ABSTRACT Objective The task of code generation aims to transform natural language descriptions into corresponding target code. Among the various approaches, syntax‐aware code generation has emerged as a significant approach that strives to generate code by directly modeling the underlying syntactic rules. However, existing works typically adopt an autoregressive approach to sequentially generate each abstract syntax rule, which inevitably neglects the rich structural semantic information inherent within the syntax rules. To address this issue, we propose an enhanced architecture of structure semantics based on Graph Neural Network for code generation. Methods Our approach explicitly models the internal structure of syntactic rules by treating them as graph data, thereby enabling the extraction of deeper structural semantics. Furthermore, we jointly model both the sequential semantics and structural semantics of syntactic rules, effectively addressing the limitations of solely sequence‐based approaches in capturing the inherent structural semantics of code. Results Experimental results on two widely used code generation datasets demonstrate that the proposed model consistently outperforms strong baselines, with gains of up to 2.14 BLEU points and 2.02 CodeBLEU points, highlighting the effectiveness of our structural‐semantic modeling approach for code generation.

Constrained optimization is an active research topic in evolutionary computation. It challenges evolutionary algorithms in allocating fitness evaluations to the minimization of constraint violations and the optimization of objectives. Most existing evolutionary algorithms implement fixed allocation schemes by using non-priority, priority, or priority-complete comparison criteria. This paper argues that different constrained optimization problems should be solved by algorithms with a dynamic allocation scheme, and the key to adjusting the allocation scheme is a judgement on whether the objective optimization or the constraint violation minimization is beneficial to finding the optimum. In this paper, correlations between objectives and constraints are measured for the judgement. Based on the correlations, a dynamic allocation scheme for fitness evaluations is proposed for constrained evolutionary algorithms. The objective priority criterion or the objective priority-complete criterion is dynamically selected to allocate more fitness evaluations to the objective optimization if the optimization of objectives is beneficial. Otherwise, the constraint priority criterion or the constraint priority-complete criterion is selected to allocate fitness evaluations. Experimental results show that algorithms with the selected criterion significantly outperform state-of-the-art algorithms in terms of attaining feasible solutions with better objective values. Furthermore, algorithms with the dynamic allocation scheme have the advantage of consistently finding feasible solutions with better objective values than algorithms based on non-beneficial, fixed, and randomly selected schemes. The results demonstrate the positive impact of the correlation-based dynamic allocation scheme on evolutionary algorithms for solving constrained optimization problems.

Handling energy resource management (ERM) in today’s energy systems is complex and challenging due to uncertainties arising from the high penetration of distributed energy resources. Such penetration introduces various uncertain factors, such as renewable energy, energy storage, and electric vehicles, making it difficult for traditional mathematical methods to find effective solutions. However, Evolutionary Algorithms (EAs) have shown good performance in solving this problem. Therefore, in this paper, a self-adaptive collaborative differential evolution algorithm (SADEA) is proposed to solve the ERM problem under uncertainty. In SADEA, a three-stage adaptive collaboration strategy, includes boundary randomization stage, knowledge-assisted collaboration stage, and range restructuration stage, is used to generate collaborative solutions. The collaborative solutions generated in the above stages will jointly participate in the perturbation of DE strategies to explore promising solutions. In addition, different DE strategies are selected according to count values and random factors. At the end of the algorithm, boundary control, elite selection and retention are used to ensure the legitimacy and robustness of solutions. The proposed SADEA is compared to several state-of-the-art algorithms on a real-world distribution network located in Salamanca, Spain. The results show that SADEA is superior to its competitors in terms of the objective function, ranking index, and convergence. In summary, the proposed algorithm is effective to handle the ERM problem under uncertainty.

