Solving unequal-area static and dynamic facility layout problems using modified particle swarm optimization

Heuristics for the dynamic facility layout problem with unequal-area departments

Most facility layout problems have departments with unequal areas and have significant rearrangement costs. This paper describes a model and improved algorithm which simultaneously handles these parameters. An existing algorithm solves the dynamic facilities layout problem while permitting the departments to have unequal areas. One part of the algorithm solves a mixed integer programming problem to find the desired block diagram layout. This large, complex problem could only be solved optimally for small problems. Therefore a preprocessing method was developed to prespecify certain obvious department pair orientations, which had previously required binary variables. The method uses estimated location, department sizes, and flow costs to determine the probable variable values. Then, a revised branch and bound strategy solves for the less obvious department pair orientations. Test results show a significant cost reduction on a variety of previously published problems, and feasible solutions to previously unsolved problems. The algorithm found a layout solution to the standard . CRAFT problem which has 10 5% lower costs than the previously best published layout.

The dynamic facility layout problem (DFLP) deals with the arrangement of facilities/departments in a factory for different periods so that the location of the facilities can be changed from one period to another one. Traditionally, this problem is formulated to minimize the sum of material handling and rearrangement costs in the planning horizon by assuming that all parameters are deterministic. In this paper, we assume that the material flow between departments and rearrangement costs are uncertain and, accordingly, develop the robust counterpart (RC) of the DFLP model. The model is computationally intractable; therefore, we propose a hybrid algorithm based on nested partitions (NP) and simulated annealing (SA) algorithms, namely NP-SA. Moreover, we develop a heuristic algorithm to compute the values of the additional variables used in the RC model. The numerical results indicate that the NP-SA algorithm is very effective in giving a good solution in a short time. Furthermore, a simulation study demonstrates that, on average, robust solutions are better than nominal solutions.

The problem of rearranging manufacturing facilities over time is known as Dynamic Facility Layout Problem (DFLP). The objective is to minimize the sum of the material handling and the rearrangement costs. The problem is NP-hard and has begun to receive attention very recently. In this paper, an approximate algorithm/ heuristic for solving DFLP is presented. The proposed heuristics has been applied to eight different data sets of a problem set (containing 48 data sets) given by Balakrishnan and Cheng [1], and it has been found that the proposed heuristic provide good solutions having about 12% of deviation from the best known solution available in the published literature. Further, as a future scope of research work, an improvement heuristic can be developed or some meta-heuristic approach such as simulated annealing, and tabu search can be further applied to improve the solution quality obtained from the proposed approximate algorithm.

Hybrid ant systems for the dynamic facility layout problem

During the past few decades, developing efficient methods to solve dynamic facility layout problems has been focused on significantly by practitioners and researchers. More specifically meta-heuristic algorithms, especially genetic algorithm, have been proven to be increasingly helpful to generate sub-optimal solutions for large-scale dynamic facility layout problems. Nevertheless, the uncertainty of the manufacturing factors in addition to the scale of the layout problem calls for a mixed genetic algorithm–robust approach that could provide a single unlimited layout design. The present research aims to devise a customized permutation-based robust genetic algorithm in dynamic manufacturing environments that is expected to be generating a unique robust layout for all the manufacturing periods. The numerical outcomes of the proposed robust genetic algorithm indicate significant cost improvements compared to the conventional genetic algorithm methods and a selective number of other heuristic and meta-heuristic techniques.

Finding positions of departments on the plant floor for multiple periods while minimizing the sum of material handling and rearrangement costs is the base consideration of dynamic facility layout problems (DFLP). In this paper, a new kind of DFLP using flexible bay structure is studied. In a plant layout, based on flexible bay structure, departments are assigned to parallel bays in a plant floor. Departments could be free oriented and may have unequal areas as well as a mixed integer programming formulated to find optimal solutions. Due to complexity, only small-size problems could be solved in logical time while using exact methods. Therefore, a genetic algorithm (GA) was proposed to solve this optimization problem. This method was tested on some test problems of the DFLP literature. The results show the effectiveness of the proposed algorithm.

Solutions for the constrained dynamic facility layout problem

In this chapter we discuss the ant colony optimization meta-heuristic (ACO) and its application to static and dynamic constraint satisfaction optimization problems, in particular the static and dynamic maximum satisfiability problems (MAX-SAT). In the first part of the chapter we give an introduction to meta-heuristics in general and ant colony optimization in particular, followed by an introduction to constraint satisfaction and static and dynamic constraint satisfaction optimization problems. Then, we describe how to apply the ACO algorithm to the problems, and do an analysis of the results obtained for several benchmarks. The adapted ant colony optimization accomplishes very well the task of dealing with systematic changes of dynamic MAX-SAT instances derived from static problems.

Certain dynamic and static contact problems of the theory of elasticity for a circular cylinder of finite size

This paper proposes an integrated approach for dynamic facility layout problem considering the material handling equipment (MHE). The objectives of this problem are minimization of the fixed costs of MHE, minimization of material handling cost (MHC) and minimization of machine rearrangement costs (MRC). To be more realistic, MHE fixed costs, MRC and MHC, which might be of different importance to decision maker, are considered separately in three objective functions. An integrated model is proposed which is able to simultaneously select the MHE along with the arranging and re-arranging facilities. The model belongs to the class of multi-objective nonlinear mathematical programming models. Considering the NP-hard nature of the model and inspiring the existing water flow like algorithm, a novel Pareto-based meta-heuristic algorithm called multi-objective water flow like algorithm (MOWFA)is developed to solve the problem. We comprehensively discuss the parameter tuning of the algorithms utilizing Taguchi method. Finally, the performance of the proposed MOWFA is evaluated against two well-known meta-heuristic algorithms called non-dominated sorting genetic algorithm (NSGA-II) and non-dominated ranking genetic algorithm (NRGA). Computational results indicate the greater efficiency of the algorithm compared to the two addressed algorithms for solving the given multi-objective problem.

An Improved Pigeon-inspired Optimization Algorithm for Solving Dynamic Facility Layout Problem with Uncertain Demand

The unequal area facility layout problem (UA-FLP) refers to the reasonable arrangement of a certain number of facilities in a given layout area. The facility layout should satisfy given layout constraints and optimize given optimization objectives as far as possible. In this paper, a method combining improved lowest horizontal line method and particle swarm optimization algorithm is proposed to solve UA-FLP, which achieves multi-objective optimization of material handling cost, the adjacent value and the utilization rate of floor shop. On the one hand, the algorithm formulates facility packing rules through the improved lowest horizontal line method, which simplifies the legalization of facility layout. On the other hand, a modified particle swarm optimization (PSO) algorithm combining objective space division method (OSD) and niche technology is used for multi-objective optimization. The proposed algorithm overcomes the shortcomings of previous facility layout methods such as complex overlapping interference process, large amount of calculation and long time for multi-objective optimization. Compared with the comparison methods, the results show that material handling cost is reduced by 1%–6% and the utilization ratio of floor shop is increased by 2%–7%.

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.

An evolutionary optimal green layout design for a production facility by simulated annealing algorithm