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This research presents an original and efficient elite archive-assisted adaptive memetic algorithm (EAMA) to deal with a realistic hybrid differentiation flowshop scheduling problem (HDFSP) with the objective of total completion time minimization. In this scheduling problem, each job consists of multiple parts and the jobs are divided into different types. The manufacturing of a job is comprised of three consecutive stages: 1) parts fabrication on first-stage parallel machines; 2) parts assembly on second-stage single machine; and 3) job differentiation on one of third-stage dedicated machines. We provide a mixed-integer programming model, derive three lower bounds, and further present the EAMA metaheuristic for HDFSP. The EAMA is initialized heuristically, and its global exploration is performed by a differential evolution, which includes three newly designed operators: 1) elite-driven discretized differential mutation; 2) probability crossover; and 3) biased selection. To enhance the local search, an external elite archive is set and evolved in parallel with global exploration by a meta-Lamarckian learning-based adaptive multistage local search and a variable length-based adaptive block-insertion local search. After the global exploration and local exploitation, an elite sharing strategy is used to exchange the excellent information between population and elite archive, and an adaptive restart strategy is used to diversify the population. The influence of parameter setting on EAMA is surveyed by using an improved design-of-experiment. The statistical results from extensive computational experiments demonstrate the effectiveness of the special designs and show that EAMA performs more efficient than the existing algorithms in solving the problem under consideration.

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Design—especially of physical objects—can be understood as creative acts solving practical problems. In this article, we describe a biologically inspired developmental model as the basis of a generative form-finding system. Using local interactions between cells in a 2-D environment, then capturing the state of the system at every time step, complex three-dimensional (3-D) forms can be generated by the system. Unlike previous systems, our method is capable of directly producing 3-D printable objects, eliminating intermediate transformations and manual manipulation often necessary to ensure the 3-D form is printable. We devise fitness measures for optimizing 3-D printability and aesthetic complexity and use a covariance matrix adaptation evolutionary strategies algorithm (CMA-ES) to find 3-D forms that are both aesthetically interesting and physically printable using fused deposition modeling printing techniques. We investigate the system’s capabilities by evolving and 3-D printing objects at different levels of structural consistency, and assess the quality of the fitness measures presented to explore the design space of our generative system. We find that by evolving first for aesthetic complexity, then evolving for structural consistency until the form is “just printable,” gives the best results.

Route planning, also known as pathfinding, is one of the key elements in logistics, mobile robotics, and other applications, where engineers face many conflicting objectives. Most route planning algorithms consider only up to three objectives. In this article, we propose a scalable many-objective benchmark problem covering most of the important features for routing applications based on real-world data. We define five objective functions representing distance, traveling time, delays caused by accidents, and two route-specific features, such as curvature and elevation. We analyze several different instances for this test problem and provide their true Pareto front to analyze the problem difficulties. Additionally, we apply four well-known evolutionary multiobjective algorithms. Since this test benchmark can be easily transferred to real-world routing problems, we construct a routing problem from OpenStreetMap data. We evaluate the three optimization algorithms and observe that we are able to provide promising results for such a real-world application. The proposed benchmark represents a scalable many-objective route planning optimization problem enabling researchers and engineers to evaluate their many-objective approaches.

Visualizing the search behavior of a series of points or populations in their native domain is critical in understanding biases and attractors in an optimization process. Distance-based many-objective optimization test problems have been developed to facilitate visualization of search behavior in a 2-D design space with arbitrarily many objective functions. Previous works have proposed a few commonly seen problem characteristics into this problem framework, such as the definition of disconnected Pareto sets and dominance resistant regions of the design space. The authors’ previous work has advanced this research further by providing a problem generator to automatically create user-defined problem instances featuring any combination of these problem features as well as newly introduced ones, such as landscape discontinuities, varying objective ranges, and neutrality. This work makes a number of additional contributions including the proposal of an enhanced, open-source feature-rich problem generator that can create user-defined problem instances exhibiting a range of problem features—some of which are newly introduced here or form extensions of existing features. A comprehensive validation of the problem generator is also provided using popular multiobjective optimization algorithms, and some problem generator settings to create instances exhibiting different challenges for an optimizer are identified.

