||Creative Design in Optimization - Metaheuristics Applied to Multi-modal Continuous Functions
||Schulz, Peter Georg
||Vidal, Rene Victor Valqui (Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
||Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
||The application of a number of metaheuristic methods to multi-modal continuous functions is described. Metaheuristics included are Descent Methods, Simulated Annealing, Tabu Search, Nelder-Mead simplex, Ant Colony Optimization, Genetic Algorithms, Evolution Strategies, Memetic Algorithms and Iterated Local Search. The Memetic Algorithm is chosen for implementation based on comparison and a modified SWOT analysis as it has the best possibilities of utilizing a divergent/convergent search strategy.
The problem solving process follows a creative approach where both brainstorming and SWOT analysis is used. A creative design process using brainstorming outlines the final algorithm. A creative search strategy based on divergent and convergent search is designed. In this way the metaheuristic search is guided around the search space. Two versions of the final algorithm are implemented. One, is the Memetic Algorithm with a divergent/convergent search strategy. Second, is a combination of the Memetic Algorithm and Simulated Annealing which is used to optimize parameter settings of the Memetic Algorithm.
The final algorithm is tested on five mathematically defined multi-modal continuous functions. The tests provide results similar to those found in the paper .
The final algorithm is used for parameter optimization of a groundwater simulation model. This case is used to verify the final algorithm on a black box problem, where the relation between input and output is hidden in the simulation model. Four different setups are used to compare manual calibration to that made by the metaheuristic approach. The objective function value has improved by 3-7 % in three out of four setups whereas, the objective value has worsened by 5% for one setup.
It is seen that the final algorithm is useful for parameter optimization of ground- water models. Thus, it is concluded that the purpose of designing a method for optimization of multi-modal continuous functions is fulfilled. Furthermore, creative thinking has been utilized in the problem solving process and the search strategy design.
Finally, the project is evaluated in retrospective view. Parts of the design process is described taking departure in the creative thinking of professional designers studied by .
||Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU : DK-2800 Kgs. Lyngby, Denmark
Creation date: 2006-10-06
Update date: 2012-12-18