Aimo A. Törn

Population set-based global optimization algorithms: some modifications and numerical studies

This paper studies the efficiency and robustness of some recent and well known population set-based direct search global optimization methods such as Controlled Random Search, Differential Evolution and the Genetic Algorithm. Some modifications are made to Differential Evolution and to the Genetic Algorithm to improve their efficiency and robustness. All methods are tested on two sets of test problems, one composed of easy but commonly used problems and the other of a number of relatively difficult problems.

Stochastic Global Optimization: Problem Classes and Solution Techniques

There is a lack of a representative set of test problems for comparing global optimization methods. To remedy this a classification of essentially unconstrained global optimization problems into unimodal, easy, moderately difficult, and difficult problems is proposed. The problem features giving this classification are the chance to miss the region of attraction of the global minimum, embeddedness of the global minimum, and the number of minimizers. The classification of some often used test problems are given and it is recognized that most of them are easy and some even unimodal. Global optimization solution techniques treated are global, local, and adaptive search and their use for tackling different classes of problems is discussed. The problem of fair comparison of methods is then adressed. Further possible components of a general global optimization tool based on the problem classes and solution techniques is presented.

Application of stochastic global optimization algorithms to practical problems

We describe global optimization problems from three different fields representing many-body potentials in physical chemistry, optimal control of a chemical reactor, and fitting a statistical model to empirical data. Historical background for each of the problems as well as the practical significance of the first two are given. The problems are solved by using eight recently developed stochastic global optimization algorithms representing controlled random search (4 algorithms), simulated annealing (2 algorithms), and clustering (2 algorithms). The results are discussed, and the importance of global optimization in each respective field is focused.

A Numerical Comparison of Some Modified Controlled Random Search Algorithms

In this paper we propose a new version of the Controlled Random Search(CRS) algorithm of Price. The new algorithmhas been tested on thirteen global optimization test problems. Numericalexperiments indicate that the resulting algorithm performs considerablybetter than the earlier versions of the CRS algorithms. The algorithm,therefore, could offer a reasonable alternative to many currently availablestochastic algorithms, especially for problems requiring ’direct search‘type methods. Also a classification of the CRS algorithms is made based on’global technique‘ – ’local technique‘ and the relative performance ofclasses is numerically explored.

Topographical global optimization using pre-sampled points

A method for global minimization of a functionf(x), x εA ⊂Rn by using presampled global points inA is presented. The global points are obtained by uniform sampling, discarding points too near an already accepted point to obtain a very uniform covering. The accepted points and their nearest-neighbours matrix are stored on a file. When optimzing a given function these pre-sampled points and the matrix are read from file. Then the function value of each point is computed and itsk nearest neighbours that have larger function values are marked. The points for which all its neighbours are marked are extracted as promising starting points for local minimizations. Results from a parallel implementation are presented. The working of a sequential version in Fortran is illustrated.

A direct search variant of the simulated annealing algorithm for optimization involving continuous variables

Abstract A memory-based simulated annealing algorithm is proposed which fundamentally differs from the previously developed simulated annealing algorithms for continuous variables by the fact that a set of points rather than a single working point is used. The implementation of the new method does not need differentiability properties of the function being optimized. The method is well tested on a range of problems classified as easy, moderately difficult and difficult. The new algorithm is compared with other simulated annealing methods on both test problems and practical problems. Results showing an improved performance in finding the global minimum are given. Scope and purpose The inherent difficulty of global optimization problems lies in finding the very best optimum (maximum or minimum) from a multitude of local optima. Many practical global optimization problems of continuous variables are non-differentiable and noisy and even the function evaluation may involve simulation of some process. For such optimization problems direct search approaches are the methods of choice. Simulated annealing is a stochastic global optimization algorithm, initially designed for combinatorial (discrete) optimization problems. The algorithm that we propose here is a simulated annealing algorithm for optimization problems involving continuous variables. It is a direct search method. The strengths of the new algorithm are: it does not require differentiability or any other properties of the function being optimized and it is memory-based. Therefore, the algorithm can be applied to noisy and/or not exactly known functions. Although the algorithm is stochastic in nature, it can memorise the best solution. The new simulated annealing algorithm has been shown to be reliable, fast, general purpose and efficient for solving some difficult global optimization problems.

A model for IS quality

Different concepts of software quality are reviewed and discussed in this paper. Based on this, a hierarchical model of information system (IS) quality concepts developed in the research project SOLE* is presented. This model aims at a division of quality concepts consistent with the different decision makers and decisions made during the software life-cycle. The main division is into IS cost effectiveness, IS use quality and IS work quality. The last two are further divided into requirement quality, interface quality, and efficient IS management, evolution quality and operation quality, respectively.

A sampling-search-clustering approach for exploring the feasible/efficient solutions of MCDM problems

Abstract Decision making under certainty of a single decision maker (DM) is considered. The interaction between the DM and a computerized decision aid (DA) is discussed. The DA can submit feasible, efficient or optimal solutions depending on the formal problem discription provided by the DM. It is proposed that the definition of optimal solution for MCDM problems should be based on the DMs confidence that this solution has been obtained. Methods based on the confidence concept are designed. The suitability of the presented approach for tackling non-linear, non-convex and multi-modal MCDM problems is demonstrated with the aid of two sample problems.

Simulation nets, a simulation modeling and validation tool

Simulation nets can serve as a tool for discrete-event simulation. This tool is based on Petri nets with extensions for modeling, validating, and experimenting. Petri nets have been extensively explored since 1962. The resulting publications are easy to understand and are structured in a hierarchical fashion; the descriptions are so exact that they may be regarded as a pro gramming language. This language does not describe how the simulation should be performed but only what the underlying model looks like (i.e., it is a non-procedural description of the simulation program). Thus, it is possible to obtain simulation results in only a fraction of the time needed for tools requiring programming.

Optimization of Carbon and Silicon Cluster Geometry for Tersoff Potential using Differential Evolution

In this paper we propose a new version of the Differential Evolution (DE) Algorithm for large scale optimization problems. The new algorithm, for exploration and localization of search, periodically uses topographical information on the objective function, in particular the k g -nearest neighbour graph. The algorithm is tested on hard practical problems from computational chemistry. These are the problems of semi-empirical many-body potential energy functions considered for carbon-carbon and silicon-silicon atomic interactions. The minimum binding energies of both carbon and silicon clusters consisting of upto 15 particles are reported.