A problem space algorithm for single machine weighted tardiness problems (original) (raw)
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Single Machine Total Weighted Tardiness Problem with Genetic Algorithms
2007 IEEE/ACS International Conference on Computer Systems and Applications, 2007
Scheduling problems are important NP-hard problems. Genetic algorithms can provide good solutions for such optimization problems. In this paper, we present a genetic algorithm to solve the single machine total weighted tardiness scheduling problem, which is a strong NP-hard problem. The algorithm uses the natural permutation representation of a chromosome, heuristic dispatching rules combined with random method to create the initial population, position-based crossover and order-based mutation operators, and the best members of the population during generations. The computational results of problem examples with 10 and 25 jobs and general problems with 50, 100, 200 and 500 jobs show the good performance and the efficiency of the developed algorithm.
Local Search Heuristics for the Single Machine Total Weighted Tardiness Scheduling Problem
INFORMS Journal on Computing, 1998
This paper presents several local search heuristics for the problem of scheduling a single machine to minimize total weighted tardiness. We introduce a new binary encoding scheme to represent solutions, together with a heuristic to decode the binary representations into actual sequences. This binary encoding scheme is compared to the usual “natural” permutation representation for descent, simulated annealing, threshold accepting, tabu search and genetic algorithms on a large set of test problems. Computational results indicate that all of the heuristics which employ our binary encoding are very robust in that they consistently produce good quality solutions, especially when multistart implementations are used instead of a single long run. The binary encoding is also used in a new genetic algorithm which performs very well and requires comparatively little computation time. A comparison of neighborhood search methods which use the permutation and binary representations shows that the...
The International Journal of Advanced Manufacturing Technology, 2004
In this paper, an intensive search evolutionary algorithm is proposed to solve single machine total weighted tardiness scheduling problems. A specialised locally improved random swap mutation operator and an ordered crossover operator are used for evolution. The proposed algorithm starts with a pair of sequences: one generated by a greedy heuristic, namely, a backward phase heuristic acts as one parent, and a randomly generated sequence acts as the other. A computational experiment is conducted by applying the mutation operator on the backward phase sequence and the proposed algorithm with the same number of generations as the termination criteria. A total of 125 benchmark instances for sizes 40, 50 and 100 available in the OR library are solved and the results are compared with the available best-known results. It is observed that the proposed evolutionary algorithm provides better results than others.
Hybrid heuristic algorithms for single machine total weighted tardiness scheduling problems
International Journal of Intelligent Systems Technologies and Applications, 2008
This paper addresses on solving a well known Non Polynomial (NP) hard type problem, namely the single machine total weighted-tardiness problem. The performances of three hybrid heuristic algorithms to solve the single machine scheduling problems with the objective of minimising the total weighted tardiness are presented and compared. In the first hybrid algorithm, a dynamic dispatching rule, namely Modified Due Date (MDD), is hybridised with local search mechanism. In the second hybrid algorithm, a greedy heuristic, namely backward phase, is proposed and hybridised with local search mechanisms. The third hybrid algorithm hybridises the backward phase heuristics with an iterated local search (ILS) having an evolutionary perturbation tool. The algorithms are tested by solving all the 125 benchmark problem instances available in the OR-Library for different sizes and compared with the best known values. It is observed that the hybrid algorithm with evolutionary perturbation tool is performing better than the others.
Operations Research Letters, 2004
Based on the work by Congram, Potts and Van de Velde, we develop for the single-machine total weighted tardiness scheduling problem an enhanced dynasearch neighborhood obtained by the generalized pairwise interchange (GPI) operators. Despite of the wider neighborhood considered, a fast search procedure using also elimination criteria is developed. The computational results signiÿcantly improve over those of Congram, Potts and Van de Velde.
Metaheuristics for the single machine weighted quadratic tardiness scheduling problem
Computers & Operations Research
This paper considers the single machine scheduling problem with weighted quadratic tardiness costs. Three metaheuristics are presented, namely iterated local search, variable greedy and steady-state genetic algorithm procedures. These address a gap in the existing literature, which includes branch-andbound algorithms (which can provide optimal solutions for small problems only) and dispatching rules (which are efficient and capable of providing adequate solutions for even quite large instances). A simple local search procedure which incorporates problem specific information is also proposed. The computational results show that the proposed metaheuristics clearly outperform the best of the existing procedures. Also, they provide an optimal solution for all (or nearly all, in the case of the variable greedy heuristic) the smaller size problems. The metaheuristics are quite close in what regards solution quality. Nevertheless, the iterated local search method provides the best solution, though at the expense of additional computational time. The exact opposite is true for the variable greedy procedure, while the genetic algorithm is a good all-around performer.
Heuristic Algorithm for the Parallel Machine Total Weighted Tardiness Scheduling Problem
This paper presents a heuristic algorithm for the parallel machine weighted tardiness scheduling problem (P || w j T j ). The main innovative feature of the algorithm is its representation of a multi-machine schedule by a single sequence, greatly simplifying the treatment of that problem. The single sequence is optimized using an iterated local search over generalized pairwise interchange moves, improved with a suitable tie breaking criterion. Extensive tests on instances, with 2 and 4 machines, and with up to 50 jobs, obtained very good results, finding optimal solutions in almost all cases.
This paper addresses Single-machine total weighted tardiness scheduling problem with dependent setup time. The problem, even in absence of setup time, is strongly NP-hard and cannot be solved using common optimization methods in reasonable time. In this paper, first a mathematical model for solving the problem is presented and then, two meta-heuristics; Genetic Algorithm (GA) and Simulated Annealing (SA), as well as a hill climbing heuristic are suggested. Each algorithm is examined individually and then two hybrid models are considered. The computational result shows that SA performs more efficient among the non-hybrid models while the hybrid of SA and Hill climbing is the best solution in general.
A hybrid algorithm for the single-machine total tardiness problem
Computers & Operations Research, 2009
We propose a hybrid algorithm based on the Ant Colony Optimization (ACO) meta-heuristic, in conjunction with four well-known elimination rules, to tackle the N P -hard single-machine scheduling problem to minimize the total job tardiness. The hybrid algorithm has the same running time as that of ACO. We conducted extensive computational experiments to test the performance of the hybrid algorithm and ACO. The computational results show that the hybrid algorithm can produce optimal or near-optimal solutions quickly, and its performance compares favourably with that of ACO for handling standard instances of the problem.