arXiv subjects

Kalyanmoy Deb

Publications and source records attributed to Kalyanmoy Deb.

At least 37 records · Page 2Linked to original sources

arXiv2020

Enhanced Innovized Repair Operator for Evolutionary Multi- and Many-objective Optimization

"Innovization" is a task of learning common relationships among some or all of the Pareto-optimal (PO) solutions in multi- and many-objective optimization problems. Recent studies have shown that a chronological sequence of non-dominated solutions obtained in consecutive iterations during an optimization run also possess salient patterns that can be used to learn problem features to help create new and improved solutions. In this paper, we propose a machine-learning- (ML-) assisted modelling approach that learns the modifications in design variables needed to advance population members towards the Pareto-optimal set. We then propose to use the resulting ML model as an additional innovized repair (IR2) operator to be applied on offspring solutions created by the usual genetic operators, as a novel mean of improving their convergence properties. In this paper, the well-known random forest (RF) method is used as the ML model and is integrated with various evolutionary multi- and many-objective optimization algorithms, including NSGA-II, NSGA-III, and MOEA/D. On several test problems ranging from two to five objectives, we demonstrate improvement in convergence behaviour using the proposed IR2-RF operator. Since the operator does not demand any additional solution evaluations, instead using the history of gradual and progressive improvements in solutions over generations, the proposed ML-based optimization opens up a new direction of optimization algorithm development with advances in AI and ML approaches.

cs.NE↗

arXiv2020

Multi-Objective Evolutionary Design of Deep Convolutional Neural Networks for Image Classification

Early advancements in convolutional neural networks (CNNs) architectures are primarily driven by human expertise and by elaborate design processes. Recently, neural architecture search was proposed with the aim of automating the network design process and generating task-dependent architectures. While existing approaches have achieved competitive performance in image classification, they are not well suited to problems where the computational budget is limited for two reasons: (1) the obtained architectures are either solely optimized for classification performance, or only for one deployment scenario; (2) the search process requires vast computational resources in most approaches. To overcome these limitations, we propose an evolutionary algorithm for searching neural architectures under multiple objectives, such as classification performance and floating-point operations (FLOPs). The proposed method addresses the first shortcoming by populating a set of architectures to approximate the entire Pareto frontier through genetic operations that recombine and modify architectural components progressively. Our approach improves computational efficiency by carefully down-scaling the architectures during the search as well as reinforcing the patterns commonly shared among past successful architectures through Bayesian model learning. The integration of these two main contributions allows an efficient design of architectures that are competitive and in most cases outperform both manually and automatically designed architectures on benchmark image classification datasets: CIFAR, ImageNet, and human chest X-ray. The flexibility provided from simultaneously obtaining multiple architecture choices for different compute requirements further differentiates our approach from other methods in the literature. Code is available at https://github.com/mikelzc1990/nsganetv1

cs.CV↗

arXiv2020

Evaluating Nonlinear Decision Trees for Binary Classification Tasks with Other Existing Methods

Classification of datasets into two or more distinct classes is an important machine learning task. Many methods are able to classify binary classification tasks with a very high accuracy on test data, but cannot provide any easily interpretable explanation for users to have a deeper understanding of reasons for the split of data into two classes. In this paper, we highlight and evaluate a recently proposed nonlinear decision tree approach with a number of commonly used classification methods on a number of datasets involving a few to a large number of features. The study reveals key issues such as effect of classification on the method's parameter values, complexity of the classifier versus achieved accuracy, and interpretability of resulting classifiers.

cs.LG↗

arXiv2020

Search-Based Software Engineering for Self-Adaptive Systems: Survey, Disappointments, Suggestions and Opportunities

Search-Based Software Engineering (SBSE) is a promising paradigm that exploits the computational search to optimize different processes when engineering complex software systems. Self-adaptive system (SAS) is one category of such complex systems that permits to optimize different functional and non-functional objectives/criteria under changing environments (e.g., requirements and workload), which involves problems that are subject to search. In this regard, over years, there has been a considerable amount of work that investigates SBSE for SASs. In this paper, we provide the first systematic and comprehensive survey exclusively on SBSE for SASs, covering papers in 27 venues from 7 repositories, which eventually leads to several key statistics from the most notable 74 primary studies in this particular field of research. Our results, surprisingly, have revealed five disappointments that are of utmost importance and can result in serve consequences but have been overwhelmingly ignored in existing studies. We provide theoretical and/or experimental evidence to justify our arguments against the disappointments, present suggestions, and highlight the promising research opportunities towards their mitigation. We also elaborate on three other emergent, but currently under-explored opportunities for future work on SBSE for SASs. By mitigating the disappointments revealed in this work, together with the highlighted opportunities, we hope to be able to excite a much more significant growth in this particular research direction.

