Large Language Models (LLMs) have shown remarkable performance in automated code generation. However, existing approaches often rely heavily on pre-defined test cases, which become impractical in scenarios where such cases are unavailable. While prior works explore filtering techniques between programs and test cases, they overlook the refinement of test cases. To address this limitation, we introduce CoCoEvo, a novel LLM-based co-evolution framework that simultaneously evolves programs and test cases. CoCoEvo eliminates the dependency on pre-defined test cases by generating both programs and test cases directly from natural language problem descriptions and function headers. The framework employs specialized evolutionary operators, including LLM-based crossover and mutation operators for program evolution, along with an additional test case generation operator for test case evolution. Additionally, we propose optimization strategies such as a crossover rate scheduler to balance exploration and convergence, and a multi-objective optimization method for test case selection. Experimental results on multiple state-of-the-art LLMs demonstrate that CoCoEvo surpasses existing methods, achieving state-of-the-art performance in automated code generation and testing. These results underscore the potential of co-evolutionary techniques in advancing the field of automated programming.

Automated unit test generation has been widely studied, with Large Language Models (LLMs) recently showing significant potential. LLMs like GPT-4, trained in vast text and code data, excel in various code-related tasks, including unit test generation. However, existing LLM-based approaches often focus solely on the context within the code itself, such as referenced variables, while neglecting broader task-specific contexts, such as the utility of referring to existing tests of relevant methods in unit test generation. Moreover, in the context of unit test generation, these tools prioritize high code coverage, often at the expense of practical usability, correctness, and maintainability. In response, we propose Reference-Based Retrieval Augmentation , a novel mechanism that extends LLM-based Retrieval-Augmented Generation (RAG) to retrieve relevant information by considering task-specific context. In the unit test generation task, for a given focal method, the reference relationships is defined as the reusability or referentiality of tests between the focal method and other methods. To generate high-quality unit tests for the focal method, the test reference relationships are then used to retrieve relevant methods and their existing unit tests. Specifically, we account for the unique structure of unit tests by dividing the test generation process into Given , When , and Then phases. When generating unit tests for a focal method, we retrieve pre-existing tests of other relevant methods, which can provide valuable insights for any of the Given , When , and Then phases. We implement this approach in a tool called RefTest , which sequentially performs preprocessing, test reference retrieval, and unit test generation, using an incremental strategy in which newly generated tests guide the creation of subsequent ones. We evaluated RefTest on 12 open source projects with 1,515 methods, and the results demonstrate that RefTest consistently outperforms existing tools in terms of correctness, completeness, and maintainability of the generated tests.

The rapid advancement of large language models (LLMs) such as GPT-4 has revolutionized the landscape of software engineering, positioning these models at the core of modern development practices. To fully realize their potential in producing secure source code autonomously, LLMs must not only generate code but also identify and repair vulnerabilities in their outputs, thereby improving security iteratively. Despite growing prominence, LLMs’ effectiveness in performing such end-to-end tasks remains unexplored. This paper bridges this gap by systematically investigating the capability of LLMs to generate source code, evaluate their own outputs for vulnerabilities, and apply necessary repairs to improve the security of their self-generated code.

Autonomous aerial vehicles (AAVs) are gaining more and more attention due to their low cost and high efficiency in delivery problems, and they can be converted into job shop scheduling problems (JSPs). In this article, a AAVs delivery problem is modeled as an energy-efficient distributed heterogeneous flexible JSP (EEDHFJSP), an extension of the flexible JSP, with the objectives of minimizing makespan and total energy consumption (TEC). We propose a memetic algorithm with a novel neighborhood structure and a heuristic selection strategy (NSHSM). A new neighborhood structure is designed to consider energy efficiency, combined with a classic neighborhood structure for flexible job shop scheduling to perform local search. Additionally, a heuristic selection operator strategy is developed based on the characteristics of these two neighborhood structures. NSHSM is compared with five state-of-the-art multiobjective optimization algorithms, including MOEA/D, NSGA-II, TS-NSGA-II, IMANS, and DQCE. Experimental results demonstrate that NSHSM outperforms the compared algorithms in terms of both makespan and TEC, highlighting its effectiveness in solving the EEDHFJSP and AAVs delivery problem.

