Block approach—tabu search algorithm for single machine total weighted tardiness problem

On heuristic search for the single machine total weighted tardiness problem – Some theoretical insights and their empirical verification

Single machine total weighted tardiness problem (SMTWTP) is one of the fundamental combinatorial optimization problems. The problem consists of a set of independent jobs with distinct processing times, weights, and due dates to be scheduled on a single machine. The goal of the problem is to minimize the total weighted tardiness. Several swarm intelligence (SI) motivated techniques have been proposed to solve SMTWTP. Still, the solution for large scale SMTWTP instances within a reasonable amount of time is a challenging task. Artificial bee colony (ABC) algorithm is one of the efficient SI based techniques to solve real world optimization problems. This article presents an effective amended ABC based strategy to solve SMTWTP. A local search (LS) approach, influenced from the lunar cycle is proposed and hybridized with ABC to escalate the exploitation capacity of the algorithm. The proposed LS approach is titled as the lunar inspired LS (LLS) approach and the proposed hybridized strategy is known as lunar inspired ABC (LuABC) algorithm. The proposed LuABC algorithm has been applied on 25 large SMTWTP instances of job size 1000. The obtained outcomes prove that the proposed algorithm obtains the optimum solutions for all the considered instances within a reasonable amount of time.

Scheduling of jobs has been a challenging task in manufacturing and the most real life scheduling problems, which involves multi-objectives and multi-machine environments. This paper presents tabu search and simulated annealing approaches for scheduling jobs on identical parallel machines. The identical parallel machine scheduling problem has been considered to minimize the mean tardiness for the jobs. Initially, an initial solution has been obtained using EDD dispatching rule then, simulated annealing and tabu search have been applied to reach a near optimal solution. Computational experiments are performed on problems with up to 10 machines and 150 jobs. The computational results indicate that the two proposed approaches are capable of obtaining better solutions for the given scheduling problem. Moreover, the tabu search approach provides better solution then simulated annealing approach.

An efficient tabu search approach for the two-machine preemptive open shop scheduling problem

The cell planning problem with capacity expansion is examined in wireless communications. The problem decides the location and capacity of each new base station to cover expanded and increased traffic demand. The objective is to minimize the cost of new base stations. The coverage by the new and existing base stations is constrained to satisfy a proper portion of traffic demands. The received signal power at the base station also has to meet the receiver sensitivity. The cell planning is formulated as an integer linear programming problem and solved by a tabu search algorithm. In the tabu search intensification by add and drop move is implemented by short-term memory embodied by two tabu lists. Diversification is designed to investigate proper capacities of new base stations and to restart the tabu search from new base station locations. Computational results show that the proposed tabu search is highly effective. A 10% cost reduction is obtained by the diversification strategies. The gap from the optimal solutions is approximately 1/spl sim/5% in problems that can be handled in appropriate time limits. The proposed tabu search also outperforms the parallel genetic algorithm. The cost reduction by the tabu search approaches 10/spl sim/20% in problems: with 2500 traffic demand areas (TDAs) in code division multiple access (CDMA).

A particle swarm optimization algorithm (PSO) has been used to solve the single machine total weighted tardiness problem (SMTWT) with unequal release date. To find the best solutions three different solution approaches have been used. To prepare subhybrid solution system, genetic algorithms (GA) and simulated annealing (SA) have been used. In the subhybrid system (GA and SA), GA obtains a solution in any stage, that solution is taken by SA and used as an initial solution. When SA finds better solution than this solution, it stops working and gives this solution to GA again. After GA finishes working the obtained solution is given to PSO. PSO searches for better solution than this solution. Later it again sends the obtained solution to GA. Three different solution systems worked together. Neurohybrid system uses PSO as the main optimizer and SA and GA have been used as local search tools. For each stage, local optimizers are used to perform exploitation to the best particle. In addition to local search tools, neurodominance rule (NDR) has been used to improve performance of last solution of hybrid-PSO system. NDR checked sequential jobs according to total weighted tardiness factor. All system is named as neurohybrid-PSO solution system.

In This work we present a particle swarm optimization algorithm to solve the single machine total weighted tardiness problem. A heuristic rule, the smallest position value (SPV) rule, is developed to enable the continuous particle swarm optimization algorithm to be applied to all classes of sequencing problems, which are NP-hard in the literature. A simple but very efficient local search method is embedded in the particle swarm optimization algorithm. The computational results show that the particle swarm algorithm is able to find the optimal and best-known solutions on all instances of widely used benchmarks from the OR library.

