Ramon Companys

HEURISTICS AND EXACT ALGORITHMS FOR SOLVING THE MONDEN PROBLEM

Abstract Sequencing units on an assembly line in order to obtain a regular requirement of resources is a problem that can be modelled in a variety of ways. One of the most popular is known as the Monden problem, and the heuristic proposed to obtain a ‘satisfactory’ solution is called ‘goal-chasing’ ethod. In the paper the myopic behaviour of this heuristic is shown, and some improvements are proposed. An exact procedure, based on BDP, is also proposed. By relaxing the assumptions, the BDP procedure becomes a new, powerful heuristic. A sample of computational results is included.

Local search heuristics for the assembly line balancing problem with incompatibilities between tasks

This paper deals with the assembly line balancing problem considering incompatibilities between the tasks with the aim of: first minimizing the number of workstations, and then minimizing the cycle time for the minimum number of workstations. In order to solve the problem we propose the use of a greedy randomized adaptive search procedure obtained from the application of some classic heuristics based on priority rules, and a genetic algorithm that searches for the solution in the heuristic space. A computational experience is included to illustrate the performance of the proposed approach.

An efficient Discrete Artificial Bee Colony algorithm for the blocking flow shop problem with total flowtime minimization

A high performing DABC algorithm is proposed for the Fm|block|ΣCi.An efficient procedure to generate the initial food sources is presented.Some strategies for each phase of the algorithm were tested.The selection of the best strategies was decided by means a design of experiments. This paper presents a high performing Discrete Artificial Bee Colony algorithm for the blocking flow shop problem with flow time criterion. To develop the proposed algorithm, we considered four strategies for the food source phase and two strategies for each of the three remaining phases (employed bees, onlookers and scouts). One of the strategies tested in the food source phase and one implemented in the employed bees phase are new. Both have been proved to be very effective for the problem at hand. The initialization scheme named HPF2(λ,µ) in particular, which is used to construct the initial food sources, is shown in the computational evaluation to be one of the main procedures that allow the DABC_RCT to obtain good solutions for this problem. To find the best configuration of the algorithm, we used design of experiments (DOE). This technique has been used extensively in the literature to calibrate the parameters of the algorithms but not to select its configuration. Comparing it with other algorithms proposed for this problem in the literature demonstrates the effectiveness and superiority of the DABC_RCT.

Different behaviour of a double branch-and-bound algorithm on Fm|prmu|Cmax and Fm|block|Cmax problems

In this paper we face the permutation flow-shop scheduling problem with a makespan objective function in two variants, with and without storage space between machines. We use an improved branch and bound algorithm, suitable for parallel computation, to solve these problems, and auxiliary heuristics to attain an initial good solution. The auxiliary heuristics proposed are built by two steps: in the first step a permutation is obtained; in the second step a local search procedure is applied. The improvement obtained by the local search procedure on NEH heuristic as first step is shown. Since the flow-shop scheduling problem with storage space is a relaxation of the problem without storage space, some elements and procedures developed for that problem can be used in both problems. In particular, some bounding procedures, for instance Nabeshima or Lageweg bounding schema, can be adapted. Moreover, the reversibility property holds on both problems. Consequently a double branch and bound algorithm can be applied simultaneously to the direct and the inverse instances. The same sets of data are submitted to heuristics and to the double branch-and-bound algorithm, LOMPEN, assuming first they are instances of flow-shop scheduling problem with storage space and later they are instances of flow-shop scheduling problem without storage space. The algorithms are coded in a similar way; therefore the behaviour and performance can be compared.

Comparing three-step heuristics for the permutation flow shop problem

In this paper a three steps heuristic for the permutation flow shop problem is proposed. The objective is to minimize the maximum time for completing the jobs, or the makespan. The first two steps are inspired by the NEH heuristic, to which a new tie breaking strategy has been incorporated in the insertion phase. Furthermore, the reversibility property of the problem dealt with is taken as a tool for improving the obtained solution. The third step consists of an iterated local search procedure with an embedded local search which is a variant of the non exhaustive descent algorithm. The statistical analysis of the results shows the effectiveness of the proposed procedures.

