Terminal Trajectory Planning for Synthetic Aperture Radar Imaging Guidance Based on Chronological Iterative Search Framework.

Synthetic aperture radar (SAR) is capable of obtaining the high-resolution 2-D image of the interested target scene, which enables advanced remote sensing and military applications, such as missile terminal guidance. In this article, the terminal trajectory planning for SAR imaging guidance is first investigated. It is found that the guidance performance of an attack platform is determined by the adopted terminal trajectory. Therefore, the aim of the terminal trajectory planning is to generate a set of feasible flight paths to guide the attack platform toward the target and meanwhile obtain the optimized SAR imaging performance for enhanced guidance precision. The trajectory planning is then modeled as a constrained multiobjective optimization problem given a high-dimensional search space, where the trajectory control and SAR imaging performance are comprehensively considered. By utilizing the temporal-order-dependent property of the trajectory planning problem, a chronological iterative search framework (CISF) is proposed. The problem is decomposed into a series of subproblems, where the search space, objective functions, and constraints are reformulated in chronological order. The difficulty of solving the trajectory planning problem is thus significantly alleviated. Then, the search strategy of CISF is devised to solve the subproblems successively. The optimization results of the preceding subproblem can be utilized as the initial input of the subsequent subproblems to enhance the convergence and search performance. Finally, a trajectory planning method is put forward based on CISF. Experimental studies demonstrate the effectiveness and superiority of the proposed CISF compared with the state-of-the-art multiobjective evolutionary methods. The proposed trajectory planning method can generate a set of feasible terminal trajectories with optimized mission performance.

Improving Performance Insensitivity of Large-Scale Multiobjective Optimization via Monte Carlo Tree Search.

The large-scale multiobjective optimization problem (LSMOP) is characterized by simultaneously optimizing multiple conflicting objectives and involving hundreds of decision variables. Many real-world applications in engineering can be modeled as LSMOPs; simultaneously, engineering applications require insensitivity in performance. This requirement typically means that the algorithm should not only produce good results in terms of performance for every run but also the performance of multiple runs should not fluctuate too much. However, existing large-scale multiobjective optimization algorithms often focus on improving algorithm performance, but pay little attention to improving the insensitivity characteristic of algorithms. This directly leads to substantial limitations when solving practical problems. In this work, we propose an evolutionary algorithm called large-scale multiobjective optimization algorithm via Monte Carlo tree search, which is based on the Monte Carlo tree search and aims to improve the performance and insensitivity of solving LSMOPs. The proposed method samples decision variables to construct new nodes on the Monte Carlo tree for optimization and evaluation, and it selects nodes with good evaluations for further searches in order to reduce the performance sensitivity caused by large-scale decision variables. We propose two metrics to measure the sensitivity of the algorithm and compare the proposed algorithm with several state-of-the-art designs on different benchmark functions and metrics. The experimental results confirm the effectiveness and performance insensitivity of the proposed design for solving LSMOPs.

Learn to Adapt for Self-Supervised Monocular Depth Estimation.

Monocular depth estimation is one of the fundamental tasks in environmental perception and has achieved tremendous progress by virtue of deep learning. However, the performance of trained models tends to degrade or deteriorate when employed on other new datasets due to the gap between different datasets. Though some methods utilize domain adaptation technologies to jointly train different domains and narrow the gap between them, the trained models cannot generalize to new domains that are not involved in training. To boost the transferability of self-supervised monocular depth estimation models and mitigate the issue of meta-overfitting, we train the model in the pipeline of meta-learning and propose an adversarial depth estimation task. We adopt model-agnostic meta-learning (MAML) to obtain universal initial parameters for further adaptation and train the network in an adversarial manner to extract domain-invariant representations for easing meta-overfitting. In addition, we propose a constraint to impose upon cross-task depth consistency to compel the depth estimation to be identical in different adversarial tasks, which improves the performance of our method and smoothens the training process. Experiments on four new datasets demonstrate that our method adapts quite fast to new domains. Our method trained after 0.5 epoch achieves comparable results with the state-of-the-art methods trained at least 20 epochs.

Split-Level Evolutionary Neural Architecture Search With Elite Weight Inheritance.

