arXiv subjects

Xiaojun Zhou

Publications and source records attributed to Xiaojun Zhou.

25 records · Page 2Linked to original sources

arXiv2012

A Comparative Study of State Transition Algorithm with Harmony Search and Artificial Bee Colony

We focus on a comparative study of three recently developed nature-inspired optimization algorithms, including state transition algorithm, harmony search and artificial bee colony. Their core mechanisms are introduced and their similarities and differences are described. Then, a suit of 27 well-known benchmark problems are used to investigate the performance of these algorithms and finally we discuss their general applicability with respect to the structure of optimization problems.

math.OC↗

arXiv2012

Improved Canonical Dual Algorithms for the Maxcut Problem

By introducing a quadratic perturbation to the canonical dual of the maxcut problem, we transform the integer programming problem into a concave maximization problem over a convex positive domain under some circumstances, which can be solved easily by the well-developed optimization methods. Considering that there may exist no critical points in the dual feasible domain, a reduction technique is used gradually to guarantee the feasibility of the reduced solution, and a compensation technique is utilized to strengthen the robustness of the solution. The similar strategy is also applied to the maxcut problem with linear perturbation and its hybrid with quadratic perturbation. Experimental results demonstrate the effectiveness of the proposed algorithms when compared with other approaches.

math.OC↗

arXiv2012

Global solutions to a class of CEC benchmark constrained optimization problems

This paper aims to solve a class of CEC benchmark constrained optimization problems that have been widely studied by nature-inspired optimization algorithms. Global optimality condition based on canonical duality theory is derived. Integrating the dual solutions with the KKT conditions, we are able to obtain the approximate solutions or global solutions easily.

math.OC↗

arXiv2012

Four strategies to develop canonical dual algorithms for global optimization problems

The canonical duality theory has provided with a unified analytic solution to a range of discrete and continuous problems in global optimization, which can transform a nonconvex primal problem to a concave maximization dual problem over a convex domain without duality gap. This paper shows that under certain conditions, this canonical dual problem is equivalent to the standard semi-definite programming (SDP) problem, which can be solved by well-developed software packages. In order to avoid certain difficulties of using the SDP method, four strategies are proposed based on unconstrained approaches, which can be used to develop algorithms for solving some challenging problems. Applications are illustrated by fourth-order polynomials benchmark optimization problems.

math.OC↗

arXiv2012

Initial Version of State Transition Algorithm

In terms of the concepts of state and state transition, a new algorithm-State Transition Algorithm (STA) is proposed in order to probe into classical and intelligent optimization algorithms. On the basis of state and state transition, it becomes much simpler and easier to understand. As for continuous function optimization problems, three special operators named rotation, translation and expansion are presented. While for discrete function optimization problems, an operator called general elementary transformation is introduced. Finally, with 4 common benchmark continuous functions and a discrete problem used to test the performance of STA, the experiment shows that STA is a promising algorithm due to its good search capability.

math.OC↗

arXiv2012

A new transformation into State Transition Algorithm for finding the global minimum

To promote the global search ability of the original state transition algorithm, a new operator called axesion is suggested, which aims to search along the axes and strengthen single dimensional search. Several benchmark minimization problems are used to illustrate the advantages of the improved algorithm over other random search methods. The results of numerical experiments show that the new transformation can enhance the performance of the state transition algorithm and the new strategy is effective and reliable.

math.OC↗

arXiv2012

Global solutions to general polynomial benchmark optimization problems

The goal of this paper is to solve a class of high-order polynomial benchmark optimization problems, including the Goldstein-Price problem and the Three Hump Camel Back problem. By using a generalized canonical duality theory, we are able to transform the nonconvex primal problems to concave dual problems over convex domain(without duality gap), which can be solved easily to obtain global solutions.

math.OC↗