the hypermutation types studied in this article, especially the inverse mutation followed by pairwise mutation, can be used to obtain good results within short computation times.     

A methodology for solving the unequal area facility layout problem using distance and shape-based measures

This paper presents a methodology for solving the unequal area facility layout problem commonly encountered in industry practice. A mixed-binary nonlinear-programming model is formulated to capture the operational issues encountered on the shop floor. In particular, in addition to the distance measure that is typically used to quantify the material handling costs, the impact of geometry or the shape of the departments is quantified in the formulation of the model. A higher-level heuristic solution algorithm, based on a concept known as ‘tabu search’, is proposed to efficiently solve industry-relevant problems. The methodology not only considers the impact of both distance and shape-based measures simultaneously in the proposed initial solution finding mechanism, but also in the evaluation of the objective function during the entire search procedure, in the hope that it will lead to identifying a better final solution. Taking into consideration fixed and variable tabu list sizes, along with long-term memory with maximum and minimum frequencies, has led to developing six different heuristics for the solution algorithm. A single factor experiment based on randomized block design has been used to compare the performances of the six different heuristics on three different problem structures—small, medium, and large—using the total cost as the criterion. Based on this experiment, the characterizations of search procedures have been recommended to facilitate identifying the best solution for each problem structure. The proposed method is also compared with those in the published literature by solving fairly well known unequal area facility layout problems. When an improvement is observed, the comparison has led to identifying a percentage improvement in total cost of approximately 2.8% to 11.8%, thus demonstrating the effectiveness of the model and the algorithm.     

A multi-objective particle swarm optimisation algorithm for unequal sized dynamic facility layout problem with pickup/drop-off locations

This paper deals with a multi-objective unequal sized dynamic facility layout problem (DFLP) with pickup/drop-off locations. First, a mathematical model to obtain optimal solutions for small size instances of the problem is developed. Then, a multi-objective particle swarm optimisation (MOPSO) algorithm is implemented to find near optimal solutions. Two new heuristics to prevent overlapping of the departments and to reduce ‘unused gaps’ between the departments are introduced. The performance of the MOPSO is examined using some sets of available test problems in the literature and various random test problems in small, medium, and large sizes. The percentage of improvements on the initial solutions is calculated for small, medium and large size instances. Also, the generation metric and the space metric for non-dominated solutions are examined. These experiments show the good performance of the developed MOPSO and sensitivity analysis show the robustness of the obtained solutions.     

A particle swarm optimizer for constrained multi-objective engineering design problems

This article presents a particle swarm optimizer (PSO) capable of handling constrained multi-objective optimization problems. The latter occur frequently in engineering design, especially when cost and performance are simultaneously optimized. The proposed algorithm combines the swarm intelligence fundamentals with elements from bio-inspired algorithms. A distinctive feature of the algorithm is the utilization of an arithmetic recombination operator, which allows interaction between non-dominated particles. Furthermore, there is no utilization of an external archive to store optimal solutions. The PSO algorithm is applied to multi-objective optimization benchmark problems and also to constrained multi-objective engineering design problems. The algorithmic effectiveness is demonstrated through comparisons of the PSO results with those obtained from other evolutionary optimization algorithms. The proposed particle swarm optimizer was able to perform in a very satisfactory manner in problems with multiple constraints and/or high dimensionality. Promising results were also obtained for a multi-objective engineering design problem with mixed variables.     

A divide-and-conquer strategy with particle swarm optimization for the job shop scheduling problem

An optimization algorithm based on the ‘divide-and-conquer’ methodology is proposed for solving large job shop scheduling problems with the objective of minimizing total weighted tardiness. The algorithm adopts a non-iterative framework. It first searches for a promising decomposition policy for the operation set by using a simulated annealing procedure in which the solutions are evaluated with reference to the upper bound and the lower bound of the final objective value. Subproblems are then constructed according to the output decomposition policy and each subproblem is related to a subset of operations from the original operation set. Subsequently, all these subproblems are sequentially solved by a particle swarm optimization algorithm, which leads directly to a feasible solution to the original large-scale scheduling problem. Numerical computational experiments are carried out for both randomly generated test problems and the real-world production data from a large speed-reducer factory in China. Results show that the proposed algorithm can achieve satisfactory solution quality within reasonable computational time for large-scale job shop scheduling problems.     

