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Proceedings of GO 2005, pp. 127 – 132.On the goodness of Global Optimisation AlgorithmsEligius M.T. HendrixOperationele Research en Logistiek Groep, Wageningen Universiteit, eligius.hendrix@wur.nlAbstractKeywords:The aim of the paper is to arrive at introductory text for students on the concepts of Global Optimizationalgorithms. Target is to learn to read and interpret optimisation algorithms and to analyse themon goodness. Before going deeper into mathematical analysis, it would be good for students to get aflavour of the difficulty by letting them experiment with simple algorithms that can be followed byhand or spreadsheet calculations. Two simple one-dimensional examples are introduced and in thisabstract two NLP algorithms are elaborated. In the final talk this is widened to some deterministicand stochastic GO methods.Efficiency, Effectiveness.1. IntroductionIn this presentation, several criteria are discussed to measure effectiveness and efficiency ofalgorithms. Examples are given of basic algorithms. To do so, one should first introducethe concept of optimisation algorithms. An algorithm is a description of steps to be takenpreferably implemented into a computer program with the aim to find an approximation ofan optimum point. The aim as such can be several: reach a local optimum point, reach aglobal optimum point, find all global optimum points, reach all global and local optimumpoints. We will come back to that. In general, an algorithm generates a series of points x k thatapproximates a (or the or all) optimum point. According to the generic description of [6]:x k+1 = Alg(x k , x k−1 , ..., x 0 , ξ) (1)where ξ is a random variable and index k is the iteration counter. So the idea it describes isthat a next point x k+1 is generated and evaluated based on the information in all former pointsx k , x k−1 , ..., x 0 (x 0 is usually called the starting point) and possibly some random effect. In thecomplete paper, three types of algorithms are described.Nonlinear optimisation algorithms, that based on a starting point will try to capture the"nearest" local minimum point.Deterministic GO methods which guarantee to approach the global optimum and requirea certain mathematical structure.Stochastic GO methods which are based on the random generation of feasible trial pointsand nonlinear local optimization procedures.We will consider several examples for illustrative purposes. There are two questions to addressif we investigate the quality of algorithms.Effectiveness: does the algorithm find what we want?Efficiency: what are the computational costs?Several measurable performance indicators can be defined for these global criteria.