Dynamically Dimensioned Search Embedded with Piecewise Opposition-Based Learning for Global Optimization

Abstract

Dynamically dimensioned search (DDS) is a well-known optimization algorithm in the field of single solution-based heuristic global search algorithms. Its successful application in the calibration of watershed environmental parameters has attracted researcher’s extensive attention. The dynamically dimensioned search algorithm is a kind of algorithm that converges to the global optimum under the best condition or the good local optimum in the worst case. In other words, the performance of DDS is easily affected by the optimization conditions. Therefore, this algorithm has also suffered from low robustness and limited scalability. In this work, an improved version of DDS called DDS-POBL is proposed. In the DDS-POBL, two effective methods are applied to improve the performance of the DDS algorithm. Piecewise opposition-based learning is introduced to guide DDS search in the right direction, and the golden section method is used to search for more promising areas. Numerical experiments are performed on a set of 23 classic test functions, and the results represent significant improvements in the optimization performance of DDS-POBL compared to DDS. Several experimental results using different parameter values demonstrate the high solution quality, strong robustness, and scalability of the proposed DDS-POBL algorithm. A comparative performance analysis between the DDS-POBL and other powerful algorithms has been carried out by statistical methods by using the significance of the results. The results show that DDS-POBL works better than PSO, CoDA, MHDA, NaFA, and CMA-ES and gives very competitive results when compared to INMDA and EEGWO. Moreover, the parameter calibration application of the Xinanjiang model shows the effectiveness of the DDS-POBL in the real optimization problem.

Noninferior Solution Grey Wolf Optimizer with an Independent Local Search Mechanism for Solving Economic Load Dispatch Problems

“…Step 2.2 If the valve-point loading effects are considered in the ELD problem, then map these initialized grey wolf individuals to the feasible domain of the practical operation constraints according to Equation (26), and employ the loss coefficients B, B 0 , and B 00 to calculate the transmission loss P loss while using Equation (17). Calculate the total cost function of n committed generation units using Equation (27) as the fitness value.…”

“…In other words, one approach may show very promising results on a particular class of problems, but the same algorithm may show poor results on a different set of problems [24]. Therefore, more researchers improve the current approaches or propose new meta-heuristics for solving different complex problems every year, such as the dragonfly algorithm, is hybridized with the improved Nelder-Mead algorithm (INMDA) for function optimization and multilayer perceptron training [25], the dynamically dimensioned search is improved by embedding with piecewise opposition-based learning (DDS-POBL) for global optimization [26], and this also motivates our attempts in this paper to improve the GWO algorithm for solving complex ELD problems.…”

Dynamically Dimensioned Search Grey Wolf Optimizer Based on Positional Interaction Information

“…As the number of iterations approached the maximum, the algorithm evolved into a local search. e key idea for the DDS algorithm to transit from a global search to a local search is to dynamically and probabilistically reducing the number of dimensions to be perturbed in the neighborhood of the current best solution [11,43]. e operation to dynamically and probabilistically reduce the number of dimensions to be perturbed can be summarized as follows: in each iteration, the jth variable is randomly selected with the probability P t from m decision variables for inclusion in the neighborhood I perturb .…”

“…e guided local search (GLS) approach is introduced for multiuser detection in ultra-wideband systems [6]. e dynamically dimensioned search (DDS) is introduced for automatic calibration in watershed simulation models [7][8][9][10][11].…”

“…Compared with single-solution-based algorithms, the research and applications of population-based algorithms are more extensive because of the following three main advantages [11,12]: more information can be obtained to guide the trial solutions toward a promising area within the search space by a set of trial solutions; local optimization can be e ectively avoided because of the interaction of a set of trial solutions; and in terms of exploration ability, population-based heuristic algorithms are superior to singlesolution-based heuristic algorithms. e genetic algorithm (GA) is used to address the characterization of hyperelastic materials [12,13].…”