Neural architecture search (NAS) has recently gained extensive interest in the deep learning community because of its great potential in automating the construction process of deep models. Among a variety of NAS approaches, evolutionary computation (EC) plays a pivotal role with its merit of gradient-free search ability. However, a massive number of the current EC-based NAS approaches evolve neural architectures in an absolutely discrete manner, which makes it tough to flexibly handle the number of filters for each layer, since they often reduce it to a limit set rather than searching for all possible values. Moreover, EC-based NAS methods are often criticized for their inefficiency in performance evaluation, which usually requires laborious full training for hundreds of candidate architectures generated. To address the inflexible search issue on the number of filters, this work proposes a split-level particle swarm optimization (PSO) approach. Each dimension of the particle is subdivided into an integer part and a fractional part, encoding the configurations of the corresponding layer, and the number of filters within a large range, respectively. In addition, the evaluation time is greatly saved by a novel elite weight inheritance method based on an online updating weight pool, and a customized fitness function considering multiple objectives is developed to well control the complexity of the searched candidate architectures. The proposed method, termed split-level evolutionary NAS (SLE-NAS), is computationally efficient, and outperforms many state-of-the-art peer competitors at much lower complexity across three popular image classification benchmark datasets.

Automatic Design of Convolutional Neural Network Architectures Under Resource Constraints.

With the rise of various smart electronics and mobile/edge devices, many existing high-accuracy convolutional neural network (CNN) models are difficult to be applied in practice due to the limited resources, such as memory capacity, power consumption, and spectral efficiency. In order to meet these constraints, researchers have carefully designed some lightweight networks. Meanwhile, to reduce the reliance on manual design on expert experience, some researchers also work to improve neural architecture search (NAS) algorithms to automatically design small networks, exploiting the multiobjective approaches that consider both accuracy and other important goals during optimization. However, simply searching for smaller network models is not consistent with the current research belief of "the deeper the better" and may affect the effectiveness of the model and thus waste the limited resources available. In this article, we propose an automatic method for designing CNNs architectures under constraint handling, which can search for optimal network models meeting the preset constraint. Specifically, an adaptive penalty algorithm is used for fitness evaluation, and a selective repair operation is developed for infeasible individuals to search for feasible CNN architectures. As a case study, we set the complexity (the number of parameters) as a resource constraint and perform multiple experiments on CIFAR-10 and CIFAR-100, to demonstrate the effectiveness of the proposed method. In addition, the proposed algorithm is compared with a state-of-the-art algorithm, NSGA-Net, and several manual-designed models. The experimental results show that the proposed algorithm can successfully solve the problem of the uncertain size of the optimal CNN model under the random search strategy, and the automatically designed CNN model can satisfy the predefined resource constraint while achieving better accuracy.

Solving Expensive Multimodal Optimization Problem by a Decomposition Differential Evolution Algorithm.

An expensive multimodal optimization problem (EMMOP) is that the computation of the objective function is time consuming and it has multiple global optima. This article proposes a decomposition differential evolution (DE) based on the radial basis function (RBF) for EMMOPs, called D/REM. It mainly consists of two phases: the promising subregions detection (PSD) and the local search phase (LSP). In PSD, a population update strategy is designed and the mean-shift clustering is employed to predict the promising subregions of EMMOP. In LSP, a local RBF surrogate model is constructed for each promising subregion and each local RBF surrogate model tracks a global optimum of EMMOP. In this way, an EMMOP is decomposed into many expensive global optimization subproblems. To handle these subproblems, a popular DE variant, JADE, acts as the search engine to deal with these subproblems. A large number of numerical experiments unambiguously validate that D/REM can solve EMMOPs effectively and efficiently.

An Evolutionary Algorithm With Constraint Relaxation Strategy for Highly Constrained Multiobjective Optimization.

Highly constrained multiobjective optimization problems (HCMOPs) refer to constrained multiobjective optimization problems (CMOPs) with complex constraints and small feasible regions, which are commonly encountered in many real-world applications. Current constraint-handling techniques will face two difficulties when dealing with HCMOPs: 1) feasible solution is hard to be found and too much search effort is spent in locating the feasible region and 2) since the total feasible region of an HCMOP can consist of several disconnected subregions, the search process might be stuck in the comparatively larger feasible subregion, which does not contain the whole Pareto front (PF). To address these two issues, an evolutionary algorithm with constraint relaxation strategy based on differential evolution algorithm, that is, CRS-DE, is proposed in this article. In each generation, the CRS-DE relaxes the constraints by dividing the infeasible solutions into two subpopulations based on total constraint violation, that is, the "semifeasible" subpopulation (SF) and "infeasible" subpopulation (IF), respectively. The SF provides information on the promising regions of finding the feasible solution and is the driving force for convergence toward the PF, while the IF focuses on global exploration for new promising regions. Corresponding reproduction and selection strategies are devised for the SF, IF, and feasible subpopulations, which create a clear division of labor with cooperation to facilitate the search for feasible solutions. To leverage the influence of CRS and prevent the population from premature convergence, a mobility restriction mechanism is developed to restrict the individuals in the SF and IF from entering the feasible subpopulation and enhance the diversity of the whole population. Comprehensive experiments on a series of benchmark test problems and a real-world CMOP demonstrate the competitiveness of our method compared with other representative algorithms in terms of effectiveness and reliability in finding a set of well-distributed optimal solutions for HCMOPs.