cs.SE↗

arXiv2020

Interpretable Rule Discovery Through Bilevel Optimization of Split-Rules of Nonlinear Decision Trees for Classification Problems

For supervised classification problems involving design, control, other practical purposes, users are not only interested in finding a highly accurate classifier, but they also demand that the obtained classifier be easily interpretable. While the definition of interpretability of a classifier can vary from case to case, here, by a humanly interpretable classifier we restrict it to be expressed in simplistic mathematical terms. As a novel approach, we represent a classifier as an assembly of simple mathematical rules using a non-linear decision tree (NLDT). Each conditional (non-terminal) node of the tree represents a non-linear mathematical rule (split-rule) involving features in order to partition the dataset in the given conditional node into two non-overlapping subsets. This partitioning is intended to minimize the impurity of the resulting child nodes. By restricting the structure of split-rule at each conditional node and depth of the decision tree, the interpretability of the classifier is assured. The non-linear split-rule at a given conditional node is obtained using an evolutionary bilevel optimization algorithm, in which while the upper-level focuses on arriving at an interpretable structure of the split-rule, the lower-level achieves the most appropriate weights (coefficients) of individual constituents of the rule to minimize the net impurity of two resulting child nodes. The performance of the proposed algorithm is demonstrated on a number of controlled test problems, existing benchmark problems, and industrial problems. Results on two to 500-feature problems are encouraging and open up further scopes of applying the proposed approach to more challenging and complex classification tasks.

cs.LG↗

arXiv2020

A Non-Dominated Sorting Based Customized Random-Key Genetic Algorithm for the Bi-Objective Traveling Thief Problem

In this paper, we propose a method to solve a bi-objective variant of the well-studied Traveling Thief Problem (TTP). The TTP is a multi-component problem that combines two classic combinatorial problems: Traveling Salesman Problem (TSP) and Knapsack Problem (KP). We address the BI-TTP, a bi-objective version of the TTP, where the goal is to minimize the overall traveling time and to maximize the profit of the collected items. Our proposed method is based on a biased-random key genetic algorithm with customizations addressing problem-specific characteristics. We incorporate domain knowledge through a combination of near-optimal solutions of each subproblem in the initial population and use a custom repair operator to avoid the evaluation of infeasible solutions. The bi-objective aspect of the problem is addressed through an elite population extracted based on the non-dominated rank and crowding distance. Furthermore, we provide a comprehensive study showing the influence of each parameter on the performance. Finally, we discuss the results of the BI-TTP competitions at EMO-2019 and GECCO-2019 conferences where our method has won first and second places, respectively, thus proving its ability to find high-quality solutions consistently.

cs.NE↗

arXiv2020

Image-Based Benchmarking and Visualization for Large-Scale Global Optimization

In the context of optimization, visualization techniques can be useful for understanding the behaviour of optimization algorithms and can even provide a means to facilitate human interaction with an optimizer. Towards this goal, an image-based visualization framework, without dimension reduction, that visualizes the solutions to large-scale global optimization problems as images is proposed. In the proposed framework, the pixels visualize decision variables while the entire image represents the overall solution quality. This framework affords a number of benefits over existing visualization techniques including enhanced scalability (in terms of the number of decision variables), facilitation of standard image processing techniques, providing nearly infinite benchmark cases, and explicit alignment with human perception. Furthermore, image-based visualization can be used to visualize the optimization process in real-time, thereby allowing the user to ascertain characteristics of the search process as it is progressing. To the best of the authors' knowledge, this is the first realization of a dimension-preserving, scalable visualization framework that embeds the inherent relationship between decision space and objective space. The proposed framework is utilized with 10 different mapping schemes on an image-reconstruction problem that encompass continuous, discrete, binary, combinatorial, constrained, dynamic, and multi-objective optimization. The proposed framework is then demonstrated on arbitrary benchmark problems with known optima. Experimental results elucidate the flexibility and demonstrate how valuable information about the search process can be gathered via the proposed visualization framework.

