Abstract. In the paper, the global optimization problem of a multidimensional "black-box" function satisfying the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant is considered. A new efficient algorithm for solving this problem is presented. At each iteration of the method a number of possible Lipschitz constants is chosen from a set of values varying from zero to infinity. This idea is unified with an efficient diagonal partition strategy. A novel technique balancing usage of local and global information during partitioning is proposed. A new procedure for finding lower bounds of the objective function over hyperintervals is also considered. It is demonstrated by extensive numerical experiments performed on more than 1600 multidimensional test functions that the new algorithm shows a very promising performance.

Global optimization problems where evaluation of the objective function is an expensive operation arise frequently in engineering, decision making, optimal control, etc. There exist two huge but almost completely disjoint communities (they have different journals, different conferences, different test functions, etc.) solving these problems: a broad community of practitioners using stochastic nature-inspired metaheuristics and people from academia studying deterministic mathematical programming methods. In order to bridge the gap between these communities we propose a visual technique for a systematic comparison of global optimization algorithms having different nature. Results of more than 800,000 runs on 800 randomly generated tests show that both stochastic nature-inspired metaheuristics and deterministic global optimization methods are competitive and surpass one another in dependence on the available budget of function evaluations.

No abstract

No abstract

This is a summary of the author's PhD thesis, supervised by Yaroslav D. Sergeyev and defended on May 5, 2006, at the University of Rome "La Sapienza". The thesis is written in English and is available from the author upon request. In this work, the global optimization problem of a multidimensional "black-box" function satisfying the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant is considered. The objective function is assumed hard to evaluate. A new efficient diagonal scheme for constructing fast algorithms for solving this problem is examined and illustrated by developing several powerful global optimization methods. A deep theoretical study is performed which highlights the benefit of the approach introduced over traditionally used diagonal algorithms. Theoretical conclusions are confirmed by results of extensive numerical experiments.Keywords Global optimization · Black-box functions · Derivative-free methods · Partition strategies · Diagonal approach MSC classification (2000) 65K05 · 90C26 · 90C56 1 Problem statement Many decision-making problems arising in various fields of human activity (technological processes, engineering design, economic models, biology studies, etc.) can be