Description:
Global optimization problems continue to be a challenge in computational mathematics. The field is progressing in two streams: deterministic and heuristic approaches. In this paper, we present a hybrid method that uses the discrete gradient method, which is a derivative free local search method, and evolutionary strategies. We show that the hybridization of the two methods is better than each of them in isolation.
Description:
Global optimization problems continue to be a challenge in computational mathematics. The field is progressing in two streams: deterministic and heuristic approaches. In this paper, we present a hybrid method that uses the discrete gradient method, which is a derivative free local search method, and evolutionary strategies. We show that the hybridization of the two methods is better than each of them in isolation.
Description:
In recent years large-scale global optimization (GO) problems have drawn considerable attention. These problems have many applications, in particular in data mining and biochemistry. Numerical methods for GO are often very time consuming and could not be applied for high-dimensional non-convex and/or non-smooth optimization problems. The study of new algorithms which allow one to solve large-scale GO problem is very important. One technique is to use hybrid of global and local/global search algorithms. This paper presents two hybrid methods for solving the large-scale Lennard-Jones potential GO problem. The methods do not guarantee the calculation of a global solution; however results of numerical experiments show that they, as a rule, calculate a solution which is global one or close to it. One hybrid method is successfully applied to the construction of optimal atomic-resolution structures of prion (113-120) AGAAAAGA amyloid fibrils. Two successful structures constructed in this paper might be useful in furthering the goals of medicinal chemistry in this field.