Multipopulation-Based Differential Evolution for Large-Scale Many-Objective Optimization.

In recent years, numerous efficient many-objective optimization evolutionary algorithms have been proposed to find well-converged and well-distributed nondominated optimal solutions. However, their scalability performance may deteriorate drastically to solve large-scale many-objective optimization problems (LSMaOPs). Encountering high-dimensional solution space with more than 100 decision variables, some of them may lose diversity and trap into local optima, while others may achieve poor convergence performance. This article proposes a multipopulation-based differential evolution algorithm, called LSMaODE, which can solve LSMaOPs efficiently and effectively. In order to exploit and explore the exponential decision space, the proposed algorithm divides the population into two groups of subpopulations, which are optimized with different strategies. First, the randomized coordinate descent technique is applied to 10% of individuals to exploit the decision variables independently. This subpopulation maintains diversity in the decision space to avoid premature convergence into local optimum. Second, the remaining 90% of individuals are optimized with the nondominated guided random interpolation strategy, which interpolates individual among three nondominated solutions randomly. The strategy can guide the population convergent toward the nondominated solutions quickly, meanwhile, maintain good distribution in objective space. Finally, the proposed LSMaODE is evaluated on the LSMOP test suites from the scalability in both decision and objective dimensions. The performance is compared against five state-of-the-art large-scale many-objective evolutionary algorithms. The experimental results show that LSMaODE provides highly competitive performance.

Mission Planning for Energy-Efficient Passive UAV Radar Imaging System Based on Substage Division Collaborative Search.

In our earlier study, an energy-efficient passive UAV radar imaging system was formulated, which comprehensively analyzed the system performance. In this article, based on the evaluator set, a mission planning framework for the underlying energy-efficient passive UAV radar imaging system is proposed to achieve optimized mission performance for a given remote sensing task. First, the mission planning problem is defined in the context of the proposed synthetic aperture radar (SAR) system and a general framework is outlined, including mission specification, illuminator selection, and path planning. It is found that the performance of the system is highly dependent upon the flight path adopted by the UAV platform in a 3-D terrain environment, which offers the potential of optimizing the mission performance by adjusting the UAV path. Then, the path planning problem is modeled as a single-objective optimization problem with multiple constraints. Path planning can be divided into two substages based on different mission orientations and low mutual correlation. Based on this property, a path planning method, called substage division collaborative search (Sub-DiCoS), is proposed. The problem is divided into two subproblems with the corresponding decision space and subpopulation, which significantly relax the constraints for each subproblem and facilitates the search for feasible solutions. Then, differential evolution and the whole-stage best guidance technique are devised to cooperatively lead the subpopulations to search for the best solution. Finally, simulations are presented to demonstrate the effectiveness of the proposed Sub-DiCoS method. The result of the mission planning method can be used to guide the UAV platform to safely travel through a 3-D rough terrain in an energy-efficient manner and achieve optimized SAR imaging and communication performance during the flight.

A Survey on Evolutionary Neural Architecture Search.

Deep neural networks (DNNs) have achieved great success in many applications. The architectures of DNNs play a crucial role in their performance, which is usually manually designed with rich expertise. However, such a design process is labor-intensive because of the trial-and-error process and also not easy to realize due to the rare expertise in practice. Neural architecture search (NAS) is a type of technology that can design the architectures automatically. Among different methods to realize NAS, the evolutionary computation (EC) methods have recently gained much attention and success. Unfortunately, there has not yet been a comprehensive summary of the EC-based NAS algorithms. This article reviews over 200 articles of most recent EC-based NAS methods in light of the core components, to systematically discuss their design principles and justifications on the design. Furthermore, current challenges and issues are also discussed to identify future research in this emerging field.