cs.NE↗

arXiv2020

NSGANetV2: Evolutionary Multi-Objective Surrogate-Assisted Neural Architecture Search

In this paper, we propose an efficient NAS algorithm for generating task-specific models that are competitive under multiple competing objectives. It comprises of two surrogates, one at the architecture level to improve sample efficiency and one at the weights level, through a supernet, to improve gradient descent training efficiency. On standard benchmark datasets (C10, C100, ImageNet), the resulting models, dubbed NSGANetV2, either match or outperform models from existing approaches with the search being orders of magnitude more sample efficient. Furthermore, we demonstrate the effectiveness and versatility of the proposed method on six diverse non-standard datasets, e.g. STL-10, Flowers102, Oxford Pets, FGVC Aircrafts etc. In all cases, NSGANetV2s improve the state-of-the-art (under mobile setting), suggesting that NAS can be a viable alternative to conventional transfer learning approaches in handling diverse scenarios such as small-scale or fine-grained datasets. Code is available at https://github.com/mikelzc1990/nsganetv2

cs.CV↗

arXiv2020

Many-Objective Software Remodularization using NSGA-III

Software systems nowadays are complex and difficult to maintain due to continuous changes and bad design choices. To handle the complexity of systems, software products are, in general, decomposed in terms of packages/modules containing classes that are dependent. However, it is challenging to automatically remodularize systems to improve their maintainability. The majority of existing remodularization work mainly satisfy one objective which is improving the structure of packages by optimizing coupling and cohesion. In addition, most of existing studies are limited to only few operation types such as move class and split packages. Many other objectives, such as the design semantics, reducing the number of changes and maximizing the consistency with development change history, are important to improve the quality of the software by remodularizing it. In this paper, we propose a novel many-objective search-based approach using NSGA-III. The process aims at finding the optimal remodularization solutions that improve the structure of packages, minimize the number of changes, preserve semantics coherence, and re-use the history of changes. We evaluate the efficiency of our approach using four different open-source systems and one automotive industry project, provided by our industrial partner, through a quantitative and qualitative study conducted with software engineers.

cs.SE↗

arXiv2020

Evolutionary Multi Objective Optimization Algorithm for Community Detection in Complex Social Networks

Most optimization-based community detection approaches formulate the problem in a single or bi-objective framework. In this paper, we propose two variants of a three-objective formulation using a customized non-dominated sorting genetic algorithm III (NSGA-III) to find community structures in a network. In the first variant, named NSGA-III-KRM, we considered Kernel k means, Ratio cut, and Modularity, as the three objectives, whereas the second variant, named NSGA-III-CCM, considers Community score, Community fitness and Modularity, as three objective functions. Experiments are conducted on four benchmark network datasets. Comparison with state-of-the-art approaches along with decomposition-based multi-objective evolutionary algorithm variants (MOEA/D-KRM and MOEA/D-CCM) indicates that the proposed variants yield comparable or better results. This is particularly significant because the addition of the third objective does not worsen the results of the other two objectives. We also propose a simple method to rank the Pareto solutions so obtained by proposing a new measure, namely the ratio of the hyper-volume and inverted generational distance (IGD). The higher the ratio, the better is the Pareto set. This strategy is particularly useful in the absence of empirical attainment function in the multi-objective framework, where the number of objectives is more than two.

cs.NE↗

arXiv2020

MUXConv: Information Multiplexing in Convolutional Neural Networks

Convolutional neural networks have witnessed remarkable improvements in computational efficiency in recent years. A key driving force has been the idea of trading-off model expressivity and efficiency through a combination of $1\times 1$ and depth-wise separable convolutions in lieu of a standard convolutional layer. The price of the efficiency, however, is the sub-optimal flow of information across space and channels in the network. To overcome this limitation, we present MUXConv, a layer that is designed to increase the flow of information by progressively multiplexing channel and spatial information in the network, while mitigating computational complexity. Furthermore, to demonstrate the effectiveness of MUXConv, we integrate it within an efficient multi-objective evolutionary algorithm to search for the optimal model hyper-parameters while simultaneously optimizing accuracy, compactness, and computational efficiency. On ImageNet, the resulting models, dubbed MUXNets, match the performance (75.3% top-1 accuracy) and multiply-add operations (218M) of MobileNetV3 while being 1.6$\times$ more compact, and outperform other mobile models in all the three criteria. MUXNet also performs well under transfer learning and when adapted to object detection. On the ChestX-Ray 14 benchmark, its accuracy is comparable to the state-of-the-art while being $3.3\times$ more compact and $14\times$ more efficient. Similarly, detection on PASCAL VOC 2007 is 1.2% more accurate, 28% faster and 6% more compact compared to MobileNetV2. Code is available from https://github.com/human-analysis/MUXConv

