Adaptive three-dimensional cellular genetic algorithm for balancing exploration and exploitation processes

Abstract

This paper presents a new adaptive algorithm that aims to control the exploration/exploitation trade-off dynamically. The algorithm is designed based on three-dimensional cellular genetic algorithms (3D-cGAs). In this study, our methodology is based on the change in the global selection pressure induced by dynamic tuning of the local selection rate. The parameter tuning of the local selection method is a way to define the global selection pressure. A diversity speed measure is used to guide the algorithm. Therefore, the integration of existing techniques helps in achieving our aims. A benchmark of well-known continuous test functions and real world problems was selected to investigate the effectiveness of the algorithm proposed. In addition, we provide a comparison between the proposed algorithm and other static and dynamic algorithms in order to study the different effects on the performance of the algorithms. Overall, the results show that the proposed algorithm provides the most desirable performance in terms of efficiency, efficacy, and speed for most problems considered. The results also confirm that problems of various characteristics require different selection pressures, which are difficult to be identified.

Appendix

This section demonstrates how single value of ɛ was selected for the Convergence-Speed-Guided 3D-cGA and the dynamic 3D-cGA based on (Alba and Dorronsoro 2005). In order to facilitate the selection of single ɛ value for all the considered problems, various ɛ values that represented high to low restrictive conditions were assessed. The values are: 0.05, 0.15, 0.25, and 0.3.

Table 5 depicts the results obtained. The best results—efficiency, efficacy, and speed—for each problem are marked in bold. In order to select single ɛ value, two-level ranking was performed based on efficiency, efficacy, and speed (see Table 6). In the first level—local ranking, ɛ values were ranked independently based on the average number of generations and search success rates. The value of ɛ that achieved the lowest convergence time for most cases was assigned the highest rank (i.e., the smallest number) (column 1), and so forth. Similarly, ɛ value that resulted in the highest search success rate for most cases was assigned the highest rank (column 2), and so forth. In the second level—global ranking, ɛ values were ranked based on their local ranks; the value of ɛ that resulted in the minimum sum of local ranks was assigned the highest rank (the last column). Consequently, the best ɛ value is 0.05.

Table 5 Experimental results: efficiency, efficacy, and speed (s) obtained by Convergence-Speed-Guided 3D-cGAs for various thresholds (ɛ)

Table 6 Local and global ranking of ɛ values based on three performance metrics

A similar approach was followed in order to select single ɛ value for the dynamic 3D-cGA based on (Alba and Dorronsoro 2005). Table 7 shows the results obtained, in which the best results achieved for each problem are marked in bold. In addition, the ranking process is depicted in Table 8. Hence, it can be seen that the best ɛ value is 0.05, which is similar to the value selected for Convergence-Speed-Guided 3D-cGA.

Table 7 Experimental results: efficiency, efficacy, and speed (s) obtained by dynamic 3D-cGAs based on Alba and Dorronsoro (2005) for various thresholds (ɛ)

Table 8 Local and global rankings of ɛ values for dynamic 3D-cGAs based on Alba and Dorronsoro (2005)