Differential evolution algorithms for constrained global optimization

In this thesis we propose four new methods for solving constrained global optimization problems. The first proposed algorithm is a differential evolution (DE) algorithm using penalty functions for constraint handling. The second algorithm is based on the first DE algorithm but also incorporates a filter set as a diversification mechanism. The third algorithm is also based on DE but includes an additional local refinement process in the form of the pattern search (PS) technique. The last algorithm incorporates both the filter set and PS into the DE algorithm for constrained global optimization. The superiority of feasible points (SFP) and the parameter free penalty (PFP) schemes are used as constraint handling mechanisms. The new algorithms were numerically tested using two sets of test problems and the results where compared with those of the genetic algorithm (GA). The comparison shows that the new algorithms outperformed GA. When the new methods are compared to each other, the last three methods performed better than the first method i.e. the DE algorithm. The new algorithms show promising results with potential for further research. Keywords: constrained global optimization, differential evolution, pattern search, filter method, penalty function, superiority of feasible points, parameter free penalty. i

Modified constrained differential evolution for solving nonlinear global optimization problems

Nonlinear optimization problems introduce the possibility of multiple local optima. The task of global optimization is to find a point where the objective function obtains its most extreme value while satisfying the constraints. Some methods try to make the solution feasible by using penalty function methods, but the performance is not always satisfactory since the selection of the penalty parameters for the problem at hand is not a straightforward issue. Differential evolution has shown to be very efficient when solving global optimization problems with simple bounds. In this paper, we propose a modified constrained differential evolution based on different constraints handling techniques, namely, feasibility and dominance rules, stochastic ranking and global competitive ranking and compare their performances on a benchmark set of problems. A comparison with other solution methods available in literature is also provided. The convergence behavior of the algorithm to handle discrete and integer variables is analyzed using four well-known mixed-integer engineering design problems. It is shown that our method is rather effective when solving nonlinear optimization problems.Fundação para a Ciência e a Tecnologia (FCT

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