روش کنترل پارامتر الگوریتم های تکاملی با استفاده از اکتشاف و بهره برداری از اقدامات همراه با برنامه های عملی برای مدل انتقال جرم اتصالات Sovova

Exploration and exploitation are omnipresent terms in evolutionary computation community that have been broadly utilized to explain how evolutionary algorithms perform search. However, only recently exploration and exploitation measures were presented in a quantitative way enabling to measure amounts of exploration and exploitation. To move a step further, this paper introduces a parameter control approach that utilizes such measures as feedback to adaptively control evolution processes. The paper shows that with new exploration and exploitation measures, the evolution process generates relatively well results in terms of fitness and/or convergence rate when applying to a practical chemical engineering problem of fitting Sovova's model. We also conducted an objective statistical analysis using Bonferroni–Dunn test and sensitivity analysis on the experimental results. The statistical analysis results again proved that the parameter control strategy using exploration and exploitation measures is competitive to the other approaches presented in the paper. The sensitivity analysis results also showed that different initial values may affect output in different magnitude.

Exploration and exploitation [10] and [14] are two essential cornerstones of evolutionary algorithms (EAs) [4], [17], [22] and [38] that drive an evolution process toward optimization and/or convergence. In fact, these two processes are essential for search processes when using any metaheuristic approach [6] and [7]. Exploration is defined as visiting entirely new regions of a search space, while exploitation is defined as visiting those regions of a search space within the neighborhood of previously visited points [10]. However, to our best knowledge, not until exploration and exploitation measures using an ancestry tree approach were recently introduced by Črepinšek et al. [9], there had not been a quantitative way to measure exploration and exploitation and analyze how these essential cornerstones influence and balance the inner work of an evolution process. Our previous work in Ref. [9] primarily focused on introducing exploration and exploitation measures. In Ref. [33] we further applied such measures to investigate and explain the inner work of VEGA [43] and SPEA2 [49]. Given the usefulness on investigating the inner work of EAs using exploration and exploitation measures, this paper attempts to validate a hypothesis: by using finer-grained exploration and exploitation measures as feedback, an evolution process adapted by parameter control approaches [15] may perform relatively competitive or generate even better results in terms of optimization and/or convergence on a selected practical chemical engineering problem. To validate the hypothesis, this paper extends the implementation of an existing domain-specific language [37], called PPCea (Programmable Parameter Control for Evolutionary Algorithms) introduced by Liu et al. [31] and [32], so that all exploration and exploitation measures from Črepinšek et al. [9] can be computed by the PPCea interpreter on-the-fly. With such, users may introduce PPCea programs to adaptively control evolution processes using the measures as feedback. The paper is organized as follows. Section 2 reviews the ancestor-tree approach. Section 3 presents how PPCea can be used to (re)produce the parameter tuning and four parameter control algorithms, including the one controlled by exploration and exploitation measures. A practical Chemical Engineering problem is shown in Section 4. The experimental results of the four parameter control strategies and two parameter tuning approaches are presented in Section 5, followed by the conclusion in Section 6.

A main objective of this paper is to validate a hypothesis: “By using finer-grained exploration and exploitation measures as feedback, an evolution process adapted by parameter control approaches [15] may perform relatively competitive or generate even better results in terms of average solutions and/or convergence on a selected practical chemical engineering problem.″ The aforementioned hypothesis was statistically test by the Bonferroni-Dunn test, which shows the superiority of the EE-driven approach over the Fogarty and parameter tuning (F = 0.5, CR = 0.9) approaches, while the EE-driven approach is relatively competitive to the parameter tuning (F = 0.9, CR = 0.9), 1/5 success rule, and entropy-driven approaches. Additionally, the competence and usefulness of using exploration and exploitation measures as “tools″ to analyze an evolution process in a finer-grained way is also demonstrated. By applying exploration and exploitation measures on the problem of fitting Sovova's model we can conclude that those algorithms which achieved lower exploreGap (frequently changing to new unexplored regions), higher exploreProgressiveness (exploration is sustainable), lower exploreSelectionPressure (exploration is performed widely through different individuals), higher exploitProgressiveness (exploitation is sustainable), and higher exploitSelectionPressure (exploitation is performed selectively on the best individuals) obtain better results in term of optimization and/or convergence. All of the above shows the capability of PPCea (with exploration and exploitation measures) toward optimization and/or convergence as well as its potentials to further inspirit more open and imaginable parameter control strategies by including also other exploration and exploitation measures (e.g., exploreSelectionPressure, exploitSelectionPressure). To the best of our knowledge this is the first adaptive parameter control approach based on exploration and exploitation measures. As such it needs additional validation on standard benchmark functions and on other real world problems. Our future work is inline with these goals.