Combining Filter Method and Dynamically Dimensioned Search for Constrained Global Optimization

Abstract

In this work we present an algorithm that combines the filter technique and the dynamically dimensioned search (DDS) for solving nonlinear and nonconvex constrained global optimization problems. The DDS is a stochastic global algorithm for solving bound constrained problems that in each iteration generates a randomly trial point perturbing some coordinates of the current best point. The filter technique controls the progress related to optimality and feasibility defining a forbidden region of points refused by the algorithm. This region can be given by the flat or slanting filter rule. The proposed algorithm does not compute or approximate any derivatives of the objective and constraint functions. Preliminary experiments show that the proposed algorithm gives competitive results when compared with other methods.

Dynamically Dimensioned Search Grey Wolf Optimizer Based on Positional Interaction Information

“…DDS is a point-to-point stochastic-based heuristic global search algorithm with no parameter tuning; global solutions are obtained by scaling within a user-specified maximum number of function evaluations (MaxIter) [43]. Since it is a simple model that is easily programmed and a global search algorithm, many researchers have focused their great attention on it.…”

“…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 .…”

“…In this section, to validate the performance of the proposed DGWO algorithm, 23 benchmark problems with various complexity and sizes are collected from studies [21,23,43]. e characteristics of the selected test functions are summarized in Table 1, where f min denotes the global optimal value.…”

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

“…end for (14) for j � 1 to n do (15) if (19) end if (20) end if (21) if (25) end if (26) end if (27) end for (28) Evaluate…”

“…is special search mechanism of the DDS algorithm is achieved by dynamically and probabilistically reducing the number of dimensions in the neighborhood [7]. Different versions of DDS have been proposed and successfully applied to practical engineering optimization problems such as the hybrid discrete dynamically dimensioned search (HD-DDS) which was used to solve discrete, single-objective, constrained water distribution system (WDS) design problems [8], the modified dynamically dimensioned search (MDDS) which was presented to optimize the parameter for distributed hydrological model [16], the DDS algorithm which was used to automate the calibration process of an unsteady river flow model [17], the Pareto archived dynamically dimensioned search (PA-DDS) which was applied for multi-objective optimization [18], and the combining filter method and dynamically dimensioned search which was designed for constrained global optimization problems [19]. Although the DDS algorithm partly overcomes the common drawback of single solution-based search algorithms to some extent, it does not still provide an ideal solution to address the poor and slow convergence of the global optimum in the best case or an acceptable local optimum in the worst case completely.…”