A Review of the Application of Meta-Heuristic Algorithms to 2D Strip Packing Problems

This paper is a review of the approachesdeveloped to solve 2D packing problems withmeta-heuristic algorithms. As packing tasks arecombinatorial problems with very large searchspaces, the recent literature encourages theuse of meta-heuristic search methods, inparticular genetic algorithms. The objective ofthis paper is to present and categorise thesolution approaches in the literature for 2Dregular and irregular strip packing problems.The focus is hereby on the analysis of themethods involving genetic algorithms. Anoverview of the methods applying othermeta-heuristic algorithms including simulatedannealing, tabu search, and artificial neuralnetworks is also given.     

A hybrid meta-heuristic for multi-objective vehicle routing problems with time windows

The Capacitated Vehicle Routing Problem with Time Windows is an important combinatorial optimization problem consisting in the determination of the set of routes of minimum distance to deliver goods, using a fleet of identical vehicles with restricted capacity, so that vehicles must visit customers within a time frame. A large number of algorithms have been proposed to solve single-objective formulations of this problem, including meta-heuristic approaches, which provide high quality solutions in reasonable runtimes. Nevertheless, in recent years some authors have analyzed multi-objective variants that consider additional objectives to the distance travelled. This paper considers not only the minimum distance required to deliver goods, but also the workload imbalance in terms of the distances travelled by the used vehicles and their loads. Thus, MMOEASA, a Pareto-based hybrid algorithm that combines evolutionary computation and simulated annealing, is here proposed and analyzed for solving these multi-objective formulations of the VRPTW. The results obtained when solving a subset of Solomon’s benchmark problems show the good performance of this hybrid approach.     

Meta-heuristics for a complex push–pull production system

Hybrid push/pull production systems have received recent attention in the literature. This paper investigates a hybrid push/pull system originating from a foundry. The aim is to determine safety stock and replenishment levels for a large inventory situated at the junction point between component production and assembly operations. Components are produced according to a make-to-stock policy and are received into inventory when completed. Assembled goods are made-to-order, pulling components from the inventory when required. Classical techniques cannot be used in such a complex environment because they are based on invalid assumptions. This study proposes heuristically controlled simulations for attaining good solutions to the problem. Experimental results demonstrate and compare the proposed methods.     

基于格局变换策略的不等圆Packing问题求解算法*

采用基于格局变换策略的算法ACP-Solver求解不等圆Packing问题。ACP-Solver由连续优化方法、格局变换算子和接收准则组成。连续优化方法可从任一初始格局收敛至对应的局部最优格局。格局变换算子将当前格局变换为新格局。接收准则决定是否接收变换所得格局。基于24个国际公开算例的计算实验表明,ACP-Solver能在可接受的计算时间内改进或持平绝大多数算例的当前最优记录。实验结果表明了ACP-Solver的高效性能。     

An effective approach to multi-item capacitated dynamic lot-sizing problems

In this study we solve the multi-item capacitated dynamic lot-sizing problem, where each item faces a series of dynamic demands, and in each period multiple items share limited production resources. The objective is to find the optimal production plan so as to minimise the total cost, including production cost, inventory holding cost, and fixed setup cost. We consider both single-level and multi-level cases. In the multi-level case, some items are consumed in order to produce some other items and therefore items face internally generated demand in addition to external demands. We propose a simple three-stage approach that is applicable to both classes of problems. In the first stage we perform preprocessing, which is designed to deal with the difficulty due to the joint setup cost (a fixed cost incurred whenever production occurs in a period). In the second stage we adopt a period-by-period heuristic to construct a feasible solution, and in the final stage we further improve the solution by solving a series of subproblems. Extensive experiments show that the approach exhibits very good performance. We then analyse how the superior performance is achieved. In addition to its performance, one appealing feature of our method is its simplicity and general applicability.     