Connected Autonomous Vehicle (CAV) Driving, as a data-driven intelligent driving technology within the Internet of Vehicles (IoV), presents significant challenges to the efficiency and security of real-time data management. The combination of Web3.0 and edge content caching holds promise in providing low-latency data access for CAVs’ real-time applications. Web3.0 enables the reliable pre-migration of frequently requested content from content providers to edge nodes. However, identifying optimal edge node peers for joint content caching and replacement remains challenging due to the dynamic nature of traffic flow in IoV. Addressing these challenges, this article introduces GAMA-Cache, an innovative edge content caching methodology leveraging Graph Attention Networks (GAT) and Multi-Agent Reinforcement Learning (MARL). GAMA-Cache conceptualizes the cooperative edge content caching issue as a constrained Markov decision process. It employs a MARL technique predicated on cooperation effectiveness to discern optimal caching decisions, with GAT augmenting information extracted from adjacent nodes. A distinct collaborator selection mechanism is also developed to streamline communication between agents, filtering out those with minimal correlations in the vector input to the policy network. Experimental results demonstrate that, in terms of service latency and delivery failure, the GAMA-Cache outperforms other state-of-the-art MARL solutions for edge content caching in IoV.

Physics-Informed Neural Networks (PINNs) have recently received increasing attention, however, optimizing the loss function of PINNs is notoriously difficult, where the landscape of the loss function is often highly non-convex and rugged. Local optimization methods based on gradient information can converge quickly but are prone to being trapped in local minima for training PINNs. Evolutionary algorithms (EAs) are well known for the global search ability, which can help escape from local minima. It has been reported in the literature that EAs show some advantages over gradient-based methods in training PINNs. Inspired by the Memetic Algorithm, we combine global-search based EAs and local-search based batch gradient descent in order to make the best of both word. In addition, since the PINN loss function is composed of multiple terms, balancing these terms is also a challenging issue. Therefore, we also attempt to combine EAs with multiple-gradient descent algorithm for multi-objective optimization. Our experiments provide strong evidence for the superiority of the above algorithms.

Compared with the traditional transportation data, the transportation big data (TBD) is under the background of “Internet + traffic.” It is a great challenge for analyzing and processing TBD because of its complex and unstructured characteristics, such as sequence, strong relevance, accuracy, and closed loop. This Special Issue provides high-quality and up-to-date technology related to the application of SP and AI into TBD and their applications in the COVID-19 scenario and beyond and serves as a forum for researchers all over the world to discuss their works and recent advancements in the field, especially for defensing COVID-19 in public transportation.

Software defect prediction technology aids the reliability assurance team in identifying defect-prone code and assists the team in reasonably allocating limited testing resources. Recently, researchers assumed that the topological associations among code fragments could be harnessed to construct defect prediction models. Nevertheless, existing graph-based methods only concentrate on features of single-view association, which fail to fully capture the rich information hidden in the code. In addition, software defects may involve multiple code fragments simultaneously, but traditional binary graph structures are insufficient for representing these multivariate associations. To address these two challenges, this article proposes a multiview hypergraph representation learning approach (MVHR-DP) to amplify the potency of code features in defect prediction. MVHR-DP initiates by creating hypergraph structures for each code view, which are then amalgamated into a comprehensive fusion hypergraph. Following this, a hypergraph neural network is established to extract code features from multiple views and intricate associations, thereby enhancing the comprehensiveness of representation in the modeling data. Empirical study shows that the prediction model utilizing features generated by MVHR-DP exhibits superior area under the curve (AUC), F-measure, and matthews correlation coefficient (MCC) results compared to baseline approaches across within-project, cross-version, and cross-project prediction tasks.

Digital-twin-enabled cloud-centric architecture is a promising evolution trend of sixth generation (6G) network, which brings new opportunities and challenges for mobile video streaming-related services requiring the exponentially increasing traffic demands. Device-to-Device (D2D) communication paradigm is an attractive technique to alleviate the problem. However, the previous research work on D2D built on individuals’ random mobility or position snapshot and cannot guarantee the stable communication flow. In this paper, we leverage the cybertwin as a centric controller and take advantages of crowdsourcing technology to attract mobile users to follow the specified path and share their network resources with other users. The design of the specified path is formulated as a problem of user recruitment optimization with cost constraint, which is a NP-Hard problem. Firstly, we investigate a special case of only one mobile user to offer the network resource and present a pseudo-polynomial time algorithm. Secondly, we present a graph-partition-based approach to solve the more complex case of multiple mobile users. Thirdly, we discuss the least expected budget to achieve the maximum utility in an ideal model. Fourthly, we perform extensive experiments to evaluate and compare the performance with the typical ones in simulated digital-twin-enabled 6G networks.

