Track: Operations Research
Abstract
This article presents a novel direct search method of optimization, Game of Patterns (GoP) method, so-called by the author, for solving unconstrained mixed integer nonlinear optimization problems. The GoP method is based on: a set of η random patterns search, which initially forms the set of η active players, namely, {H[0]1,...,H[0]η}; and a game rule framework. At each κth game round, each pth player H[k]p will explore inside his own pattern in the current κth round, if the player is active. The strategy of each pth player is given by a random quantity S[k]p, which will allow each player to explore inside his own pattern by a set of trial S[k]p points. At the beginning of each κth game round, each active pth player bets according to his budget Mp for each round. At the end of each κth round, the player that had identified the best objective function value is considered the winner of the κth round, therefore the rest of active players must pay off the winner their bets. This process is recurrently repeated until that had been disqualified players from the game. It is worthwhile to point out that any player will be disqualified if his balance account is less than his budget for each round.