A competitive variable neighbourhood search algorithm for the blocking flow shop problem

This paper analyses the performance of two variable neighbourhood search (VNS) methods for the Fm | block | Cmax problem. The main difference between both is the strategy used to change the neighbourhood in the improvement phase. The first strategy, named parallel version, randomly chooses between swap and insertion neighbourhoods to improve the solution. The second strategy, named serial version, begins the search in one of the neighbourhoods and continues the search in the other one. Additionally, we have analysed and improved the effectiveness of several NEH-based procedures to generate the initial solution. Moreover, we have tested each VNS strategy with two types of local search which led us to define four procedures that were tested with the Taillard benchmark and with a test-bed created ad hoc. The computational evaluation showed that these algorithms and especially the serial VNS which uses PW/PWE2 to generate the initial solution would be very competitive.

An efficient iterated local search algorithm for the total tardiness blocking flow shop problem

This paper deals with the blocking flow shop problem and proposes an Iterated Local Search (ILS) procedure combined with a variable neighbourhood search (VNS) for the total tardiness minimisation. The proposed ILS makes use of a NEH-based procedure to generate the initial solution, and uses a local search to intensify the exploration that combines the insertion and swap neighbourhood and uses a perturbation mechanism consisting of three neighbourhood operators to diversify the search. The computational evaluation has shown the effectiveness of combining the insertion and swap neighbourhood during the search despite the insertion neighbourhood being more effective than the swap neighbourhood for this problem. Finally, the computation of this algorithm when evaluated against two other algorithms from the literature shows good performance.

Modelling and solving the production rate variation problem (PRVP)

Several families of objective functions for the PRV problem (minimizing the variation in the rate at which different products are produced on an assembly line) are formalized, relationships between them are established and it is demonstrated that, in very general conditions, they can be optimized by solving an assignment problem or a polynomially bounded sequence of assignment problems.

Efficient heuristics for the parallel blocking flow shop scheduling problem

New Constructive heuristic for both the PBFSP and the DBFSP.Combination of IGA and ILS methods with two types of VNS.A MILP model solved for small-sized instances.The proposed methods are very effective. We consider the NP-hard problem of scheduling n jobs in F identical parallel flow shops, each consisting of a series of m machines, and doing so with a blocking constraint. The applied criterion is to minimize the makespan, i.e., the maximum completion time of all the jobs in F flow shops (lines). The Parallel Flow Shop Scheduling Problem (PFSP) is conceptually similar to another problem known in the literature as the Distributed Permutation Flow Shop Scheduling Problem (DPFSP), which allows modeling the scheduling process in companies with more than one factory, each factory with a flow shop configuration. Therefore, the proposed methods can solve the scheduling problem under the blocking constraint in both situations, which, to the best of our knowledge, has not been studied previously. In this paper, we propose a mathematical model along with some constructive and improvement heuristics to solve the parallel blocking flow shop problem (PBFSP) and thus minimize the maximum completion time among lines. The proposed constructive procedures use two approaches that are totally different from those proposed in the literature. These methods are used as initial solution procedures of an iterated local search (ILS) and an iterated greedy algorithm (IGA), both of which are combined with a variable neighborhood search (VNS). The proposed constructive procedure and the improved methods take into account the characteristics of the problem. The computational evaluation demonstrates that both of them -especially the IGA- perform considerably better than those algorithms adapted from the DPFSP literature.

Efficient heuristic algorithms for the blocking flow shop scheduling problem with total flow time minimization

Two efficient constructive heuristics for the Fm|block|ΣCi are proposed.We show that the insertion phase of heuristic NEH can worsen the solution.The structure of each constructive method is used in a GRASP combined with VNS.The computational evaluation shows the good performance of these algorithms. This paper proposes two constructive heuristics, i.e. HPF1 and HPF2, for the blocking flow shop problem in order to minimize the total flow time. They differ mainly in the criterion used to select the first job in the sequence since, as it is shown, its contribution to the total flow time is not negligible. Both procedures were combined with the insertion phase of NEH to improve the sequence. However, as the insertion procedure does not always improve the solution, in the resulting heuristics, named NHPF1 and NHPF2, the sequence was evaluated before and after the insertion to keep the best of both solutions. The structure of these heuristics was used in Greedy Randomized Adaptive Search Procedures (GRASP) with variable neighborhood search in the improvement phase to generate greedy randomized solutions. The performance of the constructive heuristics and of the proposed GRASPs was evaluated against other heuristics from the literature. Our computational analysis showed that the presented heuristics are very competitive and able to improve 68 out of 120 best known solutions of Taillards instances for the blocking flow shop scheduling problem with the total flow time criterion.