6 results
Search Results
2. Randomized priority algorithms
- Author
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Angelopoulos, Spyros and Borodin, Allan
- Subjects
- *
COMPUTER scheduling , *MATHEMATICAL optimization , *CASE studies , *APPROXIMATION theory , *ALGORITHMS , *MATHEMATICAL analysis - Abstract
Abstract: Borodin, Nielsen and Rackoff introduced the class of priority algorithms as a framework for modeling deterministic greedy-like algorithms. In this paper we address the effect of randomization in greedy-like algorithms. More specifically, we consider approximation ratios within the context of randomized priority algorithms. As case studies, we prove inapproximation results for two well-studied optimization problems, namely facility location and makespan scheduling. [Copyright &y& Elsevier]
- Published
- 2010
- Full Text
- View/download PDF
3. Scheduling with families of jobs and delivery coordination under job availability
- Author
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Li, Shisheng and Yuan, Jinjiang
- Subjects
- *
PRODUCTION scheduling , *CONSUMERS , *ALGORITHMS , *MATHEMATICAL analysis , *NP-complete problems , *MATHEMATICAL optimization , *MACHINE theory - Abstract
Abstract: We consider in this paper the scheduling of families of jobs in which both processing and delivery are coordinated together. Only one vehicle is available to deliver the jobs to specified customers. The jobs can be processed together to form processing batches on the machine and setups of batches are required when the machine is changing from one family to another. Jobs from different families cannot be transported together by the vehicle. The objective is to minimize the time when the vehicle finishes delivering the last delivery batch to its customer and returns to the machine. We propose an -time optimal algorithm for the scheduling problem under the group technology assumption. For the scheduling problem without the group technology assumption, we show that the problem is NP-hard and give an -time dynamic programming algorithm, where is the number of jobs, and is the number of families; we also provide a heuristic algorithm with a performance ratio of 3/2. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
4. Two semi-online scheduling problems on two uniform machines
- Author
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Ng, C.T., Tan, Zhiyi, He, Yong, and Cheng, T.C.E.
- Subjects
- *
COMPUTER networks , *SCHEDULING software , *ALGORITHMS , *MACHINE learning , *MATHEMATICAL optimization , *MATHEMATICAL analysis , *MAXIMA & minima - Abstract
Abstract: This paper considers two semi-online scheduling problems, one with known optimal value and the other with known total sum, on two uniform machines with a machine speed ratio of . For the first problem, we provide an optimal algorithm for , and improved algorithms or/and lower bounds for , over which the optimal algorithm is unknown. As a result, the largest gap between the competitive ratio and the lower bound decreases to 0.02192. For the second problem, we also present algorithms and lower bounds for . The largest gap between the competitive ratio and the lower bound is 0.01762, and the length of the interval over which the optimal algorithm is unknown is 0.47382. Our algorithms and lower bounds for these two problems provide insights into their differences, which are unusual from the viewpoint of the known results on these two semi-online scheduling problems in the literature. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
5. Comparing evolutionary algorithms to the (1+1) -EA
- Author
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Borisovsky, P.A. and Eremeev, A.V.
- Subjects
- *
ALGORITHMS , *MATHEMATICAL optimization , *MATHEMATICAL models , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, we study the conditions in which the random hill-climbing algorithm (1 + 1)-EA compares favorably to other evolutionary algorithms (EAs) in terms of fitness function distribution at a given iteration and with respect to the average optimization time. Our approach is applicable when the reproduction operator of an evolutionary algorithm is dominated by the mutation operator of the (1 + 1)-EA. In this case one can extend the lower bounds obtained for the expected optimization time of the (1 + 1)-EA to other EAs based on the dominated reproduction operator. This method is demonstrated on the sorting problem with HAM landscape and the exchange mutation operator. We consider several simple examples where the (1 + 1)-EA is the best possible search strategy in the class of the EAs. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
6. Ant colony optimization theory: A survey
- Author
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Dorigo, Marco and Blum, Christian
- Subjects
- *
MATHEMATICAL optimization , *COMBINATORIAL optimization , *ALGORITHMS , *MATHEMATICAL analysis - Abstract
Abstract: Research on a new metaheuristic for optimization is often initially focused on proof-of-concept applications. It is only after experimental work has shown the practical interest of the method that researchers try to deepen their understanding of the method''s functioning not only through more and more sophisticated experiments but also by means of an effort to build a theory. Tackling questions such as “how and why the method works’’ is important, because finding an answer may help in improving its applicability. Ant colony optimization, which was introduced in the early 1990s as a novel technique for solving hard combinatorial optimization problems, finds itself currently at this point of its life cycle. With this article we provide a survey on theoretical results on ant colony optimization. First, we review some convergence results. Then we discuss relations between ant colony optimization algorithms and other approximate methods for optimization. Finally, we focus on some research efforts directed at gaining a deeper understanding of the behavior of ant colony optimization algorithms. Throughout the paper we identify some open questions with a certain interest of being solved in the near future. [Copyright &y& Elsevier]
- Published
- 2005
- Full Text
- View/download PDF
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