The generalised machine layout problem

The Generalised MAchine Layout Problem (GMALP) is a generalisation of the integrated machine and layout problem, which is an extension of the machine layout problem. More specifically, the GMALP is the designing of a facility layout by defining the product mix, selecting the number of machines to be used, assigning these machines to the plant floor, and assigning products to machines such that total profit is maximised. Moreover, the GMALP integrates the quadratic assignment problem with a multicommodity flow problem. Therefore, the GMALP is a computationally intractable problem. Consequently, a mixed-integer nonlinear programming model was developed and used to solve small problem instances. Also, two simple construction algorithms and a tabu search (TS) heuristic were developed for solving large GMALP instances in acceptable computation times. In addition, a test dataset was used to evaluate the performances of the TS heuristic using the different construction algorithms. The results show that the TS heuristic perform slightly better with the second construction algorithm.     

Simultaneous balancing and sequencing of mixed-model parallel two-sided assembly lines

Growing interests from customers in customised products and increasing competitions among peers necessitate companies to configure their manufacturing systems more effectively than ever before. We propose a new assembly line system configuration for companies that need intelligent solutions to satisfy customised demands on time with existing resources. A mixed-model parallel two-sided assembly line system is introduced based on the parallel two-sided assembly line system previously proposed in the literature. The mixed-model parallel two-sided assembly line balancing problem is illustrated with examples from the perspective of simultaneous balancing and sequencing. An agent-based ant colony optimisation algorithm is proposed to solve the problem. This algorithm is the first attempt in the literature to solve an assembly line balancing problem with an agent-based ant colony optimisation approach. The algorithm is illustrated with an example and its operational procedures and principles are explained and discussed.     

Meta-heuristics for the distributed two-stage assembly scheduling problem with bi-criteria of makespan and mean completion time

This paper focuses on the distributed two-stage assembly flowshop scheduling problem for minimising a weighted sum of makespan and mean completion time. This problem involves two inter-dependent decision sub-problems: (1) how to allocate jobs among factories and (2) how to schedule the assigned jobs at each factory. A mathematical model is formulated for solving the small-sized instances of the problem. Since the NP-hardness of the problem, we also proposed a variable neighbourhood search (VNS) algorithm and a hybrid genetic algorithm combined with reduced variable neighbourhood search (GA-RVNS) to solve the distributed two-stage assembly flowshop scheduling problems and approximately optimise makespan and mean completion time simultaneously. Computational experiments have been conducted to compare the performances of the model and proposed algorithms. For a set of small-sized instances, both the model and the proposed algorithms are effective. The proposed algorithms are further evaluated on a set of large-sized instances. The results statistically show that both GA-RVNS and VNS obtain much better performances than the GA without RVNS-based local search step (GA-NOV). For the instances with small numbers of jobs, VNS achieves better performances than GA-RVNS. However, for the instances with large numbers of jobs, GA-RVNS yields better performances than the VNS. It is also shown that the overall performances of VNS are very close to GA-RVNS with different numbers of factories, weights given to makespan and numbers of machines at the first stage.     

Scheduling flexible manufacturing cells using Tabu Search

Scheduling is an important aspect in the overall control of a flexible manufacturing system. The research presented focuses on production scheduling of jobs within a flexible manufacturing cell (FMC)–one type of flexible manufacturing system. Due to the complexity of the FMC scheduling problem, a 0–1 mixed-integer linear programming (MILP) model is formulated for M machines and N jobs with alternative routings. Although small instances of the problem can be solved optimally with MILP models, a two-stage Tabu Search (TS² ) algorithm that minimises the manufacturing makespan (MS) is proposed to solve medium-to-large-scale problems more efficiently. During Stage I (construction phase), two heuristics are utilised to generate an initial feasible sequence and an initial MS solution. In Stage II (improvement phase), the acquired initial solutions from Stage I are combined with a Tabu Search meta-heuristic procedure that provides improved MS solutions. The TS² algorithm provides tremendous savings in computational time for medium/large-sized multi-machine FMC problems.     

Combining Meta-Heuristics to Effectively Solve the Vehicle Routing Problems with Time Windows

The vehicle routing problemswith time windows are challenging deliveryproblems in which instances involving 100customers or more can be difficult to solve.There were many interesting heuristics proposedto handle these problems effectively. In thispaper, we examined two well-knownmeta-heuristics and carefully combined theshort-term and long-term memory-like mechanismsof both methods to achieve better results. Ourprototype was shown to compare favorablyagainst the original search methods and otherrelated search hybrids on the Solomon's testcases. More importantly, our proposal ofintegration opens up many exciting directionsfor further investigation.