A two phase local global search algorithm using new global search strategy

Abstract

In this paper, we present a two phase local global search algorithm that is used to remedy the problems associated to the presence of sensitive local optima. However, The presence of such optima in most optimization problems make the global optimization very difficult in the sense that, as soon as the design space exhibits such local optima, the optimization method falls inside and are unable to leave it to a potentially better region. To accurate this problem we propose a new global search technique, which is called Circular Design. We propose also a new point scattering design and a new population evolution scheme the new algorithm works on the principal of evaluating a set of super individuals only. The local search is invoked at each time where a reallocation of the center of the Circular Design is needed, and it has the ability of significantly enlarge the attraction basin of the global optimum in order to reduce the probability of a possible convergence to an interesting local optimum. To illustrate the effectiveness of the proposed algorithm, numerical applications are performed with different benchmark problems; and the obtained results are satisfactory in terms of the solution quality and the time need to reach the global optimum.

Diffusive representation of a fractional control using adaptive partitioning algorithm

“…The way deciding which i (t) containing the global optimum is based on the sub-regions'potential. The potential of a space can be evaluated using interval, and statistical estimation techniques [15] or fuzzy approaches [16]. For the fuzzy approaches, the degree of a membership of any point is measured by the membership function i;k of the function to minimize f (x ij ), x ij 2 D i (t), and D i (t) represents a sample set of the sub-region 0 i (t).…”

A Two-Phase Combined Gradient-Tunneling Based Algorithm for Constrained Integer Programming Problems

“…It is a concave quadratic problem subjected to linear and quadratic constraints, and bounds on the six variables. The problem is formulated as follows: The problem is solved with the initial starting vector (10,10,5,0,5,10) and four initial step sizes λ 0 = 0.1, 0.15, 0.20, 0.25. Other parameters are Δ∈ [1.15,1.5] and ℓ = 0.10.…”

“…Other parameters are Δ∈ [1.15,1.5] and ℓ = 0.10. The global optimum (5,1,5,0,5,10) is reached with function value -310 and intermediate starting vector (3,2,5,0,5,10). The results matches the solution obtained with the 3 n enumeration algorithm proposed in [46].…”

“…A heuristic approach to find the global optimum of complex nonlinear optimization problems is based on evolutionary and genetic algorithms; several works based on this approach can be found in the review papers [26,40]. Recent algorithmic and methodological developments for linear and non-linear integer programming and mixed problems can be found in [29,52,27,25,31,1,4,3,23,49,5]. Additionally, several commercial solvers for linear and non-linear integer programming problems are available.…”

Reducing Dimension in Global Optimization

“…In fact it is well known that the success of the evolutionary algorithms such as GA and EP depends strongly on their strategy that preserves the best member called the elite [Beasley et al (1989)]. Our algorithm strategy that describes the circular design [Boudjehem and Mansouri (2006)] is to use the best members in a population candidate solution to select a subregion of the search space that is the most susceptible of containing the global optimum.…”