Search

Abstract: In this paper, by solving the relaxed quasiconcave programming problem in outcome space, a new global optimization algorithm for convex multiplicative programming is presented. Two kinds of techniques are employed to establish the algorithm. The first one is outer approximation technique which is applied to shrink relaxation area of quasiconcave programming problem and to compute appropriate feasible points and to raise the capacity of bounding. And the other one is branch and bound technique which is used to guarantee global optimization. Some numerical results are presented to demonstrate the effectiveness and feasibility of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: Particle swarm optimization is a novel swarm-intelligence-based algorithm and a valid optimization technique. However, the algorithm suffers from the premature convergence problem when facing to complex optimization problem. In order to keep the balance between the global exploration and the local exploitation validly, the paper develops a knowledge-based cooperative particle swarm optimization (KCPSO). KCPSO mainly simulates the self-cognitive and self-learning process of evolutionary agents in special environment, and introduces a knowledge billboard to record varieties of search information. Moreover, KCPSO takes advantage of multi-swarm to maintain the swarm diversity and tries to guide their evolution by the shared information. Under the guide of the shared information, KCPSO manipulates each sub-swarm to go on with local exploitation in different local area, in which every particle follows a social learning behavior mode; at the same time, KCPSO carries out the global exploration through the escaping behavior and the cooperative behavior of the particles in different sub-swarms. KCPSO can maintain appropriate swarm diversity and alleviate the premature convergence validly. The proposed model was applied to some well-known benchmarks. The relative experimental results show KCPSO is a robust global optimization method for the complex multimodal functions. [Copyright &y& Elsevier]

Abstract: In this paper, a robust algorithm is proposed for globally solving a nonconvex quadratic programming problem (P1) with several additional multiplicative constraints. To our knowledge, little progress has been made so far for globally solving problem (P1). The proposed algorithm is based on a robust solution approach that provides an essential -optimal solution. This solution is also stable under small perturbations of the constraints, and it turns out that such a robust optimal solution is adequately guaranteed to be feasible and to be close to the actual optimal solution. Convergence of the algorithm is shown and three solved sample problems are given to illustrate the robust stability and feasibility of the present algorithm. [Copyright &y& Elsevier]

Abstract: Stochastic searching methods have been applied widely to areas such as continuous and combinatorial optimization problems in a number of disciplines. Many existing methods solve these problems by navigating on the surface of the possibly rugged landscape. This kind of navigation is not very effective because the property of the landscape at different resolutions can be very different. Time spent at the beginning of the search on the detailed part of the landscape is often useless. Appropriate searching strategies should be adopted at different resolutions. In this paper, we propose a new probabilistic searching model for global optimization. The main contributions of the model are (1) to provide a basis for resolution control and smoothing of search space and (2) to introduce continuous memory into stochastic search. The basis of resolution control is achieved by dividing the search space into a finite number of n-dimensional partitions structurally. The number of partitions governs the resolution of the search space. The more the partitions, the finer is the search space and the more detailed and rugged is the landscape. The benefits are twofold. First, the rugged landscape problem can be smoothed, because the ruggedness is a matter of the number of partitions. Hence, the difficulty in search due to the ruggedness of the landscape can be controlled. Second, it provides a basis to implement algorithms that may change the ‘view’ of the landscape during the search process because we can dynamically divide the search space accordingly. Another important feature that we use is continuous memory. Throughout the search process, searching experience is continuously accumulated in order to shape the global picture of the search space guiding the future searching direction. We present results on the algorithm performance in handling numerical function optimization. The empirical results show that our new model is comparable to, and in many cases performs better than, that of the other advanced methods in terms of solution quality and computation required. [Copyright &y& Elsevier]