A Software Product Line (SPL) is a set of software products that are built from a variability model. Real-world SPLs typically involve a vast number of valid products, making it impossible to individually test each of them. This arises the need for automated test suite generation, which was previously modeled as either a single-objective or a multi-objective optimization problem considering only objective functions. This article provides a completely different mathematical model by exploiting the benefits of Quality-Diversity (QD) optimization that is composed of not only an objective function (e.g., t -wise coverage or test suite diversity) but also a user-defined behavior space (e.g., the space with test suite size as its dimension). We argue that the new model is more suitable and generic than the two alternatives because it provides at a time a large set of diverse (measured in the behavior space) and high-performing solutions that can ease the decision-making process. We apply MAP-Elites, one of the most popular QD algorithms, to solve the model. The results of the evaluation, on both realistic and artificial SPLs, are promising, with MAP-Elites significantly and substantially outperforming both single- and multi-objective approaches, and also several state-of-the-art SPL testing tools. In summary, this article provides a new and promising perspective on the test suite generation for SPLs.

Constrained multiobjective optimization problems widely exist in real-world applications. To handle them, the balance between constraints and objectives is crucial, but remains challenging due to non-negligible impacts of problem types. In our context, the problem types refer particularly to those determined by the relationship between the constrained Pareto-optimal front (PF) and the unconstrained PF. Unfortunately, there has been little awareness on how to achieve this balance when faced with different types of problems. In this article, we propose a new constraint handling technique (CHT) by taking into account potential problem types. Specifically, inspired by the prior work, problems are classified into three primary types: 1) I; 2) II; and 3) III, with the constrained PF being made up of the entire, part and none of the unconstrained counterpart, respectively. Clearly, any problem must be one of the three types. For each possible type, there exists a tailored mechanism being used to handle the relationships between constraints and objectives (i.e., constraint priority, objective priority, or the switch between them). It is worth mentioning that exact problem types are not required because we just consider their possibilities in the new CHT. Conceptually, we show that the new CHT can make a tradeoff among different types of problems. This argument is confirmed by experimental studies performed on 38 benchmark problems, whose types are known, and a real-world problem (with unknown types) in search-based software engineering. Results demonstrate that within both decomposition-based and nondecomposition-based frameworks, the new CHT can indeed achieve a good tradeoff among different problem types, being better than several state-of-the-art CHTs.

Real-world software product lines (SPLs) often encompass enormous valid configurations that are impossible to enumerate. To understand properties of the space formed by all valid configurations, a feasible way is to select a small and valid sample set. Even though a number of sampling strategies have been proposed, they either fail to produce diverse samples with respect to the number of selected features (an important property to characterize behaviors of configurations), or achieve diverse sampling but with limited scalability (the handleable configuration space size is limited to 1013). To resolve this dilemma, we propose a scalable diverse sampling strategy, which uses a distance metric in combination with the novelty search algorithm to produce diverse samples in an incremental way. The distance metric is carefully designed to measure similarities between configurations, and further diversity of a sample set. The novelty search incrementally improves diversity of samples through the search for novel configurations. We evaluate our sampling algorithm on 39 real-world SPLs. It is able to generate the required number of samples for all the SPLs, including those which cannot be counted by sharpSAT, a state-of-the-art model counting solver. Moreover, it performs better than or at least competitively to state-of-the-art samplers regarding diversity of the sample set. Experimental results suggest that only the proposed sampler (among all the tested ones) achieves scalable diverse sampling.

This article proposes a simple yet effective multiobjective evolutionary algorithm (EA) for dealing with problems with irregular Pareto front. The proposed algorithm does not need to deal with the issues of predefining weight vectors and calculating indicators in the search process. It is mainly based on the thought of adaptively selecting multiple promising search directions according to crowdedness information in local objective spaces. Concretely, the proposed algorithm attempts to dynamically delete an individual of poor quality until enough individuals survive into the next generation. In this environmental selection process, the proposed algorithm considers two or three individuals in the most crowded area, which is determined by the local information in objective space, according to a probability selection mechanism, and deletes the worst of them from the current population. Thus, these surviving individuals are representative of promising search directions. The performance of the proposed algorithm is verified and compared with seven state-of-the-art algorithms [including four general multi/many-objective EAs and three algorithms specially designed for dealing with problems with irregular Pareto-optimal front (PF)] on a variety of complicated problems with different numbers of objectives ranging from 2 to 15. Empirical results demonstrate that the proposed algorithm has a strong competitiveness power in terms of both the performance and the algorithm compactness, and it can well deal with different types of problems with irregular PF and problems with different numbers of objectives.

