A new filled function method for unconstrained global optimization

ABSTRACT

Many real world problems can be modelled as optimization problems. However, the traditional algorithms for these problems often encounter the problem of being trapped in local minima. The filled function method is an effective approach to tackle this kind of problems. However the existing filled functions have the disadvantages of discontinuity, non-differentiability or sensitivity to parameters which limit their efficiency. In this paper, we proposed a new filled function which is continuous and differentiable without any parameter to tune. Compared to discontinuous or non-differentiable filled functions, the continuous and differentiable filled function mainly has three advantages: firstly, it is not easier to produce extra local minima, secondly, more efficient local search algorithms using gradient information can be applied and thirdly, a continuous and differentiable filled function can be optimized more easily. Based on the new proposed filled function, a new algorithm was designed for unconstrained global optimization problems. Numerical experiments were conducted and the results show the proposed algorithm was more efficient.

KEYWORDS:

• Filled function
• parameter free
• local search
• unconstrained global optimization
• multi-modal function

2010 AMS SUBJECT CLASSIFICATIONS:

• 65K05
• 65K10

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [No. 61472297 and No. 61402350] and the Fundamental Research Funds for the Central Universities [BDZ021430].