Evolutionary computation of unconstrained and constrained problems using a novel momentum-type particle swarm optimization

This study proposes a novel momentum-type particle swarm optimization (PSO) method, which will find good solutions of unconstrained and constrained problems using a delta momentum rule to update the particle velocity. The algorithm modifies Shi and Eberhart's PSO to enhance the computational efficiency and solution accuracy. This study also presents a continuous non-stationary penalty function, to force design variables to satisfy all constrained functions. Several well-known and widely used benchmark problems were employed to compare the performance of the proposed PSO with Kennedy and Eberhart's PSO and Shi and Eberhart's modified PSO. Additionally, an engineering optimization task for designing a pressure vessel was applied to test the three PSO algorithms. The optimal solutions are presented and compared with the data from other works using different evolutionary algorithms. To show that the proposed momentum-type PSO algorithm is robust, its convergence rate, solution accuracy, mean absolute error, standard deviation, and CPU time were compared with those of both the other PSO algorithms. The experimental results reveal that the proposed momentum-type PSO algorithm can efficiently solve unconstrained and constrained engineering optimization problems.     

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.     

Enhancing particle swarm optimization algorithm using two new strategies for optimizing design of truss structures

This work develops an augmented particle swarm optimization (AugPSO) algorithm using two new strategies,: boundary-shifting and particle-position-resetting. The purpose of the algorithm is to optimize the design of truss structures. Inspired by a heuristic, the boundary-shifting approach forces particles to move to the boundary between feasible and infeasible regions in order to increase the convergence rate in searching. The purpose of the particle-position-resetting approach, motivated by mutation scheme in genetic algorithms (GAs), is to increase the diversity of particles and to prevent the solution of particles from falling into local minima. The performance of the AugPSO algorithm was tested on four benchmark truss design problems involving 10, 25, 72 and 120 bars. The convergence rates and final solutions achieved were compared among the simple PSO, the PSO with passive congregation (PSOPC) and the AugPSO algorithms. The numerical results indicate that the new AugPSO algorithm outperforms the simple PSO and PSOPC algorithms. The AugPSO achieved a new and superior optimal solution to the 120-bar truss design problem. Numerical analyses showed that the AugPSO algorithm is more robust than the PSO and PSOPC algorithms.     

基于信息熵改进的粒子群算法在桁架结构

提出了信息熵改进的粒子群优化算法用于解决有应力约束、位移约束的桁架结构杆件截面尺寸优化设计问题.首先介绍了信息熵基本理论和基本粒子群优化算法理论,然后对粒子群优化算法作了合理的参数设置,并将信息熵引入粒子群优化算法的适应函数和停机判别准则中.最后对2个经典的优化问题进行求解并与其他算法进行了比较.数据结果表明信息熵改进后的粒子群优化算法在桁架结构优化设计中优于其他同类算法.     

A dynamic programming-based particle swarm optimization algorithm for an inventory management problem under uncertainty

This article presents a dynamic programming-based particle swarm optimization (DP-based PSO) algorithm for solving an inventory management problem for large-scale construction projects under a fuzzy random environment. By taking into account the purchasing behaviour and strategy under rules of international bidding, a multi-objective fuzzy random dynamic programming model is constructed. To deal with the uncertainties, a hybrid crisp approach is used to transform fuzzy random parameters into fuzzy variables that are subsequently defuzzified by using an expected value operator with optimistic–pessimistic index. The iterative nature of the authors’ model motivates them to develop a DP-based PSO algorithm. More specifically, their approach treats the state variables as hidden parameters. This in turn eliminates many redundant feasibility checks during initialization and particle updates at each iteration. Results and sensitivity analysis are presented to highlight the performance of the authors’ optimization method, which is very effective as compared to the standard PSO algorithm.     

A new optimization algorithm based on a combination of particle swarm optimization,convergence and divergence operators for single-objective and multi-objective problems

Particle swarm optimization (PSO) is a randomized and population-based optimization method that was inspired by the flocking behaviour of birds and human social interactions. In this work, multi-objective PSO is modified in two stages. In the first stage, PSO is combined with convergence and divergence operators. Here, this method is named CDPSO. In the second stage, to produce a set of Pareto optimal solutions which has good convergence, diversity and distribution, two mechanisms are used. In the first mechanism, a new leader selection method is defined, which uses the periodic iteration and the concept of the particle's neighbour number. This method is named periodic multi-objective algorithm. In the second mechanism, an adaptive elimination method is employed to limit the number of non-dominated solutions in the archive, which has influences on computational time, convergence and diversity of solution. Single-objective results show that CDPSO performs very well on the complex test functions in terms of solution accuracy and convergence speed. Furthermore, some benchmark functions are used to evaluate the performance of periodic multi-objective CDPSO. This analysis demonstrates that the proposed algorithm operates better in three metrics through comparison with three well-known elitist multi-objective evolutionary algorithms. Finally, the algorithm is used for Pareto optimal design of a two-degree of freedom vehicle vibration model. The conflicting objective functions are sprung mass acceleration and relative displacement between sprung mass and tyre. The feasibility and efficiency of periodic multi-objective CDPSO are assessed in comparison with multi-objective modified NSGAII.     

