One of the optimization algorithms for multi-dimensional functions is simulated annealing. In this paper, a modified simulated annealing (SA) is proposed which utilizes a memory to keep best-so-far met (visited) states/solutions. One of the worst flaws of standard SA is its tendency of oblivion and the chance of losing good points. For avoiding this defect, we use a mixture probability distribution function based on saved previous good solutions (memory) to elect next state. The best-so-far solutions are center (mean vectors) of the mixture probability distribution. So we name this approach MiGSA (Mixture Generating function Simulated Annealing). Our experiments indicate that this approach can improve convergence and stability and avoid delusive areas in benchmark functions better than SA. Each element of mixture generating function can be of Gaussian type (in Boltzmann Annealing case), Cauchy type (in Fast Annealing case) or any other type of distribution.

Many problems in system analysis in real world lead to continuous-domain optimization. Existence of sophisticated and many-variable problems in this field emerge need of efficient optimization methods. One of the optimization algorithms for multi-dimensional functions is simulated annealing (SA). In this paper, a modified simulated annealing named Dynamic Simulated Annealing (DSA) is proposed which dynamically switch between two types of generating function on traversed path of continuous Markov chain. Our experiments indicate that this approach can improve convergence and stability and avoid delusive areas in benchmark functions better than SA without any extra mentionable computational cost.

This paper presents an enhanced adaptive global-best harmony search (EAGHS) to solve global continuous optimization problems. The global-best HS (GHS) is one of the strongest versions of the classical HS algorithm that hybridizes the concepts of swarm intelligence and conventional HS. However, randomized selection of harmony in the permissible interval diverts the GHS algorithm from the global optimum. To address this issue, the proposed EAGHS method introduces a dynamic coefficient into the GHS algorithm to increase the search power in early iterations. Various complex and extensively-applied benchmark functions are used to validate the developed EAGHS algorithm. The results indicate that the EAGHS algorithm offers faster convergence and better accuracy than the standard HS, GHS and other similar algorithms. Further analysis is performed to evaluate the sensitivity of the proposed method to the changes of parameters such as harmony memory consideration rate, harmony search memory, and larger dimensions.