We propose a new surrogate-assisted evolutionary algorithm for expensive multiobjective optimization. Two classification-based surrogate models are used, which can predict the Pareto dominance relation and$\theta $-dominance relation between two solutions, respectively. To make such surrogates as accurate as possible, we formulate dominance prediction as an imbalanced classification problem and address this problem using deep learning techniques. Furthermore, to integrate the surrogates based on dominance prediction with multiobjective evolutionary optimization, we develop a two-stage preselection strategy. This strategy aims to select a promising solution to be evaluated among those produced by genetic operations, taking proper account of the balance between convergence and diversity. We conduct an empirical study on a number of well-known multiobjective and many-objective benchmark problems, over a relatively small number of function evaluations. Our experimental results demonstrate the superiority of the proposed algorithm compared with several representative surrogate-assisted algorithms.

Bug repair is a major component of software maintenance, which requires a huge amount of manpower. Evolutionary computation, particularly genetic programming (GP), is a class of promising techniques for automating this time-consuming and expensive process. Although recent research in evolutionary program repair has made significant progress, major challenges still remain. In this article, we propose ARJA-e, a new evolutionary repair system for Java code that aims to address challenges for the search space, search algorithm, and patch overfitting. To determine a search space that is more likely to contain correct patches, ARJA-e combines two sources of fix ingredients (i.e., the statement-level redundancy assumption and repair templates) with contextual analysis-based search space reduction, thereby leveraging their complementary strengths. To encode patches in GP more properly, ARJA-e unifies the edits at different granularities into statement-level edits and then uses a lower-granularity patch representation that is characterized by the decoupling of statements for replacement and statements for insertion. ARJA-e also uses a finer-grained fitness function that can make full use of semantic information contained in the test suite, which is expected to better guide the search of GP. To alleviate patch overfitting, ARJA-e further includes a postprocessing tool that can serve the purposes of overfit detection and patch ranking. We evaluate ARJA-e on 224 real Java bugs from Defects4J and compare it with the state-of-the-art repair techniques. The evaluation results show that ARJA-e can correctly fix 39 bugs in terms of the patches ranked first, achieving substantial performance improvements over the state of the art. In addition, we analyze the effect of the components of ARJA-e qualitatively and quantitatively to demonstrate their effectiveness and advantages.

Automated program repair is the problem of automatically fixing bugs in programs in order to significantly reduce the debugging costs and improve the software quality. To address this problem, test-suite based repair techniques regard a given test suite as an oracle and modify the input buggy program to make the entire test suite pass. GenProg is well recognized as a prominent repair approach of this kind, which uses genetic programming (GP) to rearrange the statements already extant in the buggy program. However, recent empirical studies show that the performance of GenProg is not fully satisfactory, particularly for Java. In this paper, we propose ARJA, a new GP based repair approach for automated repair of Java programs. To be specific, we present a novel lower-granularity patch representation that properly decouples the search subspaces of likely-buggy locations, operation types and potential fix ingredients, enabling GP to explore the search space more effectively. Based on this new representation, we formulate automated program repair as a multi-objective search problem and use NSGA-II to look for simpler repairs. To reduce the computational effort and search space, we introduce a test filtering procedure that can speed up the fitness evaluation of GP and three types of rules that can be applied to avoid unnecessary manipulations of the code. Moreover, we also propose a type matching strategy that can create new potential fix ingredients by exploiting the syntactic patterns of existing statements. We conduct a large-scale empirical evaluation of ARJA along with its variants on both seeded bugs and real-world bugs in comparison with several state-of-the-art repair approaches. Our results verify the effectiveness and efficiency of the search mechanisms employed in ARJA and also show its superiority over the other approaches. In particular, compared to jGenProg (an implementation of GenProg for Java), an ARJA version fully following the redundancy assumption can generate a test-suite adequate patch for more than twice the number of bugs (from 27 to 59), and a correct patch for nearly four times of the number (from 5 to 18), on 224 real-world bugs considered in Defects4J. Furthermore, ARJA is able to correctly fix several real multi-location bugs that are hard to be repaired by most of the existing repair approaches.

This paper presents an automatic software repair system that combines the characteristic components of several typical evolutionary computation based repair approaches into a unified repair framework so as to take advantage of their respective component strengths. We exploit both the redundancy assumption and repair templates to create a search space of candidate repairs. Then we employ a multi-objective evolutionary algorithm with a low-granularity patch representation to explore this search space, in order to find simple patches. In order to further reduce the search space and alleviate patch overfitting we introduce replacement similarity and insertion relevance to select more related statements as promising fix ingredients, and we adopt anti-patterns to customize the available operation types for each likely-buggy statement. We evaluate our system on 224 real bugs from the Defects4J dataset in comparison with the state-of-the-art repair approaches. The evaluation results show that the proposed system can fix 111 out of those 224 bugs in terms of passing all test cases, achieving substantial performance improvements over the state-of-the-art. Additionally, we demonstrate the ability of ARJA-e to fix multi-location bugs that are unlikely to be addressed by most of existing repair approaches.

