Over the last three decades, a large number of evolutionary algorithms have been developed for solving multi-objective optimization problems. However, there lacks an upto-date and comprehensive software platform for researchers to properly benchmark existing algorithms and for practitioners to apply selected algorithms to solve their real-world problems. The demand of such a common tool becomes even more urgent, when the source code of many proposed algorithms has not been made publicly available. To address these issues, we have developed a MATLAB platform for evolutionary multi-objective optimization in this paper, called PlatEMO, which includes more than 50 multiobjective evolutionary algorithms and more than 100 multi-objective test problems, along with several widely used performance indicators. With a user-friendly graphical user interface, PlatEMO enables users to easily compare several evolutionary algorithms at one time and collect statistical results in Excel or LaTeX files. More importantly, PlatEMO is completely open source, such that users are able to develop new algorithms on the basis of it. This paper introduces the main features of PlatEMO and illustrates how to use it for performing comparative experiments, embedding new algorithms, creating new test problems, and developing performance indicators. Source code of PlatEMO is now available at: http://bimk.ahu.edu.cn/index.php?s=/Index/Software/index.html.

PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization [Educational Forum]

Over the last three decades, a large number of evolutionary algorithms have been developed for solving multiobjective
optimization problems. However, there lacks an up-to-date and comprehensive software platform for
researchers to properly benchmark existing algorithms and for practitioners to apply selected algorithms to solve
their real-world problems. The demand of such a common tool becomes even more urgent, when the source code
of many proposed algorithms has not been made publicly available. To address these issues, we have developed
a MATLAB platform for evolutionary multi-objective optimization in this paper, called PlatEMO, which includes
more than 50 multi-objective evolutionary algorithms and more than 100 multi-objective test problems, along with
several widely used performance indicators. With a user-friendly graphical user interface, PlatEMO enables users
to easily compare several evolutionary algorithms at one time and collect statistical results in Excel or LaTeX files.
More importantly, PlatEMO is completely open source, such that users are able to develop new algorithms on the
basis of it. This paper introduces the main features of PlatEMO and illustrates how to use it for performing comparative
experiments, embedding new algorithms, creating new test problems, and developing performance indicators.
Source code of PlatEMO is now available at: http://bimk.ahu.edu.cn/index.php?s=/Index/Software/index.html.

pdf/platemo-a-matlab-platform-for-evolutionary-multi-objective-3ytx02xlep.pdf

PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization

In numerous industrial applications where safety, efficiency, and reliability are among primary concerns, condition-based maintenance (CBM) is often the most effective and reliable maintenance policy. Prognostics, as one of the key enablers of CBM, involves the core task of estimating the remaining useful life (RUL) of the system. Neural networks-based approaches have produced promising results on RUL estimation, although their performances are influenced by handcrafted features and manually specified parameters. In this paper, we propose a multiobjective deep belief networks ensemble (MODBNE) method. MODBNE employs a multiobjective evolutionary algorithm integrated with the traditional DBN training technique to evolve multiple DBNs simultaneously subject to accuracy and diversity as two conflicting objectives. The eventually evolved DBNs are combined to establish an ensemble model used for RUL estimation, where combination weights are optimized via a single-objective differential evolution algorithm using a task-oriented objective function. We evaluate the proposed method on several prognostic benchmarking data sets and also compare it with some existing approaches. Experimental results demonstrate the superiority of our proposed method.

Multiobjective Deep Belief Networks Ensemble for Remaining Useful Life Estimation in Prognostics

Recently, MOEA/D multi-objective evolutionary algorithm based on decomposition has achieved great success in the field of evolutionary multi-objective optimization and has attracted a lot of attention. It decomposes a multi-objective optimization problem MOP into a set of scalar subproblems using uniformly distributed aggregation weight vectors and provides an excellent general algorithmic framework of evolutionary multi-objective optimization. Generally, the uniformity of weight vectors in MOEA/D can ensure the diversity of the Pareto optimal solutions, however, it cannot work as well when the target MOP has a complex Pareto front PF; i.e., discontinuous PF or PF with sharp peak or low tail. To remedy this, we propose an improved MOEA/D with adaptive weight vector adjustment MOEA/D-AWA. According to the analysis of the geometric relationship between the weight vectors and the optimal solutions under the Chebyshev decomposition scheme, a new weight vector initialization method and an adaptive weight vector adjustment strategy are introduced in MOEA/D-AWA. The weights are adjusted periodically so that the weights of subproblems can be redistributed adaptively to obtain better uniformity of solutions. Meanwhile, computing efforts devoted to subproblems with duplicate optimal solution can be saved. Moreover, an external elite population is introduced to help adding new subproblems into real sparse regions rather than pseudo sparse regions of the complex PF, that is, discontinuous regions of the PF. MOEA/D-AWA has been compared with four state of the art MOEAs, namely the original MOEA/D, Adaptive-MOEA/D, -MOEA/D, and NSGA-II on 10 widely used test problems, two newly constructed complex problems, and two many-objective problems. Experimental results indicate that MOEA/D-AWA outperforms the benchmark algorithms in terms of the IGD metric, particularly when the PF of the MOP is complex.

/pdf/moea-d-with-adaptive-weight-adjustment-4jiz8yx52e.pdf

Moea/d with adaptive weight adjustment

During the past two decades, a variety of multiobjective evolutionary algorithms (MOEAs) have been proposed in the literature. As pointed out in some recent studies, however, the performance of an MOEA can strongly depend on the Pareto front shape of the problem to be solved, whereas most existing MOEAs show poor versatility on problems with different shapes of Pareto fronts. To address this issue, we propose an MOEA based on an enhanced inverted generational distance indicator, in which an adaptation method is suggested to adjust a set of reference points based on the indicator contributions of candidate solutions in an external archive. Our experimental results demonstrate that the proposed algorithm is versatile for solving problems with various types of Pareto fronts, outperforming several state-of-the-art evolutionary algorithms for multiobjective and many-objective optimization.

