Improving the Computational Efficiency of Thermodynamical Genetic Algorithms

Abstract

entropy in annealing to harmonize the conflicts between selective pressure and population diversity in GA. But high computational cost restricts the applications of TDGA. In order to improve the computational efficiency, a measurement method of rating-based entropy (RE) is proposed. The RE method can measure the fitness dispersal with low computational cost. Then a component thermodynamical replacement (CTR) rule is introduced to reduce the complexity of the replacement, and it is proved that the CTR rule has the approximate steepest descent ability of the population free energy. Experimental results on 0-1 knapsack problems show that the RE method and the CTR rule not only maintain the excellent performance and stability of TDGA, but also remarkably improve the computational efficiency of TDGA.

Artificial immune system application for solving dynamic optimization problems

“…But high computational cost of TDGA restricts its application. In [6], [7], Ying proposes a measurement method of ratingbased entropy(RE) and a component thermodynamic replacement (CTR), which remarkably improve the computational efficiency of TDGA.…”

A Thermodynamical Selection-Based Discrete Differential Evolution for the 0-1 Knapsack Problem

“…According to the principle of the minimal free energy, we can realize that any change from non-equilibrium to equilibrium of the system can be regarded as a consequence of the competition between the mean energy and the entropy, and the temperature T determines their relative weights in the competition [39,41,42]. Accordingly, the competition between the mean energy and the entropy in the annealing process is the same as the competition between the selective pressure and the population diversity of DE during the evolution process.…”

“…In addition, any change from non-equilibrium to equilibrium of the system at each temperature abides by the principle of the minimal free energy. This means the system will change spontaneously to reach a lower total free energy and the system achieves equilibrium when its free energy seeks a minimum [40][41][42]. The free energy F is defined by:…”

“…In order to enhance the selection operator of the traditional DE, in this section, we propose an improved selection operator, MFES, which is inspired by the principle of the minimal free energy in thermodynamics, trying to palliate the conflict between the selective pressure and the population diversity to some degree. The principle of the minimal free energy refers to [39][40][41][42], in the annealing process, a metal, beginning with high temperature and chaotic state, is gradually cooled, so that the system at any temperature approximately reaches thermodynamic equilibrium. This cooling process can be regarded as an adaptation procedure to reach the stability of the final crystalline solid.…”

“…Therefore, we can alleviate the conflict between the selective pressure and the diversity of population according to the principle of the minimal free energy. Inspired by [41][42][43], in the improved selection scheme, we firstly map the selective pressure and the population diversity of DE into the mean energy E and the entropy H in the principle of the minimal free energy, respectively. Then, the criterion of the proposed selection scheme is converted to the minimal free energy, which means that we select individuals for the next generation from the parent, and the offspring population should satisfy the principle of the minimal free energy.…”