Testing software product lines (SPLs) is difficult due to a huge number of possible products to be tested. Recently, there has been a growing interest in similarity-based testing of SPLs, where similarity is used as a surrogate metric for the$t$-wise coverage. In this context, one of the primary goals is to sample, by optimizing similarity metrics using search-based algorithms, a small subset of test cases (i.e., products) as dissimilar as possible, thus potentially making more$t$-wise combinations covered. Prior work has shown, by means of empirical studies, the great potential of current similarity-based testing approaches. However, the rationale of this testing technique deserves a more rigorous exploration. To this end, we perform correlation analyses to investigate how similarity metrics are correlated with the$t$-wise coverage. We find that similarity metrics generally have significantly positive correlations with the$t$-wise coverage. This well explains why similarity-based testing works, as the improvement on similarity metrics will potentially increase the$t$-wise coverage. Moreover, we explore, for the first time, the use of the novelty search (NS) algorithm for similarity-based SPL testing. The algorithm rewards “novel” individuals, i.e., those being different from individuals discovered previously, and this well matches the goal of similarity-based SPL testing. We find that the novelty score used in NS has (much) stronger positive correlations with the$t$-wise coverage than previous approaches relying on a genetic algorithm (GA) with a similarity-based fitness function. Experimental results on 31 software product lines validate the superiority of NS over GA, as well as other state-of-the-art approaches, concerning both$t$-wise coverage and fault detection capacity. Finally, we investigate whether it is useful to combine two satisfiability solvers when generating new individuals in NS, and how the performance of NS is affected by its key parameters. In summary, looking for novelty provides a promising way of sampling diverse test cases for SPLs.

Constrained multiobjective optimization abounds in practical applications and is gaining growing attention in the evolutionary computation community. Artificial test problems are critical to the progress in this research area. Nevertheless, many of them lack important characteristics, such as scalability and variable dependencies, which may be essential in benchmarking modern evolutionary algorithms. This article first proposes a new framework for constrained test problem construction. This framework splits a decision vector into position and distance variables and forces their optimal values to lie on a nonlinear hypersurface such that the interdependencies can be introduced among the position ones and among the distance ones individually. In this framework, two kinds of constraints are designed to introduce convergence-hardness and diversity-hardness, respectively. The first kind introduces infeasible barriers in approaching the optima, and at the same time, makes the position and distance variables interrelate with each other. The second kind restricts the feasible optimal regions such that different shapes of Pareto fronts can be obtained. Based on this framework, we construct 16 scalable and constrained test problems covering a variety of difficulties. Then, in the second part of this article, we evaluate the performance of some state of the art on the proposed test problems, showing that they are quite challenging and there is room for further enhancement of the existing algorithms. Finally, we discuss in detail the source of difficulties presented in these new problems.

The particle swarm optimizer (PSO), originally proposed for single-objective optimization problems, has been widely extended to other areas. One of them is multiobjective optimization. Recently, using the PSO to handle many-objective optimization problems (MaOPs) (i.e., problems with more than three objectives) has caught increasing attention from the evolutionary multiobjective community. In the design of a multiobjective/many-objective PSO algorithm, the selection of leaders is a crucial issue. This paper proposes an effective many-objective PSO where the above issue is properly addressed. For each particle, the leader is selected from a certain number of historical solutions by using scalar projections. In the objective space, historical solutions record potential search directions, and the leader is elected as the solution that is closest to the Pareto front in the direction determined by the nadir point and the point constructed by the objective vector of this particle. The proposed algorithm is compared with eight state-of-the-art many-objective optimizers on 37 test problems in terms of four performance metrics. The experimental results have shown the superiority and competitiveness of our proposed algorithm. The new algorithm is free of a set of weight vectors and can handle Pareto fronts with irregular shapes. Given the high performance and good properties of the proposed algorithm, it can be used as a promising tool when dealing with MaOPs.

