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

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

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

Enhanced Multi-Strategy Particle Swarm Optimization for Constrained Problems with an Evolutionary-Strategies-Based Unfeasible Local Search Operator

Nowadays, optimization problems are solved through meta-heuristic algorithms based on stochastic search approaches borrowed from mimicking natural phenomena. Notwithstanding their successful capability to handle complex problems, the No-Free Lunch Theorem by Wolpert and Macready (1997) states that there is no ideal algorithm to deal with any kind of problem. This issue arises because of the nature of these algorithms that are not properly mathematics-based, and the convergence is not ensured. In the present study, a variant of the well-known swarm-based algorithm, the Particle Swarm Optimization (PSO), is developed to solve constrained problems with a different approach to the classical penalty function technique. State-of-art improvements and suggestions are also adopted in the current implementation (inertia weight, neighbourhood). Furthermore, a new local search operator has been implemented to help localize the feasible region in challenging optimization problems. This operator is based on hybridization with another milestone meta-heuristic algorithm, the Evolutionary Strategy (ES). The self-adaptive variant has been adopted because of its advantage of not requiring any other arbitrary parameter to be tuned. This approach automatically determines the parameters’ values that govern the Evolutionary Strategy simultaneously during the optimization process. This enhanced multi-strategy PSO is eventually tested on some benchmark constrained numerical problems from the literature. The obtained results are compared in terms of the optimal solutions with two other PSO implementations, which rely on a classic penalty function approach as a constraint-handling method

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

Algorithms and the Foundations of Software technolog

Bat echolocation-inspired algorithms for global optimisation problems

Optimisation according to the definition of Merriam-Webster Dictionary is an act, process, or methodology of making something (as a design, system, or decision) as fully perfect, functional, or effective as possible. In general, optimisation is the process of obtaining either the best minimum or maximum result under specific circumstance. The optimisation process engages with defining and examining objective or fitness function that suits some parameters and constraints. Nowadays, a vast range of business, management and engineering applications utilise the optimisation approach to save time, cost and resources while gaining better profit, output, performance and efficienc