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Genetic Algorithm Approach for Solving the Task Assignment Problem

Savić, Aleksandar, Tošić, Dušan, Marić, Miroslav, Kratica, Jozef (2008)

Serdica Journal of Computing

This research was partially supported by the Serbian Ministry of Science and Ecology under project 144007. The authors are grateful to Ivana Ljubić for help in testing and to Vladimir Filipović for useful suggestions and comments.In this paper a genetic algorithm (GA) for the task assignment problem (TAP) is considered.An integer representation with standard genetic operators is used. Computational results are presented for instances from the literature, and compared to optimal solutions obtained...

Global convergence property of modified Levenberg-Marquardt methods for nonsmooth equations

Shou-qiang Du, Yan Gao (2011)

Applications of Mathematics

In this paper, we discuss the globalization of some kind of modified Levenberg-Marquardt methods for nonsmooth equations and their applications to nonlinear complementarity problems. In these modified Levenberg-Marquardt methods, only an approximate solution of a linear system at each iteration is required. Under some mild assumptions, the global convergence is shown. Finally, numerical results show that the present methods are promising.

Greedy algorithms for optimal computing of matrix chain products involving square dense and triangular matrices

Faouzi Ben Charrada, Sana Ezouaoui, Zaher Mahjoub (2011)

RAIRO - Operations Research - Recherche Opérationnelle

This paper addresses a combinatorial optimization problem (COP), namely a variant of the (standard) matrix chain product (MCP) problem where the matrices are square and either dense (i.e. full) or lower/upper triangular. Given a matrix chain of length n, we first present a dynamic programming algorithm (DPA) adapted from the well known standard algorithm and having the same O(n3) complexity. We then design and analyse two optimal O(n) greedy algorithms leading in general to different optimal solutions...

Greedy algorithms for optimal computing of matrix chain products involving square dense and triangular matrices

Faouzi Ben Charrada, Sana Ezouaoui, Zaher Mahjoub (2011)

RAIRO - Operations Research

This paper addresses a combinatorial optimization problem (COP), namely a variant of the (standard) matrix chain product (MCP) problem where the matrices are square and either dense (i.e. full) or lower/upper triangular. Given a matrix chain of length n, we first present a dynamic programming algorithm (DPA) adapted from the well known standard algorithm and having the same O(n3) complexity. We then design and analyse two optimal O(n) greedy algorithms leading in general to different optimal solutions...

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