cs.CV↗

arXiv2020

pymoo: Multi-objective Optimization in Python

Python has become the programming language of choice for research and industry projects related to data science, machine learning, and deep learning. Since optimization is an inherent part of these research fields, more optimization related frameworks have arisen in the past few years. Only a few of them support optimization of multiple conflicting objectives at a time, but do not provide comprehensive tools for a complete multi-objective optimization task. To address this issue, we have developed pymoo, a multi-objective optimization framework in Python. We provide a guide to getting started with our framework by demonstrating the implementation of an exemplary constrained multi-objective optimization scenario. Moreover, we give a high-level overview of the architecture of pymoo to show its capabilities followed by an explanation of each module and its corresponding sub-modules. The implementations in our framework are customizable and algorithms can be modified/extended by supplying custom operators. Moreover, a variety of single, multi and many-objective test problems are provided and gradients can be retrieved by automatic differentiation out of the box. Also, pymoo addresses practical needs, such as the parallelization of function evaluations, methods to visualize low and high-dimensional spaces, and tools for multi-criteria decision making. For more information about pymoo, readers are encouraged to visit: https://pymoo.org

cs.NE↗

arXiv2019

Does Preference Always Help? A Holistic Study on Preference-Based Evolutionary Multi-Objective Optimisation Using Reference Points

The ultimate goal of multi-objective optimisation is to help a decision maker (DM) identify solution(s) of interest (SOI) achieving satisfactory trade-offs among multiple conflicting criteria. This can be realised by leveraging DM's preference information in evolutionary multi-objective optimisation (EMO). No consensus has been reached on the effectiveness brought by incorporating preference in EMO (either a priori or interactively) versus a posteriori decision making after a complete run of an EMO algorithm. Bearing this consideration in mind, this paper i) provides a pragmatic overview of the existing developments of preference-based EMO; and ii) conducts a series of experiments to investigate the effectiveness brought by preference incorporation in EMO for approximating various SOI. In particular, the DM's preference information is elicited as a reference point, which represents her/his aspirations for different objectives. Experimental results demonstrate that preference incorporation in EMO does not always lead to a desirable approximation of SOI if the DM's preference information is not well utilised, nor does the DM elicit invalid preference information, which is not uncommon when encountering a black-box system. To a certain extent, this issue can be remedied through an interactive preference elicitation. Last but not the least, we find that a preference-based EMO algorithm is able to be generalised to approximate the whole PF given an appropriate setup of preference information.

cs.NE↗

arXiv2019

Approximations for Pareto and Proper Pareto solutions and their KKT conditions

In this article, we view the approximate version of Pareto and weak Pareto solutions of the multiobjective optimization problem through the lens of KKT type conditions. We also focus on an improved version of Geoffrion proper Pareto solutions and characterize them through saddle point and KKT type conditions. We present an approximate version of the improved Geoffrion proper solutions and propose our results in general settings.

math.OC↗

arXiv2019

Difficulty Adjustable and Scalable Constrained Multi-objective Test Problem Toolkit

Multi-objective evolutionary algorithms (MOEAs) have progressed significantly in recent decades, but most of them are designed to solve unconstrained multi-objective optimization problems. In fact, many real-world multi-objective problems contain a number of constraints. To promote research on constrained multi-objective optimization, we first propose a problem classification scheme with three primary types of difficulty, which reflect various types of challenges presented by real-world optimization problems, in order to characterize the constraint functions in constrained multi-objective optimization problems (CMOPs). These are feasibility-hardness, convergence-hardness and diversity-hardness. We then develop a general toolkit to construct difficulty-adjustable and scalable CMOPs (DAS-CMOPs, or DAS-CMaOPs when the number of objectives is greater than three) with three types of parameterized constraint functions developed to capture the three proposed types of difficulty. Based on this toolkit, we suggest nine difficulty-adjustable and scalable CMOPs and nine CMaOPs. The experimental results reveal that mechanisms in MOEA/D-CDP may be more effective in solving convergence-hard DAS-CMOPs, while mechanisms of NSGA-II-CDP may be more effective in solving DAS-CMOPs with simultaneous diversity-, feasibility- and convergence-hardness. Mechanisms in C-NSGA-III may be more effective in solving feasibility-hard CMaOPs, while mechanisms of C-MOEA/DD may be more effective in solving CMaOPs with convergence-hardness. In addition, none of them can solve these problems efficiently, which stimulates us to continue to develop new CMOEAs and CMaOEAs to solve the suggested DAS-CMOPs and DAS-CMaOPs.

