Multilocal programming and applications

Preprint versionMultilocal programming aims to identify all local minimizers of unconstrained or constrained nonlinear optimization problems. The multilocal programming theory relies on global optimization strategies combined with simple ideas that are inspired in deflection or stretching techniques to avoid convergence to the already detected local minimizers. The most used methods to solve this type of problems are based on stochastic procedures and a population of solutions. In general, population-based methods are computationally expensive but rather reliable in identifying all local solutions. In this chapter, a review on recent techniques for multilocal programming is presented. Some real-world multilocal programming problems based on chemical engineering process design applications are described.Fundação para a Ciência e a Tecnologia (FCT

Game Tree Algorithms and Solution Trees

. In this paper a theory of game tree algorithms is presented, entirely based upon the concept of a solution tree. Two types of solution trees are distinguished: max and min trees. Every game tree algorithm tries to prune as many nodes as possible from the game tree. A cut-o# criterion in terms of solution trees will be formulated, which can be used to eliminate nodes from the search without a#ecting the result. Further, we show that any algorithm actually constructs a superposition of a max and a min solution tree. Finally, we will see how solution trees and the related cuto# criterion are applied in major game tree algorithms like alphabeta and MTD. Keywords: Game tree search, Minimax search, Solution trees, Alphabeta, SSS*, MTD. 1 Introduction A game tree models the behavior of a two-player game. Each node n in such a tree represents a position in a game. An example of a game tree with game values is found in Figure 1. The players are called Max and Min. Max is moving from the squ..

A partition-based global optimization algorithm

Global optimization, Partition-based algorithm, DIRECT-type algorithm,

The Reachability Problem over Infinite Graphs

Abstract. We survey classical and selected recent work on the reachability problem over finitely presented infinite graphs. The problem has a history of 100 years, and it is central for automatic verification of infinitestate systems. Our focus is on graphs that are presented in terms of word or tree rewriting systems.