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  • 1. Maaranen, Heikki
    et al.
    Miettinen, Kaisa
    Helsinki School of Economics.
    Penttinen, Antti
    On initial populations of a genetic algorithm for continuous optimization problems2007In: Journal of Global Optimization, ISSN 0925-5001, E-ISSN 1573-2916, Vol. 37, no 3, p. 405-436Article in journal (Refereed)
    Abstract [en]

    Genetic algorithms are commonly used metaheuristics for global optimization, but there has been very little research done on the generation of their initial population. In this paper, we look for an answer to the question whether the initial population plays a role in the performance of genetic algorithms and if so, how it should be generated. We show with a simple example that initial populations may have an effect on the best objective function value found for several generations. Traditionally, initial populations are generated using pseudo random numbers, but there are many alternative ways. We study the properties of different point generators using four main criteria: the uniform coverage and the genetic diversity of the points as well as the speed and the usability of the generator. We use the point generators to generate initial populations for a genetic algorithm and study what effects the uniform coverage and the genetic diversity have on the convergence and on the final objective function values. For our tests, we have selected one pseudo and one quasi random sequence generator and two spatial point processes: simple sequential inhibition process and nonaligned systematic sampling. In numerical experiments, we solve a set of 52 continuous test functions from 16 different function families, and analyze and discuss the results.

  • 2.
    Sremac, Stefan
    et al.
    Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada.
    Wang, Fei
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Wolkowicz, Henrik
    Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada.
    Pettersson, Lucas
    KTH, School of Engineering Sciences (SCI), Physics.
    Noisy Euclidean Distance Matrix Completion with a Single Missing Node2019In: Journal of Global Optimization, ISSN 0925-5001, E-ISSN 1573-2916, Vol. 75, p. 973-1002Article in journal (Refereed)
    Abstract [en]

    We present several solution techniques for the noisy single source localization problem, i.e. the Euclidean distance matrix completion problem with a single missing node to locate under noisy data. For the case that the sensor locations are fixed, we show that this problem is implicitly convex, and we provide a purification algorithm along with the SDP relaxation to solve it efficiently and accurately. For the case that the sensor locations are relaxed, we study a model based on facial reduction. We present several approaches to solve this problem efficiently, and we compare their performance with existing techniques in the literature. Our tools are semidefinite programming, Euclidean distance matrices, facial reduction, and the generalized trust region subproblem. We include extensive numerical tests.

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