Sequential linear programming and particle swarm optimization for the optimization of energy districts

This article deals with the optimization of energy resource management of industrial districts, with the aim of minimizing customer energy expenses. A model of the district is employed, whose optimization gives rise to a nonlinear constrained optimization problem. Here the focus is on its numerical solution. Two different methods are considered: a sequential linear programming method and a particle swarm optimization method. Efficient implementations of both approaches are devised and the results of the tests performed on several energetic districts are reported, including a real case study.     

A sequence-pair representation and MIP-model-based heuristic for the facility layout problem with rectangular departments

In Facility Layout Problem (FLP) research, the continuous-representation-based FLP can consider all feasible all-rectangular-department solutions. Given this flexibility, this representation has become the representation of choice in FLP research. Much of this research is based on a methodology of Mixed-Integer Programming (MIP) models. However, these MIP-FLP models can only solve problems with a limited number of departments to optimality due to the large number of combinations of the binary variables used in the models to maintain feasibility with respect to departments overlapping. Our research centers around the sequence-pair representation, a concept that originated in the Very Large Scale Integration (VLSI) design literature. We show that an exhaustive search of the sequence-pair solution space will result in finding the optimal layout of the MIP-FLP and that every sequence-pair solution is position consistent (although possibly not layout feasible) in the MIP-FLP. We propose a genetic-algorithm-based heuristic that combines the sequence-pair representation with the MIP-FLP model. Numerical experiments based on different sized test problems from both the literature and industrial applications are provided and the solutions are compared with both the optimal solutions and the solutions from other heuristics to show the effectiveness and efficiency of our heuristic. For 11 data sets from the literature we provide solutions better than those previously found. For two large industrial application data sets we perform a sensitivity analysis with respect to the department aspect ratio constraint.     

A new MILP approach for the facility process-layout design problem with rectangular and L/T shape departments

We propose a new approach for the facility process-layout design problem, and introduce new mixed-integer linear programming (MILP) formulations for solving the problem. In this approach, we consider simultaneously, in a process-layout setting, the shape and location of the departments within the facility as well as the internal arrangement of the machines within the departments. Two models are suggested, the first assumes a rectangular shape of the departments and the second allows non-rectangular departments defined by an L/T shape. For the latter model, new constraints are developed to assure a correct design of the L/T shapes and to avoid irregular department shapes, and cuts are added to shorten the solution time. Finally, we conduct an extensive numerical study, in which we show the capabilities of both formulations in solving problems of medium size, and the superiority of the L/T department shape solutions over the rectangular department solutions.     

Integration of occupational health and safety in the facility layout planning,part II: design of the kitchen of a hospital

Facility layout design has an important effect on the performance of manufacturing systems. It intends to determine relative location of departments and machines within a plant. A good layout design must ensure that a set of criteria and objectives are met and optimised, e.g. area requirements, cost, communication and safety. The most common objective used in facility planning methods is to minimise the transportation cost. However, factors such as the plant safety, flexibility for future design changes, noise and aesthetics must be considered as well. In this paper, a case study is carried out to investigate the safety concerns in facility layout design. In this regard, a facility layout planning methodology, integrating occupational health and safety (OHS) is presented. This methodology considers transportation cost as well as safety in the facility design. By this means, OHS issues are considered at the design stage of the facility. In other words, this research demonstrates the improvements in the layout design by integrating safety aspects.     

Coupling ant colony optimization and the extended great deluge algorithm for the discrete facility layout problem

This article uses a hybrid optimization approach to solve the discrete facility layout problem (FLP), modelled as a quadratic assignment problem (QAP). The idea of this approach design is inspired by the ant colony meta-heuristic optimization method, combined with the extended great deluge (EGD) local search technique. Comparative computational experiments are carried out on benchmarks taken from the QAP-library and from real life problems. The performance of the proposed algorithm is compared to construction and improvement heuristics such as H63, HC63-66, CRAFT and Bubble Search, as well as other existing meta-heuristics developed in the literature based on simulated annealing (SA), tabu search and genetic algorithms (GAs). This algorithm is compared also to other ant colony implementations for QAP. The experimental results show that the proposed ant colony optimization/extended great deluge (ACO/EGD) performs significantly better than the existing construction and improvement algorithms. The experimental results indicate also that the ACO/EGD heuristic methodology offers advantages over other algorithms based on meta-heuristics in terms of solution quality.