Convolutional neural networks (CNNs) have shown outstanding results in different application tasks. However, the best performance is obtained when customized CNNs architectures are designed, which is labor intensive and requires highly specialized knowledge. Over three decades, neuroevolution (NE) has studied the application of evolutionary computation to optimize artificial neural networks (ANNs) at different levels. It is well known that the encoding of ANNs highly impacts the complexity of the search space and the optimization algorithms’ performance as well. As NE has rapidly advanced toward the optimization of CNNs topologies, researchers face the challenging duty of representing these complex networks. Furthermore, a compilation of the most widely used encoding methods is nonexistent. In response, we present a comprehensive review on the state-of-the-art of encodings for CNNs.

In recent decades, recommender systems have been well studied and widely applied. However, most recommenders unilaterally optimize the results from the buying customers’ views without considering expectations of other participants, e.g., merchants. Unfortunately, the expectations of customers and merchants in recommendation are different or even conflicted. Especially for popular group-trading markets, customers and merchants are competing in trading, i.e., customers want to meet their preferences or obtain gains with personal favorite items, while merchants want to recommend wholesale items with setting group-trading terms or conditions. In addition, some practical constraints are not fully considered by prior systems. In this article, we propose a cooperative–competitive evolutionary algorithm (i.e., CoEA) for the bidirectional recommendations in group-trading markets. Specifically, we, respectively, formalize two subproblems with designed objectives for two-sided participants in markets, and integrate the cooperative–competitive optimizations into one framework. Second, CoEA designs a binary encoding matrix for individual representation to integrate the two subproblems. Furthermore, by assembling game evolution process, CoEA designs cooperative–competitive evolution operators, i.e., the cooperative crossover and competitive mutation, which guide the solutions to equilibrium by, respectively, bridging communication between two populations of subproblems and optimizing distinctive objective in each population. Finally, we construct two real applications involving bidirectional recommendations, i.e., the group buying and P2P lending, and conduct extensive experiments with the real-world datasets. By comparing CoEA with several representative recommendation algorithms and evolutionary algorithms, the experimental results clearly demonstrate –
he effectiveness of CoEA.

In many real-world optimization applications, a goal solution (i.e., scenario) is often provided by a user according to his/her experience. Due to the presence of a wide range of uncertainties, one may be interested in identifying the robustness interval of the solution, i.e., the range of the decision variables in which the solution remains robust. This article investigates how to find the robustness intervals of the goal solution in evolutionary robust optimization and formulates this as a bilevel optimization problem. Then, a novel algorithm framework is proposed to solve the bilevel problem: an efficient heuristic-based approach is developed to optimize the upper level task, while a global optimizer is utilized to tackle the lower level task. The proposed heuristic-based approach contains four key components: 1) peak detection; 2) peak allocation; 3) calculation of the next perturbation value; and 4) robustness interval fine-tuning, aiming to enhance the efficiency of searching for the target intervals. Finally, three types of artificial test problems and a practical problem are provided to verify the effectiveness of the proposed algorithm framework. The results show that all the robustness intervals can be successfully found when the goal solution is given by means of the proposed algorithm framework.

Differential evolution is a powerful nature-inspired real-parameter optimization algorithm that has been successfully used to solve a number of hard optimization problems. It has been used to tackle both continuous and discrete optimization problems. The application of a continuous method to discrete problems involves several challenges, including solution representation and search space–solution space mapping. In this work, we study random key encoding, a popular encoding scheme that is used to represent permutations in high-dimensional continuous spaces. We analyze the search space it constitutes, study its structure and properties, and introduce two novel modifications of the encoding. We investigate the proposed encoding strategies in the context of four variants of the differential evolution algorithm and demonstrate their usefulness for two widespread permutation problems: 1) the linear ordering problem and 2) the traveling salesman problem.