Generalized descent for global optimization

Griewank, Andreas

doi:10.1007/bf00933356

Cited by 304 publications

(108 citation statements)

References 7 publications

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“…The two-dimensional Schwefel [4] and Griewank [5] functions were used as fitness landscapes for testing the genetic algorithms. Both are symmetric, separable, continuous and multimodal functions.…”

Section: Experimental Methodsmentioning

confidence: 99%

Transform Ranking: a New Method of Fitness Scaling in Genetic Algorithms

Hopgood¹,

Mierzejewska²

2009

Research and Development in Intelligent Systems XXV

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The first systematic evaluation of the effects of six existing forms of fitness scaling in genetic algorithms is presented alongside a new method called transform ranking. Each method has been applied to stochastic universal sampling (SUS) over a fixed number of generations. The test functions chosen were the two-dimensional Schwefel and Griewank functions. The quality of the solution was improved by applying sigma scaling, linear rank scaling, nonlinear rank scaling, probabilistic nonlinear rank scaling, and transform ranking. However, this benefit was always at a computational cost. Generic linear scaling and Boltzmann scaling were each of benefit in one fitness landscape but not the other. A new fitness scaling function, transform ranking, progresses from linear to nonlinear rank scaling during the evolution process according to a transform schedule. This new form of fitness scaling was found to be one of the two methods offering the greatest improvements in the quality of search. It provided the best improvement in the quality of search for the Griewank function, and was second only to probabilistic nonlinear rank scaling for the Schwefel function. Tournament selection, by comparison, was always the computationally cheapest option but did not necessarily find the best solutions.

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Section: Experimental Methodsmentioning

confidence: 99%

Transform Ranking: a New Method of Fitness Scaling in Genetic Algorithms

Hopgood¹,

Mierzejewska²

2009

Research and Development in Intelligent Systems XXV

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“…Griewank function, first introduced by Griewank [18], has been employed as a test function for global optimization algorithms in many papers. The function has a very large number of local minima, exponentially increasing with dimension [19].…”

Section: B Griewank Functionmentioning

confidence: 99%

Particle Swarm Optimization Assisted by Gaussian Processes for Multimodal Function Optimization

Zhang¹,

Zhang²

2016

Proceedings of the 2016 International Conference on Computer Engineering and Information Systems

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Abstract-In many real-world optimization problems, the location of multiple optima is often required in a search space. In order to evaluate the solution, thousands of fitness function evaluations are involved that is a time consuming or expensive processes. Therefore, standard Particle Swarm Optimization (PSO) meets a special challenge for a very large number of problem function evaluations. Applying models as a surrogate of the real fitness function is proved effective way to address this challenge. This study proposes a model assisted PSO, which uses a Gaussian Process (GP) approximation model. In this algorithm, the training datasets for establishing a GP are generated by the first two generations particle information. Once the GP model is obtained, the function value is evaluated using trained GP model instead of real function evaluation, so that the total number of function evaluation is clearly reduced. In order to improve the predictive capacity of GP, the training datasets are dynamically renewed through sorting datasets and replacing the worst dataset during iterative process. Numerical results from simulations on several 20 dimensional complex multimodal functions are presented. Furthermore, a comparison of the new algorithm with the standard PSO is also made. Results show that the new algorithm is much more efficient than standard PSO.

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“…A well known example is Rosenbrock [1960], who introduced a non-convex function, called Rosenbrock function, which is known to have a global minimum inside a long, narrow, parabolic shaped flat valley. There were also many other well known functions proposed such as Ackley [Ackley, 1987], Griewank [Griewank, 1981] and Rastrigin [Törn and Zilinskas, 1989]. These test functions have often been used to tune, improve and compare continuous optimization algorithms.…”

Section: Benchmark Functions Setsmentioning

confidence: 99%

Population-based heuristic algorithms for continuous and mixed discrete-continuous optimization problems

Liao¹

2015

4OR-Q J Oper Res

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ii SummaryContinuous optimization problems are optimization problems where all variables have a domain that typically is a subset of the real numbers; mixed discretecontinuous optimization problems have additionally other types of variables, so that some variables are continuous and others are on an ordinal or categorical scale. Continuous and mixed discrete-continuous problems have a wide range of applications in disciplines such as computer science, mechanical or electrical engineering, economics and bioinformatics. These problems are also often hard to solve due to their inherent difficulties such as a large number of variables, many local optima or other factors making problems hard. Therefore, in this thesis our focus is on the design, engineering and configuration of high-performing heuristic optimization algorithms.We tackle continuous and mixed discrete-continuous optimization problems with two classes of population-based heuristic algorithms, ant colony optimization (ACO) algorithms and evolution strategies. In a nutshell, the main contributions of this thesis are that (i) we advance the design and engineering of ACO algorithms to algorithms that are competitive or superior to recent state-of-the-art algorithms for continuous and mixed discrete-continuous optimization problems, (ii) we improve upon a specific state-of-the-art evolution strategy, the covariance matrix adaptation evolution strategy (CMA-ES), and (iii) we extend CMA-ES to tackle mixed discrete-continuous optimization problems.More in detail, we propose a unified ant colony optimization (ACO) framework for continuous optimization (UACOR). This framework synthesizes algorithmic components of two ACO algorithms that have been proposed in the literature and an incremental ACO algorithm with local search for continuous optimization, which we have proposed during my doctoral research. The design of UACOR allows the usage of automatic algorithm configuration techniques to automatically derive new, high-performing ACO algorithms for continuous optimization. We also propose iCMAES-ILS, a hybrid algorithm that loosely couples IPOP-CMA-ES, a CMA-ES variant that uses a restart schema coupled with an increasing population iii size, and a new iterated local search (ILS) algorithm for continuous optimization. The hybrid algorithm consists of an initial competition phase, in which IPOP-CMA-ES and the ILS algorithm compete for further deployment during a second phase. A cooperative aspect of the hybrid algorithm is implemented in the form of some limited information exchange from IPOP-CMA-ES to the ILS algorithm during the initial phase. Experimental studies on recent benchmark functions suites show that UACOR and iCMAES-ILS are competitive or superior to other state-of-the-art algorithms.To tackle mixed discrete-continuous optimization problems, we extend ACO MV and propose CES MV , an ant colony optimization algorithm and a covariance matrix adaptation evolution strategy, respectively. In ACO MV and CES MV , the decision variables of an optimization prob...

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Generalized descent for global optimization

Cited by 304 publications

References 7 publications

Transform Ranking: a New Method of Fitness Scaling in Genetic Algorithms

Transform Ranking: a New Method of Fitness Scaling in Genetic Algorithms

Particle Swarm Optimization Assisted by Gaussian Processes for Multimodal Function Optimization

Population-based heuristic algorithms for continuous and mixed discrete-continuous optimization problems

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