This paper integrates an estimation of distribution (EoD)-based update operator into decomposition-based multiobjective evolutionary algorithms for binary optimization. The probabilistic model in the update operator is a probability vector, which is adaptively learned from historical information of each subproblem. We show that this update operator can significantly enhance decomposition-based algorithms on a number of benchmark problems. Moreover, we apply the enhanced algorithms to the constrained optimal software product selection (OSPS) problem in the field of search-based software engineering. For this real-world problem, we give its formal definition and then develop a new repair operator based on satisfiability solvers. It is demonstrated by the experimental results that the algorithms equipped with the EoD operator are effective in dealing with this practical problem, particularly for large-scale instances. The interdisciplinary studies in this paper provide a new real-world application scenario for constrained multiobjective binary optimizers and also offer valuable techniques for software engineers in handling the OSPS problem.

We propose a new many-objective evolutionary algorithm with Pareto-adaptive reference points. In this algorithm, the shape of the Pareto-optimal front (PF) is estimated based on a ratio of Euclidean distances. If the estimated shape is likely to be convex, the nadir point is used as the reference point to calculate the convergence and diversity indicators for individuals. Otherwise, the reference point is set to the ideal point. In addition, the estimation of the nadir point is different from what was widely used in the literature. The nadir point, together with the ideal point, provides a feasible way to deal with dominance resistant solutions, which are difficult to be detected and eliminated in Pareto-based algorithms. The proposed algorithm is compared with the state-of-the-art many-objective optimization algorithms on a number of unconstrained and constrained test problems with up to 15 objectives. The experimental results show that it performs better than other algorithms in most of the test instances. Moreover, the new algorithm shows good performance on problems whose PFs are irregular (being discontinuous, degenerated, bent, or mixed). The observed high performance and inherent good properties (such as being free of weight vectors and control parameters) make the new proposal a promising tool for other similar problems.

It is generally accepted that the essential goal of many-objective optimization is the balance between convergence and diversity. For constrained many-objective optimization problems (CMaOPs), the feasibility of solutions should be considered as well. Then the real challenge of constrained many-objective optimization can be generalized to the balance among convergence, diversity, and feasibility. In this paper, a tri-goal evolution framework is proposed for CMaOPs. The proposed framework carefully designs two indicators for convergence and diversity, respectively, and converts the constraints into the third indicator for feasibility. Since the essential goal of constrained many-objective optimization is to balance convergence, diversity, and feasibility, the philosophy of the proposed framework matches the essential goal of constrained many-objective optimization well. Thus, it is natural to use the proposed framework to deal with CMaOPs. Further, the proposed framework is conceptually simple and easy to instantiate for constrained many-objective optimization. A variety of balance schemes and ranking methods can be used to achieve the balance among convergence, diversity and feasibility. Three typical instantiations of the proposed framework are then designed. Experimental results on a constrained many-objective optimization test suite show that the proposed framework is highly competitive with existing state-of-the-art constrained many-objective evolutionary algorithms for CMaOPs.

In this paper, a decomposition-based artificial bee colony (ABC) algorithm is proposed to handle many-objective optimization problems (MaOPs). In the proposed algorithm, an MaOP is converted into a number of subproblems which are simultaneously optimized by a modified ABC algorithm. The hybrid of the decomposition-based algorithm and the ABC algorithm can make full use of the advantages of both algorithms. The former, with the help of a set of weight vectors, is able to maintain a good diversity among solutions, while the latter, with a fast convergence speed, is highly effective when solving a scalar optimization problem. Therefore, the convergence and diversity would be well balanced in the new algorithm. Moreover, subproblems in the proposed algorithm are handled unequally, and computational resources are dynamically allocated through specially designed onlooker bees and scout bees. The proposed algorithm is compared with five state-of-the-art many-objective evolutionary algorithms on 13 test problems with up to 50 objectives. It is shown by the experimental results that the proposed algorithm performs better than or comparably to other algorithms in terms of both quality of the final solution set and efficiency of the algorithms. Finally, as shown by the Wilcoxon signed-rank test results, the onlooker bees and scout bees indeed contribute to performance improvements of the algorithm. Given the high quality of solutions and the rapid running speed, the proposed algorithm could be a promising tool when approximating a set of well-converged and properly distributed nondominated solutions for MaOPs.