A Novel Constraint-Based Knee- Guided Neuroevolutionary Algorithm for Context-Specific ECG Early Classification.

Cardiovascular diseases (CVDs) are considered the greatest threat to human life according to World Health Organization. Early classification of CVDs and the appropriate follow-up treatment are crucial for preventing sudden deaths. Electrocardiogram (ECG) is one of the most common non-invasive tools used to evaluate the state of the heart, which can be exploited to automatically diagnose as well. However, the importance of diagnosing CVDs is varying in different context-specific scenarios. For example, ST-segment elevation (STE) is an acute myocardial infarction indicator for patients associated with chest pain and cardiac biomarker. In in-hospital healthcare, STE should be diagnosed with a higher priority than the other phenotypes of ECG. Hence, the context-specific requirements should be considered in ECG early classification problems. We formalize the ECG early classification problem as the context-specific time series classification problem. We propose a novel Constraint-based Knee-guided Neuroevolutionary Algorithm (CKNA) based on the Snippet Policy Networks V2 to solve this problem. To validate the proposed method, we perform a series of experiments on two public ECG datasets under various context-specific simulated scenarios after consulting with physicians specializing in the area. Experimental results show that CKNA significantly improves the average recall of disease classification by 5.5% compared to the competing baseline under user-specified requirements. Moreover, experimental results prove that CKNA presents a feasible solution for the early classifying of cardiac arrhythmias under different user-specified scenarios.

Snippet Policy Network V2: Knee-Guided Neuroevolution for Multi-Lead ECG Early Classification.

Early time series classification predicts the class label of a given time series before it is completely observed. In time-critical applications, such as arrhythmia monitoring in ICU, early treatment contributes to the patient's fast recovery, and early warning could even save lives. Hence, in these cases, it is worthy of trading, to some extent, classification accuracy in favor of earlier decisions when the time series data are collected over time. In this article, we propose a novel deep reinforcement learning-based framework, snippet policy network V2 (SPN-V2), for long and varied-length multi-lead electrocardiogram (ECG) early classification. The proposed SNP-V2 contains two main components: snippet representation learning (SRL) and early classification timing learning (ECTL). The SRL is proposed to encode inner-snippet spatial correlations and inter-snippet temporal correlations into the hidden representations of the subsegment (snippet) of the input ECG. ECTL aims to learn a decision agent to classify the time series early and accurately. To optimize the proposed framework, we design a novel knee-guided neuroevolution algorithm (KGNA) to solve cardiovascular diseases' early classification problem, automatically optimizing the proposed SPN-V2 regarding the tradeoff between accuracy and earliness. In addition, we conduct a series of experiments on two real-world ECG datasets. The experimental results show the superiority of the proposed algorithm over the state-of-the-art competing methods.

Evolutionary Shallowing Deep Neural Networks at Block Levels.

Neural networks have been demonstrated to be trainable even with hundreds of layers, which exhibit remarkable improvement on expressive power and provide significant performance gains in a variety of tasks. However, the prohibitive computational cost has become a severe challenge for deploying them on resource-constrained platforms. Meanwhile, widely adopted deep neural network architectures, for example, ResNets or DenseNets, are manually crafted on benchmark datasets, which hamper their generalization ability to other domains. To cope with these issues, we propose an evolutionary algorithm-based method for shallowing deep neural networks (DNNs) at block levels, which is termed as ESNB. Different from existing studies, ESNB utilizes the ensemble view of block-wise DNNs and employs the multiobjective optimization paradigm to reduce the number of blocks while avoiding performance degradation. It automatically discovers shallower network architectures by pruning less informative blocks, and employs knowledge distillation to recover the performance. Moreover, a novel prior knowledge incorporation strategy is proposed to improve the exploration ability of the evolutionary search process, and a correctness-aware knowledge distillation strategy is designed for better knowledge transferring. Experimental results show that the proposed method can effectively accelerate the inference of DNNs while achieving superior performance when compared with the state-of-the-art competing methods.

Robust Multiobjective Optimization for Vehicle Routing Problem With Time Windows.

