A probabilistic cooperative-competitive hierarchical model for global optimization

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.