Abstract Cloudlet is a novel computing paradigm, introduced to the mobile cloud service framework, which moves the computing resources closer to the mobile users, aiming to alleviate the communication delay between the mobile devices and the cloud platform and optimize the energy consumption for mobile devices. Currently, the mobile applications, modeled by the workflows, tend to be complicated and computation‐intensive. Such workflows are required to be offloaded to the cloudlet or the remote cloud platform for execution. However, it is still a key challenge to determine the offloading resolvent for the deadline‐constrained workflows in the cloudlet‐based mobile cloud, since a cloudlet often has limited resources. In this paper, a multiobjective computation offloading method, named MCO, is proposed to address the above challenge. Technically, an energy consumption model for the mobile devices is established in the cloudlet‐based mobile cloud. Then, a corresponding computation offloading method, by improving Nondominated Sorting Genetic Algorithm II, is designed to achieve the goal of energy saving for all the mobile device while satisfying the deadline constraints of the workflows. Finally, extensive experimental evaluations are conducted to demonstrate the efficiency and effectiveness of our proposed method.

We are pleased to announce the publication of the special issue focusing on intrusion detection and prevention in cloud, fog, and Internet of Things (IoT).Internet of Things (IoT), cloud, and fog computing paradigms are as a whole provision a powerful large-scale computing infrastructure for many data and computation intensive applications.Specifically, the IoT technologies and deployment can widely perceive our physical world at a fine granularity and generate sensing data for further insight extraction.The fog computing facilities can provide computing power near the IoT devices where data are generated, aiming to achieve fast data processing for time critical applications or save the amount of data transmitted into cloud for storage or further processing.The cloud computing platforms can offer big data storage and large-scale processing services for cheap long-term storage or data intensive analytics with more advanced data mining models.Hence, it can be seen that the IoT/fog/cloud computing infrastructures can support the whole lifecycle of large-scale applications where big data collection, transmission, storage, processing, and mining can be seamlessly integrated.However, these state-of-the-art computing infrastructures still suffer from severe security and privacy threats because of their built-in properties such as the ubiquitous-access and multitenancy features of

Many-objective optimization problems bring great difficulties to the existing multiobjective evolutionary algorithms, in terms of selection operators, computational cost, visualization of the high-dimensional tradeoff front, and so on. Objective reduction can alleviate such difficulties by removing the redundant objectives in the original objective set, which has become one of the most important techniques in many-objective optimization. In this paper, we suggest to view objective reduction as a multiobjective search problem and introduce three multiobjective formulations of the problem, where the first two formulations are both based on preservation of the dominance structure and the third one utilizes the correlation between objectives. For each multiobjective formulation, a multiobjective objective reduction algorithm is proposed by employing the nondominated sorting genetic algorithm II to generate a Pareto front of nondominated objective subsets that can offer decision support to the user. Moreover, we conduct a comprehensive analysis of two major categories of objective reduction approaches based on several theorems, with the aim of revealing their strengths and limitations. Lastly, the performance of the proposed multiobjective algorithms is studied extensively on various benchmark problems and two real-world problems. Numerical results and comparisons are then shown to highlight the effectiveness and superiority of the proposed multiobjective algorithms over existing state-of-the-art approaches in the related field.

Many-objective optimization has posed a great challenge to the classical Pareto dominance-based multiobjective evolutionary algorithms (MOEAs). In this paper, an evolutionary algorithm based on a new dominance relation is proposed for many-objective optimization. The proposed evolutionary algorithm aims to enhance the convergence of the recently suggested nondominated sorting genetic algorithm III by exploiting the fitness evaluation scheme in the MOEA based on decomposition, but still inherit the strength of the former in diversity maintenance. In the proposed algorithm, the nondominated sorting scheme based on the introduced new dominance relation is employed to rank solutions in the environmental selection phase, ensuring both convergence and diversity. The proposed algorithm is evaluated on a number of well-known benchmark problems having 3-15 objectives and compared against eight state-of-the-art algorithms. The extensive experimental results show that the proposed algorithm can work well on almost all the test functions considered in this paper, and it is compared favorably with the other many-objective optimizers. Additionally, a parametric study is provided to investigate the influence of a key parameter in the proposed algorithm.