cs.NE↗

arXiv2019

NSGA-Net: Neural Architecture Search using Multi-Objective Genetic Algorithm

This paper introduces NSGA-Net -- an evolutionary approach for neural architecture search (NAS). NSGA-Net is designed with three goals in mind: (1) a procedure considering multiple and conflicting objectives, (2) an efficient procedure balancing exploration and exploitation of the space of potential neural network architectures, and (3) a procedure finding a diverse set of trade-off network architectures achieved in a single run. NSGA-Net is a population-based search algorithm that explores a space of potential neural network architectures in three steps, namely, a population initialization step that is based on prior-knowledge from hand-crafted architectures, an exploration step comprising crossover and mutation of architectures, and finally an exploitation step that utilizes the hidden useful knowledge stored in the entire history of evaluated neural architectures in the form of a Bayesian Network. Experimental results suggest that combining the dual objectives of minimizing an error metric and computational complexity, as measured by FLOPs, allows NSGA-Net to find competitive neural architectures. Moreover, NSGA-Net achieves error rate on the CIFAR-10 dataset on par with other state-of-the-art NAS methods while using orders of magnitude less computational resources. These results are encouraging and shows the promise to further use of EC methods in various deep-learning paradigms.

cs.CV↗

arXiv2018

Modeling and Multi-objective Optimization of a Kind of Teaching Manipulator

A new kind of six degree-of-freedom teaching manipulator without actuators is designed, for recording and conveniently setting a trajectory of an industrial robot. The device requires good gravity balance and operating force performance to ensure being controlled easily and fluently. In this paper, we propose a process for modeling the manipulator and then the model is used to formulate a multi-objective optimization problem to optimize the design of the testing manipulator. Three objectives, including total mass of the device, gravity balancing and operating force performance are analyzed and defined. A popular non-dominated sorting genetic algorithm (NSGA-II-CDP) is used to solve the optimization problem. The obtained solutions all outperform the design of a human expert. To extract design knowledge, an innovization study is performed to establish meaningful implicit relationship between the objective space and the decision space, which can be reused by the designer in future design process.

cs.RO↗

arXiv2017

Push and Pull Search for Solving Constrained Multi-objective Optimization Problems

This paper proposes a push and pull search (PPS) framework for solving constrained multi-objective optimization problems (CMOPs). To be more specific, the proposed PPS divides the search process into two different stages, including the push and pull search stages. In the push stage, a multi-objective evolutionary algorithm (MOEA) is adopted to explore the search space without considering any constraints, which can help to get across infeasible regions very fast and approach the unconstrained Pareto front. Furthermore, the landscape of CMOPs with constraints can be probed and estimated in the push stage, which can be utilized to conduct the parameters setting for constraint-handling approaches applied in the pull stage. Then, a constrained multi-objective evolutionary algorithm (CMOEA) equipped with an improved epsilon constraint-handling is applied to pull the infeasible individuals achieved in the push stage to the feasible and non-dominated regions. Compared with other CMOEAs, the proposed PPS method can more efficiently get across infeasible regions and converge to the feasible and non-dominated regions by applying push and pull search strategies at different stages. To evaluate the performance regarding convergence and diversity, a set of benchmark CMOPs is used to test the proposed PPS and compare with other five CMOEAs, including MOEA/D-CDP, MOEA/D-SR, C-MOEA/D, MOEA/D-Epsilon and MOEA/D-IEpsilon. The comprehensive experimental results demonstrate that the proposed PPS achieves significantly better or competitive performance than the other five CMOEAs on most of the benchmark set.

cs.NE↗