In this paper we present two recent metaheuristics, particle swarm optimization and differential evolution algorithms, to solve the single machine total weighted tardiness problem, which is a typical discrete combinatorial optimization problem. Most of the literature on both algorithms is concerned with continuous optimization problems, while a few deal with discrete combinatorial optimization problems. A heuristic rule, the smallest position value (SPV) rule, borrowed from the random key representation in genetic algorithms, is developed to enable the continuous particle swarm optimization and differential evolution algorithms to be applied to all permutation types of discrete combinatorial optimization problems. The performance of these two recent population based algorithms is evaluated on widely used benchmarks from the OR library. The computational results show that both algorithms show promise in solving permutation problems. In addition, a simple but very efficient local search method based on the variable neighbourhood search (VNS) is embedded in both algorithms to improve the solution quality and the computational efficiency. Ultimately, all the best known or optimal solutions of instances are found by the VNS version of both algorithms.

In this paper we present a population-based algo- rithm for solving permutational optimization problems. It con- sists in testing the feasible solutions which are the local minima. This method is based on the following observation: if there are the same elements in some positions in several permutations, which are local minima, then one can suppose that these ele- ments can be in the same positions in the optimal solution. The presented properties and ideas can be applied to two classical strongly NP-hard scheduling problems: 1. single machine total weighted tardiness problem 2. flow shop problem with goal function Cmax. Computational experiments on the benchmark instances from the OR-Library (3) are presented and compared with the results yielded by the best algorithms discussed in the literature. These results show that the algorithm proposed allows us to obtain the best known results for the benchmarks in a short time.

Biogeography-based Optimization (BBO) Algorithm for Single Machine Total Weighted Tardiness Problem (SMTWTP)

This paper describes a successful combination of genetic algorithm and local search procedure to find good solutions for just-in-time job-shop scheduling problem with earliness and tardiness penalties. For each job is given a specific order of machines in which its operations must be processed, and each operation has a due date, a processing time, and earliness and tardiness penalties, which are paid if the operation is completed before or after its due date. The problem is very hard to solve to optimality even for small instances, but the proposed genetic algorithm found good solutions for some problem instances, even improving its performance when a local search procedure is invoked as an additional phase. The quality of the solutions is evaluated and compared to a set of instances from the literature, with up to 20 jobs and 10 machines. The proposed algorithm improved the solution value for most of the instances.

This study considers a single machine scheduling problem with the objective of minimizing the total weighted tardiness of the jobs. This problem is one of the most famous problems in single machine scheduling theory and it is NP-hard. In this paper, we propose a hybrid heuristic which combines GRASP with Path Relinking to find good quality solutions for the considered problem. The performance of the hybrid GRASP heuristic is tested over multiple benchmark problems from the OR-Library with up to 100 jobs and experimental results show that it is very competitive with the existing good performing algorithms.

A composite heuristic for the single machine early/tardy job scheduling problem

Tabu search techniques have been applied to a wide class of optimization problems. Tabu search is a meta procedure that requires a subroutine to find local optima. In most examples of tabu search the subroutine used is problem specific. However, in order to apply tabu search successfully to general 0-1 integer programs, the subroutine must be general. The pivot and complement heuristic is a procedure that frequently finds feasible solutions for general 0-1 integer programs. In this paper we implement several elements of strategies proposed by tabu search method that result in general heuristics for 0-1 integer programs that could be included in an integer programming code. These heuristics employ the ZOOM/XMP implementation of the pivot and complement heuristic as a subroutine. Computational results indicate that these heuristics provide good bounds for many problems. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Tabu search (TS) is a metaheuristic that guides a local heuristic search procedure to explore the solution space beyond local optimality. It has achieved widespread successes in solving practical optimization problems. This paper proposes the stochastic TS strategy for discrete optimization and makes an investigation of its global convergence. The strategy considered introduces the Metropolis criterion and simulated annealing process into a general framework of TS. It has been proved that the strategy converges asymptotically to global optimal solutions, and satisfies the necessary and sufficient conditions for global asymptotic convergence. Furthermore, it produces a higher convergent rate than the simulated annealing algorithm.