Efficient heuristics for the parallel blocking flow shop scheduling problem

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.Peer ReviewedPostprint (author's final draft

Variable Annealing Length and Parallelism in Simulated Annealing

In this paper, we propose: (a) a restart schedule for an adaptive simulated annealer, and (b) parallel simulated annealing, with an adaptive and parameter-free annealing schedule. The foundation of our approach is the Modified Lam annealing schedule, which adaptively controls the temperature parameter to track a theoretically ideal rate of acceptance of neighboring states. A sequential implementation of Modified Lam simulated annealing is almost parameter-free. However, it requires prior knowledge of the annealing length. We eliminate this parameter using restarts, with an exponentially increasing schedule of annealing lengths. We then extend this restart schedule to parallel implementation, executing several Modified Lam simulated annealers in parallel, with varying initial annealing lengths, and our proposed parallel annealing length schedule. To validate our approach, we conduct experiments on an NP-Hard scheduling problem with sequence-dependent setup constraints. We compare our approach to fixed length restarts, both sequentially and in parallel. Our results show that our approach can achieve substantial performance gains, throughout the course of the run, demonstrating our approach to be an effective anytime algorithm.Comment: Tenth International Symposium on Combinatorial Search, pages 2-10. June 201

Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

Makespan Minimization in Job Shop Scheduling

In industries, the completion time of job problems in the manufacturing unit has risen significantly. In several types of current study, the job's completion time, or makespan, is reduced by taking straight paths, which is time-consuming. In this paper, we used an Improved Ant Colony Optimization and Tabu Search (ACOTS) algorithm to solve this problem by precisely defining the fault occurrence location in order to rollback. We have used a short-term memory-based rollback recovery strategy to minimise the job's completion time by rolling back to its own short-term memory. The recent movements in Tabu quest are visited using short term memory. As compared to the ACO algorithm, our proposed ACOTS-Cmax solution is more efficient and takes less time to complete

A survey of parallel hybrid applications to the permutation flow shop scheduling problem and similar problems

Parallel algorithms have focused an increased interest due to advantages in computation time and quality of solutions when applied to industrial engineering problems. This communication is a survey and classification of works in the field of hybrid algorithms implemented in parallel and applied to combinatorial optimization problems similar to the to the permutation flowshop problem with the objective of minimizing the makespan, Fm|prmu|Cmax according to the Graham notation, the travelling salesman problem (TSP), the quadratic assignment problem (QAP) and, in general, those whose solution can be expressed as a permutation