In this article, we focus on the vehicle routing problem (VRP) with time windows under uncertainty. To capture the uncertainty characteristics in a real-life scenario, we design a new form of disturbance on travel time and construct robust multiobjective VRP with the time window, where the perturbation range of travel time is determined by the maximum disturbance degree. Two conflicting objectives include: 1)the minimization of both the total distance and: 2)the number of vehicles. A robust multiobjective particle swarms optimization approach is developed by incorporating an advanced encoding and decoding scheme, a robustness measurement metric, as well as the local search strategy. First, through particle flying in the decision space, the problem space characteristic under deterministic environment is fully exploited to provide guidance for robust optimization. Then, a designed metric is adopted to measure the robustness of solutions and help to search for the robust optimal solutions during the particle flying process. In addition to the updating process of particle, two local search strategies, problem-based local search and route-based local search, are developed for further improving the performance of solutions. For comparison, we develop several robust optimization problems by adding disturbances on selected benchmark problems. The experimental results validate our proposed algorithm has a distinguished ability to generate enough robust solutions and ensure the optimality of these solutions.

Masked GAN for Unsupervised Depth and Pose Prediction With Scale Consistency.

Previous work has shown that adversarial learning can be used for unsupervised monocular depth and visual odometry (VO) estimation, in which the adversarial loss and the geometric image reconstruction loss are utilized as the mainly supervisory signals to train the whole unsupervised framework. However, the performance of the adversarial framework and image reconstruction is usually limited by occlusions and the visual field changes between the frames. This article proposes a masked generative adversarial network (GAN) for unsupervised monocular depth and ego-motion estimations. The MaskNet and Boolean mask scheme are designed in this framework to eliminate the effects of occlusions and impacts of visual field changes on the reconstruction loss and adversarial loss, respectively. Furthermore, we also consider the scale consistency of our pose network by utilizing a new scale-consistency loss, and therefore, our pose network is capable of providing the full camera trajectory over a long monocular sequence. Extensive experiments on the KITTI data set show that each component proposed in this article contributes to the performance, and both our depth and trajectory predictions achieve competitive performance on the KITTI and Make3D data sets.

A Polar-Metric-Based Evolutionary Algorithm.

Over the past two decades, numerous multi- and many-objective evolutionary algorithms (MOEAs and MaOEAs) have been proposed to solve the multi- and many-objective optimization problems (MOPs and MaOPs), respectively. It is known that the difficulty of maintaining the convergence and diversity performances rapidly grows as the number of objectives increases. This phenomenon is especially evident for the Pareto-dominance-based EAs, because the nondominated sorting often fails to provide enough convergent pressure toward the Pareto front (PF). Therefore, many researchers came up with some non-Pareto-dominance-based EAs, which are based on indicator, decomposition, and so on. In this article, we propose a polar-metric ( p -metric)-based EA (PMEA) for tackling both MOPs and MaOPs. p -metric is a recently proposed performance indicator which adopts a set of uniformly distributed direction vectors. In PMEA, we use a two-phase selection which combines both nondominated sorting and p -metric. Moreover, a modification is proposed to adjust the direction vectors of p -metric dynamically. In the experiments, PMEA is compared with six state-of-the-art EAs in total and is measured by three performance metrics, including p -metric. According to the empirical results, PMEA shows promising performances on most of the test problems, involving both MOPs and MaOPs.

Evolution Strategy-Based Many-Objective Evolutionary Algorithm Through Vector Equilibrium.

In recent years, numerous many-objective evolutionary algorithms (MaOEAs) have been developed to search for well-diversified and well-converged Pareto optimal solutions for high-dimensional many-objective optimization problems (MaOPs). However, existing MaOEAs have to tackle some daunting challenges, including the emergence of dominance resistance solutions, effective diversity preservation scheme, management of a large population size, extremely high computational complexity, sensitivity to the shape of Pareto front (PF), and overly relying on high-quality reference points. In this article, we present an evolution strategy (ES) for solving MaOPs, called MaOES, which can solve these challenges efficiently and effectively. Inspired by the Vector Equilibrium phenomenon in magnetic fields, isotropic magnetic particles would automatically repel from each other, keep the uniform distance from the nearest neighbors, and extend the entire magnetic fields as far as possible, all at the same time. In the proposed algorithm, an efficient self-adaptive Precision-Controllable Mutation operator is designed for individuals to explore and exploit the decision space. In addition, the Maximum Extension Distance strategy, which emulates the isotropic magnetic particle behavior in a magnetic field, is developed to guide individuals to keep uniform distance and extension to approximate the entire PF. As a result, the MaOES can obtain a well-converged and well-diversified PF with much less population size and far lower computational complexity. The larger the number of individuals, the sharper the contour the resulting approximate PF will be. Finally, the proposed algorithm is evaluated by the scalable MaOPs test suites on DTLZ and WFG. The experimental results have been demonstrated to provide a competitive and oftentimes better performance when compared against some chosen state-of-the-art MaOEAs.

