A novel aggregation-based dominance for Pareto-based evolutionary algorithms to configure software product lines

Abstract

In software engineering, optimal feature selection for software product lines (SPLs) is an important and complicated task, involving simultaneous optimization of multiple competing objectives in large but highly constrained search spaces. A feature model is the standard representation of features of all possible products as well as the relationships among them for an SPL. Recently, various multi-objective evolutionary algorithms have been used to search for valid product configurations. However, the issue of the balance between correctness and diversity of solutions obtained in a reasonable time has been found very challenging for these algorithms. To tackle this problem, this paper proposes a novel aggregation-based dominance (ADO) for Pareto-based evolutionary algorithms to direct the search for high-quality solutions. Our method was tested on two widely used Pareto-based evolutionary algorithms: NSGA-II and SPEA2+SDE and validated on nine different SPLs with up to 10, 000 features and two real-world SPLs with up to 7 objectives. Our experiments have shown the effectiveness and efficiency of both ADO-based NSGA-II and SPEA2+SDE: (1) Both algorithms could generate 100% valid solutions for all feature models. (2) The performance of both algorithms was improved as measured by the hypervolume metric in 7/9 and 8/9 feature models. (3) Even for the largest tested feature model with 10,000 features, it required under 40 seconds on a standard desktop to find 100% valid solutions in a single run of both algorithms.

Performance Evaluation Metrics for Multi-Objective Evolutionary Algorithms in Search-Based Software Engineering: Systematic Literature Review

“…As above-mentioned there are MOPs with no more than three objectives (2 and 3) and MaOPs with more than three objectives. As shown in Figure 12, two and three objectives are the most re-formulated problems, while there are increasing interest in the community in formulating MaOPs compared to previous studies' review [19], although there are number of studies that formulated a different number of objectives in a single study, such as References [75,76,86,91,95,96,102,108,109,117,[122][123][124][125]133,138,146,147]. Table 5 references of these objectives are stated.…”

“…This depends on the objective of the paper, some papers intend to formulate new problems while others only propose a new algorithm or compare existed algorithms by either applying existed formulated problems or considering new problem formulation. However, this does not indicate the practitioners are relaying the existed formulated problems, since the majority of them are formulating new problems with several objective functions, while we have seen studies employing a different number of objectives in a single study [75,76,86,91,95,96,102,108,109,117,[122][123][124][125]133,138,146,147]. Such practice of formulating a limited number of objectives shows the practitioners are either facing difficulties in re-formulating more objective functions that normally need a mathematical definition or defining a small number of objectives that are less expensive and easy to perform.…”

Multi‐UAV path planning utilizing the PGA algorithm for terrestrial IoT sensor network under ISAC framework

“…The former enables UAVs to be prone to paths with greater benefits while the latter helps them to escape from local optimal solutions. The fitness of $$$ {l}_i^N $$$ is expressed 37 as follows: $$$$ {fit}_i^n=1-\frac{f_i{\left({l}_i^n\right)}^{\log \left({t}_i\left(a, cGA\right)\right)}}{\sum \limits_{n^{\prime }=1}^N{f}_i{\left({l}_i^n\right)}^{\log \left({t}_i\left({a}^{\prime }, cGA\right)\right)}} $$$$ $$$$ {t}_i\left(a, cGA\right)={t}_i\left(a, cGA-1\right)+{\sum}_{n^{\prime }=1}^N\left\langle {l}_i^{n^{\prime }}=a\right\rangle $$$$ where $$$ {f}_i\left({l}_i^n\right) $$$ represents the individual objective function return value corresponding to $$$ {l}_i^n $$$; $$$ a $$$ and $$$ {a}^{\prime } $$$ are values; …”

“…In the whole solution space S, the pareto solution set is a set composed of all the non-dominated solutions. 23 The pareto frontier is defined as follows: a series of non-dominated solutions form the Pareto solution set PS, 37 and the surface composed of their corresponding vectors is pareto frontier (PF). 38 All constraints are transformed into convex, and the optimization problem can be reformulated as…”

Using Ultrasonic Sensors and a Knowledge-Based Neural Fuzzy Controller for Mobile Robot Navigation Control

“…Genetic and PSO algorithms exhibit a good global solution for space exploration capability; however, the best solution can fall in the local optima and the premature convergence problem still persists [7]. Many evolutionary algorithms have been increasingly researched over the past few decades, such as evolutionary programming algorithms and evolutionary strategies [8][9][10]. However, in the implementation of evolutionary algorithms, the user must not only determine its coding mode but also select the methods of setting appropriate parameters.…”