The decomposition-based multiobjective evolutionary algorithms (MOEAs) generally make use of aggregation functions to decompose a multiobjective optimization problem into multiple single-objective optimization problems. However, due to the nature of contour lines for the adopted aggregation functions, they usually fail to preserve the diversity in high-dimensional objective space even by using diverse weight vectors. To address this problem, we propose to maintain the desired diversity of solutions in their evolutionary process explicitly by exploiting the perpendicular distance from the solution to the weight vector in the objective space, which achieves better balance between convergence and diversity in many-objective optimization. The idea is implemented to enhance two well-performing decomposition-based algorithms, i.e., MOEA, based on decomposition and ensemble fitness ranking. The two enhanced algorithms are compared to several state-of-the-art algorithms and a series of comparative experiments are conducted on a number of test problems from two well-known test suites. The experimental results show that the two proposed algorithms are generally more effective than their predecessors in balancing convergence and diversity, and they are also very competitive against other existing algorithms for solving many-objective optimization problems.

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) uses crossover operator which often either breaks the building blocks or mix them ineffectively. Multi-objective estimation of distribution algorithm based on decomposition (MEDA/D) evolves a probability vector for each sub-problem to guide the search instead of using crossover operator.However, since the number of the weight vectors in the neighborhood of each weight vector is relatively small and MEDA/D does not provide a way to maintain diversity, the performance of MEDA/D is limited. To overcome the drawbacks of MEDA/D, we proposed a new reproduction operator. This operator could promote diversity. We introduced it into MOEA/D framework and the new algorithm is called s-MEDA/D. We also prove that the parameter newly introduced has physical significance and the reproduction operator is not susceptible to the scale of the problem. The s-MEDA/D was tested on nine instances of the 0/1 multi-objective knapsack problem. Empirical evaluation suggests that the proposed algorithm is effective and efficient.

Reference-point based multi-objective evolutionary algorithms (MOEAs) have shown promising performance in many-objective optimization. However, most of existing research within this area focused on improving the environmental selection procedure, and little work has been done on the effect of variation operators. In this paper, we conduct an experimental investigation of variation operators in a typical reference-point based MOEA, i.e., NSGA-III. First, we provide a new NSGA-III variant, i.e., NSGA-III-DE, which introduces differential evolution (DE) operator into NSGA-III, and we further examine the effect of two main control parameters in NSGA-III-DE. Second, we have an experimental analysis of the search behavior of NSGA-III-DE and NSGA-III. We observe that NSGA-III-DE is generally better at exploration whereas NSGA-III normally has advantages in exploitation. Third, based on this observation, we present two other NSGA-III variants, where DE operator and genetic operators are simply combined to reproduce solutions. Experimental results on several benchmark problems show that very encouraging performance can be achieved by three suggested new NSGA-III variants. Our work also indicates that the performance of NSGA-III is significantly bottlenecked by its variation operators, providing opportunities for the study of the other alternative ones.

In this paper, we propose new memetic algorithms (MAs) for the multiobjective flexible job shop scheduling problem (MO-FJSP) with the objectives to minimize the makespan, total workload, and critical workload. The problem is addressed in a Pareto manner, which aims to search for a set of Pareto optimal solutions. First, by using well-designed chromosome encoding/decoding scheme and genetic operators, the nondominated sorting genetic algorithm II (NSGA-II) is adapted for the MO-FJSP. Then, our MAs are developed by incorporating a novel local search algorithm into the adapted NSGA-II, where some good individuals are chosen from the offspring population for local search using a selection mechanism. Furthermore, in the proposed local search, a hierarchical strategy is adopted to handle the three objectives, which mainly considers the minimization of makespan, while the concern of the other two objectives is reflected in the order of trying all the possible actions that could generate the acceptable neighbor. In the experimental studies, the influence of two alternative acceptance rules on the performance of the proposed MAs is first examined. Afterwards, the effectiveness of key components in our MAs is verified, including genetic search, local search, and the hierarchical strategy in local search. Finally, extensive comparisons are carried out with the state-of-the-art methods specially presented for the MO-FJSP on well-known benchmark instances. The results show that the proposed MAs perform much better than all the other algorithms.

