An outer-approximation algorithm for a class of mixed-integer nonlinear programs
Mathematical Programming: Series A and B
An improved branch and bound algorithm for mixed integer nonlinear programs
Computers and Operations Research
Evolutionary algorithms in theory and practice: evolution strategies, evolutionary programming, genetic algorithms
The theory of evolution strategies
The theory of evolution strategies
Evolution and Optimum Seeking: The Sixth Generation
Evolution and Optimum Seeking: The Sixth Generation
How to analyse evolutionary algorithms
Theoretical Computer Science - Natural computing
An Evolutionary Algorithm for Integer Programming
PPSN III Proceedings of the International Conference on Evolutionary Computation. The Third Conference on Parallel Problem Solving from Nature: Parallel Problem Solving from Nature
Mutation Operators for Structure Evolutionof Neural Networks
PPSN III Proceedings of the International Conference on Evolutionary Computation. The Third Conference on Parallel Problem Solving from Nature: Parallel Problem Solving from Nature
Metric Based Evolutionary Algorithms
Proceedings of the European Conference on Genetic Programming
Analysis of the (1, λ) - ES on the Parabolic Ridge
Evolutionary Computation
Mixed-integer optimization of coronary vessel image analysis using evolution strategies
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Mixed-Integer Evolution Strategies with Dynamic Niching
Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X
PPSN'06 Proceedings of the 9th international conference on Parallel Problem Solving from Nature
Mixed-Integer evolution strategies and their application to intravascular ultrasound image analysis
EuroGP'06 Proceedings of the 2006 international conference on Applications of Evolutionary Computing
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Evolution strategies ESs are powerful probabilistic search and optimization algorithms gleaned from biological evolution theory. They have been successfully applied to a wide range of real world applications. The modern ESs are mainly designed for solving continuous parameter optimization problems. Their ability to adapt the parameters of the multivariate normal distribution used for mutation during the optimization run makes them well suited for this domain. In this article we describe and study mixed integer evolution strategies MIES, which are natural extensions of ES for mixed integer optimization problems. MIES can deal with parameter vectors consisting not only of continuous variables but also with nominal discrete and integer variables. Following the design principles of the canonical evolution strategies, they use specialized mutation operators tailored for the aforementioned mixed parameter classes. For each type of variable, the choice of mutation operators is governed by a natural metric for this variable type, maximal entropy, and symmetry considerations. All distributions used for mutation can be controlled in their shape by means of scaling parameters, allowing self-adaptation to be implemented. After introducing and motivating the conceptual design of the MIES, we study the optimality of the self-adaptation of step sizes and mutation rates on a generalized weighted sphere model. Moreover, we prove global convergence of the MIES on a very general class of problems. The remainder of the article is devoted to performance studies on artificial landscapes barrier functions and mixed integer NK landscapes, and a case study in the optimization of medical image analysis systems. In addition, we show that with proper constraint handling techniques, MIES can also be applied to classical mixed integer nonlinear programming problems.