Chaotic Dynamically Dimensioned Search Algorithm

Dynamically dimensioned search algorithm (DDS) has been proved to be an effective algorithm for solving optimization problems in actual applications, such as distributed watershed model calibration, reservoir operation, pump-and-treat problem, and Radiation Therapy (IMRT) beam angle optimization. However, it always traps in local optimal, especially for multimodal problems. To further improve the performance of DDS, this article proposes a novel chaotic dynamically dimensioned search algorithm (CDDS) by incorporating chaos theory into DDS. The improvement is performed by using three strategies: chaotic initialization, a new Gaussian mutation operator, and a chaotic search. The chaotic map generates an initial population to improve the quality of the initial solution. Chaotic initialization can enhance the exploration ability of DDS because of its intrinsic ergodic and stochastic property. A new Gaussian mutation operator is used to increase convergence speed and the exploitation ability. Meanwhile the chaotic search is utilized to jump out of the local optimal. The optimal CDDS among 13 CDDS variants is compared with other optimization algorithms on 20 classical benchmark test functions, 14 shifted rotated benchmark functions from CEC2005, and 30 benchmark functions from CEC2014 in terms of exploitation and exploration. We testify the applicability and effectiveness on a cascade reservoirs operation optimization problem in real world tasks. The experimental results and analyses demonstrate the superiority of the proposed algorithm in increasing the solution quality and accelerating the convergence.