In decomposition-based multiobjective evolutionary algorithms, the setting of search directions (or weight vectors), and the choice of reference points (i.e., the ideal point or the nadir point) in scalarizing functions, are of great importance to the performance of the algorithms. This paper proposes a new decomposition-based many-objective optimizer by simultaneously using adaptive search directions and two reference points. For each parent, binary search directions are constructed by using its objective vector and the two reference points. Each individual is simultaneously evaluated on two fitness functions-which are motivated by scalar projections-that are deduced to be the differences between two penalty-based boundary intersection (PBI) functions, and two inverted PBI functions, respectively. Solutions with the best value on each fitness function are emphasized. Moreover, an angle-based elimination procedure is adopted to select diversified solutions for the next generation. The use of adaptive search directions aims at effectively handling problems with irregular Pareto-optimal fronts, and the philosophy of using the ideal and nadir points simultaneously is to take advantages of the complementary effects of the two points when handling problems with either concave or convex fronts. The performance of the proposed algorithm is compared with seven state-of-the-art multi-/many-objective evolutionary algorithms on 32 test problems with up to 15 objectives. It is shown by the experimental results that the proposed algorithm is flexible when handling problems with different types of Pareto-optimal fronts, obtaining promising results regarding both the quality of the returned solution set and the efficiency of the new algorithm.

A feature model (FM) is a compact representation of the information of all possible products from software product lines. The optimal feature selection involves the simultaneous optimization of multiple (usually more than three) objectives in a large and highly constrained search space. By combining our previous work on many-objective evolutionary algorithm (i.e., VaEA) with two different satisfiability (SAT) solvers, this article proposes a new approach named SATVaEA for handling the optimal feature selection problem. In SATVaEA, an FM is simplified with the number of both features and constraints being reduced greatly. We enhance the search of VaEA by using two SAT solvers: one is a stochastic local search--based SAT solver that can quickly repair infeasible configurations, whereas the other is a conflict-driven clause-learning SAT solver that is introduced to generate diversified products. We evaluate SATVaEA on 21 FMs with up to 62,482 features, including two models with realistic values for feature attributes. The experimental results are promising, with SATVaEA returning 100% valid products on almost all FMs. For models with more than 10,000 features, the search in SATVaEA takes only a few minutes. Concerning both effectiveness and efficiency, SATVaEA significantly outperforms other state-of-the-art algorithms.

Taking both convergence and diversity into consideration, this paper suggests a vector angle-based evolutionary algorithm for unconstrained (with box constraints only) many-objective optimization problems. In the proposed algorithm, the maximum-vector-angle-first principle is used in the environmental selection to guarantee the wideness and uniformity of the solution set. With the help of the worse-elimination principle, worse solutions in terms of the convergence (measured by the sum of normalized objectives) are allowed to be conditionally replaced by other individuals. Therefore, the selection pressure toward the Pareto-optimal front is strengthened. The proposed method is compared with other four state-of-the-art many-objective evolutionary algorithms on a number of unconstrained test problems with up to 15 objectives. The experimental results have shown the competitiveness and effectiveness of our proposed algorithm in keeping a good balance between convergence and diversity. Furthermore, it was shown by the results on two problems from practice (with irregular Pareto fronts) that our method significantly outperforms its competitors in terms of both the convergence and diversity of the obtained solution sets. Notably, the new algorithm has the following good properties: 1) it is free from a set of supplied reference points or weight vectors; 2) it has less algorithmic parameters; and 3) the time complexity of the algorithm is low. Given both good performance and nice properties, the suggested algorithm could be an alternative tool when handling optimization problems with more than three objectives.