Abstract
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.
Highlights
In the past decades, meta-heuristic optimization algorithms have received growing attention due to their gradientfree, simplicity, and flexibility
Some novel meta-heuristic optimization algorithms were proposed such as simulated annealing (SA) [1], tabu search (TS) [2], genetic algorithm (GA) [3], differential evolution (DE) [4], particle swarm optimization (PSO) [5], ant colony optimization (ACO) [6], harmony search (HS) [7], gravitational search algorithm (GSA) [8], cuckoo search (CS) [9], bat algorithm (BA) [10], krill herd algorithm (KH) [11], Jaya algorithm(JAYA) [12], sine cosine algorithm (SCA) [13], salp swarm algorithm (SSA) [14], and harris hawks optimization (HHO) [15]
NUMERICAL SIMULATION AND RESULTS In order to evaluate the performance of the proposed algorithm, 64 benchmark functions are employed
Summary
Meta-heuristic optimization algorithms have received growing attention due to their gradientfree, simplicity, and flexibility. The singlesolution-based algorithms generate only one solution in each iteration throughout the search process They have the advantages of fast convergence speed, low computational cost and few function evaluations, but they may be easy to fall into local optimum. The population-based algorithms generate an initial population including diverse solutions randomly and improve solutions through different operators during the search process They have the advantages of self-organization, parallelism, and the superior ability to avoid local optimum, accompanied by higher computational costs and function evaluations. A novel chaotic dynamically dimensioned search algorithm (CDDS) is proposed As we know, this is the first attempt to introduce chaos theory into DDS to improve the performance. To enhance the exploitation of DDS, a new Gaussian mutation operator is employed to make full use of the information of current best solution for perturbation and obtains high accuracy solution and fast convergence.
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