Abstract:
This paper presents two different efficiency-enhancement techniques for probabilistic model building genetic algorithms. The first technique proposes the use of a mutation operator which performs local search in the sub-solution neighborhood identified through the probabilistic model. The second technique proposes building and using an internal probabilistic model of the fitness along with the probabilistic model of variable interactions. The fitness values of some offspring are estimated using the probabilistic model, thereby avoiding computationally expensive function evaluations. The scalability of the aforementioned techniques are analyzed using facetwise models for convergence time and population sizing. The speed-up obtained by each of the methods is predicted and verified with empirical results. The results show that for additively separable problems the competent mutation operator requires O(k^0.5logm)—where k is the building-block size, and m is the number of building blocks—less function evaluations than its selectorecombinative counterpart. The results also show that the use of an internal probabilistic fitness model reduces the required number of function evaluations to as low as 1-10% and yields a speed-up of 2–50.

Abstract:
A recent study Sastry and Xiao (2001) proposed a highly reliable cluster optimization algorithm which employed extended compact genetic algorithm (ECGA) along with Nelder-Mead simplex search. This study utilizes an efficiency enhancement technique for the ECGA based cluster optimizer to reduce the population size and the number of function evaluation requirements, yet retaining the high reliability of predicting the lowest energy structure. Seeding of initial population with lowest energy structures of smaller cluster has been employed as the efficiency enhancement technique. Empirical results indicate that the population size and total number of function evaluations scale up with the cluster size are reduced from O(n^4.2) and O(n^8.2) to O(n^0.83) and O(n^2.45) respectively.

Abstract:
In this study we present a detailed analysis of the extended compact genetic algorithm (ECGA). Based on the analysis, empirical relations for population sizing and convergence time have been derived and are compared with the existing relations. We then apply ECGA to a non-azeotropic binary working fluid power cycle optimization problem. The optimal power cycle obtained improved the cycle efficiency by 2.5% over that existing cycles, thus illustrating the capabilities of ECGA in solving real-world problems.