The quantum-inspired evolutionary algorithm (QEA) uses several quantum computing principles to optimize problems on a classical computer. QEA possesses a number of quantum individuals, which are all probability vectors. They work well for linear problems but fail on problems with strong interactions among variables. Moreover, many optimization problems have multiple global optima. And because of the genetic drift, these problems are difficult for evolutionary algorithms to find all global optima. Local and global migration that QEA uses to synchronize different individuals prevent QEA from finding multiple optima. To overcome these difficulties, we proposed a quantum-inspired evolutionary algorithm with linkage learning (QEALL). QEALL uses a modified concept-guide operator based on low order statistics to learn linkage. We also replaced the migration procedure by a niching technology to prevent genetic drift, accordingly to find all global optima and to expedite convergence speed. The performance of QEALL was tested on a number of benchmarks including both unimodal and multimodal problems. Empirical evaluation suggests that the proposed algorithm is effective and efficient.

Many-objective (four or more objectives) optimization problems pose a great challenge to the classical Pareto-dominance based multi-objective evolutionary algorithms (MOEAs), such as NSGA-II and SPEA2. This is mainly due to the fact that the selection pressure based on Pareto-dominance degrades severely with the number of objectives increasing. Very recently, a reference-point based NSGA-II, referred as NSGA-III, is suggested to deal with many-objective problems, where the maintenance of diversity among population members is aided by supplying and adaptively updating a number of well-spread reference points. However, NSGA-III still relies on Pareto-dominance to push the population towards Pareto front (PF), leaving room for the improvement of its convergence ability. In this paper, an improved NSGA-III procedure, called θ-NSGA-III, is proposed, aiming to better tradeoff the convergence and diversity in many-objective optimization. In θ-NSGA-III, the non-dominated sorting scheme based on the proposed θ-dominance is employed to rank solutions in the environmental selection phase, which ensures both convergence and diversity. Computational experiments have shown that θ-NSGA-III is significantly better than the original NSGA-III and MOEA/D on most instances no matter in convergence and overall performance.

In this paper, a new framework, called ensemble fitness ranking (EFR), is proposed for evolutionary many-objective optimization that allows to work with different types of fitness functions and ensemble ranking schemes. The framework aims to rank the solutions in the population more appropriately by combing the ranking results from many simple individual rankers. As to the form of EFR, it can be regarded as an extension of average and maximum ranking methods which have been shown promising for many-objective problems. The significant change is that EFR adopts more general fitness functions instead of objective functions, which would make it easier for EFR to balance the convergence and diversity in many-objective optimization. In the experimental studies, the influence of several fitness functions and ensemble ranking schemes on the performance of EFR is fist investigated. Afterwards, EFR is compared with two state-of-the-art methods (MOEA/D and NSGA-III) on well-known test problems. The computational results show that EFR significantly outperforms MOEA/D and NSGA-III on most instances, especially for those having a high number of objectives.

In this paper, a new memetic algorithm (MA) is proposed for the muti-objective flexible job shop scheduling problem (MO-FJSP) with the objectives to minimize the makespan, total workload and critical workload. By using well-designed chromosome encoding/decoding scheme and genetic operators, the non-dominated sorting genetic algorithm II (NSGA-II) is first adapted for the MO-FJSP. Then the MA is developed by incorporating a novel local search algorithm into the adapted NSGA-II, where several mechanisms to balance the genetic search and local search are employed. In the proposed local search, a hierarchical strategy is adopted to handle the three objectives, which mainly considers the minimization of makespan, while the concern of the other two objectives is reflected in the order of trying all the possible actions that could generate the acceptable neighbor. Experimental results on well-known benchmark instances show that the proposed MA outperforms significantly two off-the-shelf multi-objective evolutionary algorithms and four state-of-the-art algorithms specially proposed for the MO-FJSP.

The flexible job shop scheduling problem (FJSP) is a generalization of the classical job shop scheduling problem (JSP), where each operation is allowed to be processed by any machine from a given set, rather than one specified machine. In this paper, two algorithm modules, namely, hybrid harmony search (HHS) and large neighborhood search (LNS) are developed for the FJSP with makespan criterion. The HHS is an evolutionary-based algorithm with the memetic paradigm, while the LNS is typical of constraint-based approaches. To form a stronger search mechanism, an integrated search method is proposed for the FJSP based on the two algorithms, which starts with the HHS, and then the solution is further improved by the LNS. Computational simulations and comparisons demonstrate that, the proposed HHS alone can effectively solve some medium to large FJSP instances, when integrated with the LNS, it shows competitive performance with state-of-the-art algorithms on very hard and large-scale problems, some new upper bounds among the unsolved benchmark instances have even been found.