Adaptive Multiobjective Particle Swarm Optimization Based on Evolutionary State Estimation.

A rational leader selection strategy can enhance a swarm to manage the convergence and diversity during the entire search process. In this article, a novel adaptive multiobjective particle swarm optimization (MOPSO) is proposed on the basis of an evolutionary state estimation mechanism, which is used to detect the evolutionary environment whether in exploitation or exploration state. During the search process, different types of leaders, such as a convergence global best solution (c-gBest) and several diversity global best solutions (d-gBests), are to be selected from the external archive for particles under different evolutionary environments. The c-gBest is selected for improving the convergence when the swarm is in an exploitation state, while the d-gBests are chosen for enhancing the diversity in an exploration state. Furthermore, a modified archive maintenance strategy based on some predefined reference points is adopted to maximize the diversity of the Pareto solutions in the external archive. The experimental results demonstrate that the proposed algorithm performs significantly better than the several state-of-the-art multiobjective PSO algorithms and multiobjective evolutionary algorithms on 31 benchmark functions in terms of convergence and diversity of those obtained approximate Pareto fronts.

A Knee-Guided Evolutionary Algorithm for Compressing Deep Neural Networks.

Deep neural networks (DNNs) have been regarded as fundamental tools for many disciplines. Meanwhile, they are known for their large-scale parameters, high redundancy in weights, and extensive computing resource consumptions, which pose a tremendous challenge to the deployment in real-time applications or on resource-constrained devices. To cope with this issue, compressing DNNs for accelerating its inference has drawn extensive interest recently. The basic idea is to prune parameters with little performance degradation. However, the overparameterized nature and the conflict between parameters reduction and performance maintenance make it prohibitive to manually search the pruning parameter space. In this paper, we formally establish filter pruning as a multiobjective optimization problem, and propose a knee-guided evolutionary algorithm (KGEA) that can automatically search for the solution with quality tradeoff between the scale of parameters and performance, in which both conflicting objectives can be optimized simultaneously. In particular, by incorporating a minimum Manhattan distance approach, the search effort in the proposed KGEA is explicitly guided toward the knee area, which greatly facilitates the manual search for a good tradeoff solution. Moreover, the parameter importance is directly estimated on the criterion of performance loss, which can robustly identify the redundancy. In addition to the knee solution, a performance-improved model can also be found in a fine-tuning-free fashion. The experiments on compressing fully convolutional LeNet and VGG-19 networks validate the superiority of the proposed algorithm over the state-of-the-art competing methods.

Evolutionary Algorithm for Knee-Based Multiple Criteria Decision Making.

Although numerous effective and efficient multiobjective evolutionary algorithms have been developed in recent years to search for a well-converged and well-diversified Pareto optimal front, most of these designs are computationally expensive and have to maintain a large population of individuals throughout the evolutionary process. Once the Pareto optimal front is found satisfactorily, the cognitive burden is then imposed upon decision makers to handpick one solution for implementation among a massive number of candidates even with powerful multicriteria decision-making tools. With the increase in the number of decision variables and objective functions in the face of real-world applications, these problems have become a daunting challenge. In this article, we propose a recursive evolutionary algorithm, called EvoKneer, to directly search for global knee solutions, but also multiple local knee solutions using the minimum Manhattan distance approach as opposed to an enormous number of Pareto optimal solutions. Compared with the traditional evolutionary approaches, the proposed design herein only preserves nondominated solutions in rank one in each generation. Boundary Individuals Selection is tailored to select only M 2 boundary individuals where M is the number of objectives. Relieving the burden of maintaining a large population size and its diversity throughout a lengthy evolutionary process, this design with a very low computational cost allows the evolutionary algorithm to converge to knee solutions quickly. To facilitate the experimental validations, a simulator with a graphical user interface is developed under the Delphi XE7 platform and made available for public use. In addition, the proposed algorithm is evaluated with the DO2DK, DEB2DK, DEB2DK2, and DEB3DK benchmark functions. The comparison results validate that the proposed EvoKneer algorithm is computationally and efficiently finding all global and local knee solutions.