Markov Chain Analysis of Evolution Strategies on a Linear Constraint Optimization Problem

This paper analyses a $(1,\lambda)$-Evolution Strategy, a randomised comparison-based adaptive search algorithm, on a simple constraint optimisation problem. The algorithm uses resampling to handle the constraint and optimizes a linear function with a linear constraint. Two cases are investigated: first the case where the step-size is constant, and second the case where the step-size is adapted using path length control. We exhibit for each case a Markov chain whose stability analysis would allow us to deduce the divergence of the algorithm depending on its internal parameters. We show divergence at a constant rate when the step-size is constant. We sketch that with step-size adaptation geometric divergence takes place. Our results complement previous studies where stability was assumed.Comment: Amir Hussain; Zhigang Zeng; Nian Zhang. IEEE Congress on Evolutionary Computation, Jul 2014, Beijing, Chin

Fast Multi-Objective CMODE-Type Optimization of PM Machines Using Multicore Desktop Computers

Large-scale design optimization of electric machines is oftentimes practiced to achieve a set of objectives, such as the minimization of cost and power loss, under a set of constraints, such as maximum permissible torque ripple. Accordingly, the design optimization of electric machines can be regarded as a constrained optimization problem (COP). Evolutionary algorithms (EAs) used in the design optimization of electric machines including differential evolution (DE), which has received considerable attention during recent years, are unconstrained optimization methods that need additional mechanisms to handle COPs. In this paper, a new optimization algorithm that features combined multi-objective optimization with differential evolution (CMODE) has been developed and implemented in the design optimization of electric machines. A thorough comparison is conducted between the two counterpart optimization algorithms, CMODE and DE, to demonstrate CMODE\u27s superiority in terms of convergence rate, diversity and high definition of the resulting Pareto fronts, and its more effective constraint handling. More importantly, CMODE requires a lesser number of simultaneous processing units which makes its implementation best suited for state-of-the-art desktop computers reducing the need for high-performance computing systems and associated software licenses

Integration of Genetic Algorithm and Cultural Particle Swarm Algorithms for Constrained Optimization of Industrial Organization and Diffusion Efficiency Analysis in Equipment Manufacturing Industry

Abstract: Aiming at industrial organization multi-objective optimization problem in Equipment Manufacturing Industry, The paper proposes a new type of double layer evolutionary cultural particle swarm optimization algorithm. The algorithm combines the advantages of the particle swarm optimization algorithm and cultural algorithm. It not only revises the problem that the particles are easy to "premature", but also overcomes the drawback of penalty function method. Firstly, improved topology structure of Particle swarm optimization algorithm. Secondly, using crossover strategy and niche competition mechanism. Verified by the test functions, the proposed algorithm has good performance. Through the analysis of the manufacturing performance based on the algorithm, the paper proposes some optimization strategies such as improving the manufacturing industry market concentration, improving the manufacturing level of industry product differentiation and so on

Integration of Genetic Algorithm and Cultural Particle Swarm Algorithms for Constrained Optimization of Industrial Organization and Diffusion Efficiency Analysis in Equipment Manufacturing Industry

Aiming at industrial organization multi-objective optimization problem in Equipment Manufacturing Industry, The paper proposes a new type of double layer evolutionary cultural particle swarm optimization algorithm. The algorithm combines the advantages of the particle swarm optimization algorithm and cultural algorithm. It not only revises the problem that the particles are easy to "premature", but also overcomes the drawback of penalty function method. Firstly, improved topology structure of Particle swarm optimization algorithm. Secondly, using crossover strategy and niche competition mechanism. Verified by the test functions, the proposed algorithm has good performance. Through the analysis of the manufacturing performance based on the algorithm, the paper proposes some optimization strategies such as improving the manufacturing industry market concentration, improving the manufacturing level of industry product differentiation and so on

A modified bats echolocation-based algorithm for solving constrained optimisation problems

A modified adaptive bats sonar algorithm (MABSA) is presented that utilises the concept of echolocation of a colony of bats to find prey. The proposed algorithm is applied to solve the constrained optimisation problems coupled with penalty function method as constraint handling technique. The performance of the algorithm is verified through rigorous tests with four constrained optimisation benchmark test functions. The acquired results show that the proposed algorithm performs better to find optimum solution in terms of accuracy and convergence speed. The statistical results of MABSA to solve all the test functions also has been compared with the results from several existing algorithms taken from literature on similar test functions. The comparative study has shown that MABSA outperforms other establish algorithms, and thus, it can be an efficient alternative method in the solving constrained optimisation problems

Blended Biogeography-based Optimization for Constrained Optimization

Biogeography-based optimization (BBO) is a new evolutionary optimization method that is based on the science of biogeography. We propose two extensions to BBO. First, we propose a blended migration operator. Benchmark results show that blended BBO outperforms standard BBO. Second, we employ blended BBO to solve constrained optimization problems. Constraints are handled by modifying the BBO immigration and emigration procedures. The approach that we use does not require any additional tuning parameters beyond those that are required for unconstrained problems. The constrained blended BBO algorithm is compared with solutions based on a stud genetic algorithm (SGA) and standard particle swarm optimization 2007 (SPSO 07). The numerical results demonstrate that constrained blended BBO outperforms SGA and performs similarly to SPSO 07 for constrained single-objective optimization problems

Solving the G-problems in less than 500 iterations: Improved efficient constrained optimization by surrogate modeling and adaptive parameter control

Constrained optimization of high-dimensional numerical problems plays an important role in many scientific and industrial applications. Function evaluations in many industrial applications are severely limited and no analytical information about objective function and constraint functions is available. For such expensive black-box optimization tasks, the constraint optimization algorithm COBRA was proposed, making use of RBF surrogate modeling for both the objective and the constraint functions. COBRA has shown remarkable success in solving reliably complex benchmark problems in less than 500 function evaluations. Unfortunately, COBRA requires careful adjustment of parameters in order to do so. In this work we present a new self-adjusting algorithm SACOBRA, which is based on COBRA and capable to achieve high-quality results with very few function evaluations and no parameter tuning. It is shown with the help of performance profiles on a set of benchmark problems (G-problems, MOPTA08) that SACOBRA consistently outperforms any COBRA algorithm with fixed parameter setting. We analyze the importance of the several new elements in SACOBRA and find that each element of SACOBRA plays a role to boost up the overall optimization performance. We discuss the reasons behind and get in this way a better understanding of high-quality RBF surrogate modeling