An Indicator-Based Multiobjective Evolutionary Algorithm With Reference Point Adaptation for Better Versatility

State-of-the-art multiobjective evolutionary algorithms (MOEAs) treat all the decision variables as a whole to optimize performance. Inspired by the cooperative coevolution and linkage learning methods in the field of single objective optimization, it is interesting to decompose a difficult high-dimensional problem into a set of simpler and low-dimensional subproblems that are easier to solve. However, with no prior knowledge about the objective function, it is not clear how to decompose the objective function. Moreover, it is difficult to use such a decomposition method to solve multiobjective optimization problems (MOPs) because their objective functions are commonly conflicting with one another. That is to say, changing decision variables will generate incomparable solutions. This paper introduces interdependence variable analysis and control variable analysis to deal with the above two difficulties. Thereby, an MOEA based on decision variable analyses (DVAs) is proposed in this paper. Control variable analysis is used to recognize the conflicts among objective functions. More specifically, which variables affect the diversity of generated solutions and which variables play an important role in the convergence of population. Based on learned variable linkages, interdependence variable analysis decomposes decision variables into a set of low-dimensional subcomponents. The empirical studies show that DVA can improve the solution quality on most difficult MOPs. The code and supplementary material of the proposed algorithm are available at http://web.xidian.edu.cn/fliu/paper.html .

A Multiobjective Evolutionary Algorithm Based on Decision Variable Analyses for Multiobjective Optimization Problems With Large-Scale Variables

MOEA/D decomposes a multi-objective optimization problem (MOP) into a set of scalar sub-problems with evenly spread weight vectors. Recent studies have shown that the fixed weight vectors used in MOEA/D might not be able to cover the whole Pareto front (PF) very well. Due to this, we developed an adaptive weight adjustment method in our previous work by removing subproblems from the crowded parts of the PF and adding new ones into the sparse parts. Although it performs well, we found that the sparse measurement of a subproblem which is determined by the m-nearest (m is the dimensional of the object space) neighbors of its solution can be more appropriately defined. In this work, the neighborhood relationship between subproblems is defined by using Delaunay triangulation (DT) of the points in the population.

MOEA/D with a delaunay triangulation based weight adjustment

With rich visual data, such as images, becoming readily associated with items, visually-aware recommendation systems (VARS) have been widely used in different applications. Recent studies have shown that VARS are vulnerable to item-image adversarial attacks, which add human-imperceptible perturbations to the clean images associated with those items. Attacks on VARS pose new security challenges to a wide range of applications such as e-Commerce and social networks where VARS are widely used. How to secure VARS from such adversarial attacks becomes a critical problem. Currently, there is still a lack of systematic study on how to design secure defense strategies against visual attacks on VARS. In this paper, we attempt to fill this gap by proposing an adversarial image reconstruction and detection framework to secure VARS. Our proposed method can simultaneously (1) secure VARS from adversarial attacks characterized by local perturbations by image reconstruction based on global vision transformers; and (2) accurately detect adversarial examples using a novel contrastive learning approach. Meanwhile, our framework is designed to be used as both a filter and a detector so that they can be jointly trained to improve the flexibility of our defense strategy to a variety of attacks and VARS models. We have conducted extensive experimental studies with two popular attack methods (FGSM and PGD). Our experimental results on two real-world datasets show that our defense strategy against visual attacks is effective and outperforms existing methods on different attacks. Moreover, our method can detect adversarial examples with high accuracy.

pdf/securing-visually-aware-recommender-systems-an-adversarial-121avbth.pdf

Securing Visually-Aware Recommender Systems: An Adversarial Image Reconstruction and Detection Framework

MOEA/D with opposition-based learning for multiobjective optimization problem

Graphical abstractThis figure illustrates the two searching strategies of the proposed differential evolution inspired recombination operator: move towards the target Pareto set to improve the approximation and search along the current Pareto set to enhance the diversity. Display Omitted HighlightsA DE inspired recombination operator is developed for continuous MOPs.The proposed operator performs two complementary searching behaviors.The proposed operator can be integrated with any MOEAs. According to the regularity of continuous multi-objective optimization problems (MOPs), an immune multi-objective optimization algorithm with differential evolution inspired recombination (IMADE) is proposed in this paper. In the proposed IMADE, the novel recombination provides two types of candidate searching directions by taking three recombination parents which distribute along the current Pareto set (PS) within a local area. One of the searching direction provides guidance for finding new points along the current PS, and the other redirects the search away from the current PS and moves towards the target PS. Under the background of the SBX (Simulated binary crossover) recombination which performs local search combined with random search near the recombination parents, the new recombination operator utilizes the regularity of continuous MOPs and the distributions of current population, which helps IMADE maintain a more uniformly distributed PF and converge much faster. Experimental results have demonstrated that IMADE outperforms or performs similarly to NSGAII, NNIA, PESAII and OWMOSaDE in terms of solution quality on most of the ten testing MOPs. IMADE converges faster than NSGAII and OWMOSaDE. The efficiency of the proposed DE recombination and the contributions of DE and SBX recombination to IMADE have also been experimentally investigated in this work.

An immune multi-objective optimization algorithm with differential evolution inspired recombination

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