Multiobjective evolutionary algorithms based on decomposition (MOEA/D) have attracted tremendous attention and achieved great success in the fields of optimization and decision-making. MOEA/Ds work by decomposing the target multiobjective optimization problem (MOP) into multiple single-objective subproblems based on a set of weight vectors. The subproblems are solved cooperatively in an evolutionary algorithm framework. Since weight vectors define the search directions and, to a certain extent, the distribution of the final solution set, the configuration of weight vectors is pivotal to the success of MOEA/Ds. The most straightforward method is to use predefined and uniformly distributed weight vectors. However, it usually leads to the deteriorated performance of MOEA/Ds on solving MOPs with irregular Pareto fronts. To deal with this issue, many weight vector adjustment methods have been proposed by periodically adjusting the weight vectors in a random, predefined, or adaptive way. This article focuses on weight vector adjustment on a simplex and presents a comprehensive survey of these weight vector adjustment methods covering the weight vector adaptation strategies, theoretical analyses, benchmark test problems, and applications. The current limitations, new challenges, and future directions of weight vector adjustment are also discussed.

A Survey of Weight Vector Adjustment Methods for Decomposition-Based Multiobjective Evolutionary Algorithms

Evolutionary multi-objective optimization aims to provide a representative subset of the Pareto front to decision makers. In practice, however, decision makers are usually interested in only a particular part of the Pareto front of the multi-objective optimization problem. This is particularly true when the number of objectives becomes large. Over the past decade, preference-based multi-objective optimization has attracted increasing attention from both academia and industry due to its significance in both theory and practice. Significant progress has been made in evolutionary multi-objective optimization and multi-criteria decision communities, although many open issues still remain to be addressed. This paper provides a concise review on preference-based multi-objective optimization, including various preference modeling methods and existing preference-based optimization methods, as well as a brief discussion of the main future challenges.

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A mini-review on preference modeling and articulation in multi-objective optimization: current status and challenges

Considering the diversity of uniform distribution for the solutions of multi-objective optimization problems, we propose the multi-objective genetic algorithm based on fitting (MOGA/F) and interpolation (MOGA/I). The selected operator is based on the optimal reference points uniformly distributed in the objective space, which is calculated by applying a fitting function or interpolation method from a finite set of objective values. After sorting the ranks of the population, the objective space for the last front can be easily calculated by using fitting and interpolation functions, and the uniformly distributed points can be obtained without parameter setting. The individuals with the shortest Euclidean distance to the reference points are chosen according to the error matrix. This method can maintain the diversity and spread of the solutions without destroying the convergence. In this paper, MOGA/F and MOGA/I are compared with the traditional methods, non-dominated sorting genetic algorithm-II and multi-objective evolutionary algorithm based on decomposition, by optimizing the mathematical problems. The numerical examples show that MOGA/F and MOGA/I have a much higher performance in terms of diversity and convergence of the final solutions.

A Multi-Objective Genetic Algorithm Based on Fitting and Interpolation

Change detection is an essential and widely utilized task in remote sensing that aims to detect and analyze changes occurring in the same geographical area over time, which has broad applications in urban development, agricultural surveys, and land cover monitoring. Detecting changes in remote sensing images is a complex challenge due to various factors, including variations in image quality, noise, registration errors, illumination changes, complex landscapes, and spatial heterogeneity. In recent years, deep learning has emerged as a powerful tool for feature extraction and addressing these challenges. Its versatility has resulted in its widespread adoption for numerous image-processing tasks. This paper presents a comprehensive survey of significant advancements in change detection for remote sensing images over the past decade. We first introduce some preliminary knowledge for the change detection task, such as problem definition, datasets, evaluation metrics, and transformer basics, as well as provide a detailed taxonomy of existing algorithms from three different perspectives: algorithm granularity, supervision modes, and frameworks in the Methodology section. This survey enables readers to gain systematic knowledge of change detection tasks from various angles. We then summarize the state-of-the-art performance on several dominant change detection datasets, providing insights into the strengths and limitations of existing algorithms. Based on our survey, some future research directions for change detection in remote sensing are well identified. This survey paper sheds some light the topic for the community and will inspire further research efforts in the change detection task. 

Change Detection Methods for Remote Sensing in the Last Decade: A Comprehensive Review

With strong penetrability and high resolution, synthetic aperture radar (SAR) images have been widely used in remote sensing image change detection. With the essence of heuristics, metaheuristics are suitable for the needs of most real-life optimization problems according to the expected solution quality and allowable calculation time. To improve the accuracy of change detection, this paper proposes a novel efficient metaheuristic change detection procedure. More specifically, we develop a superpixel-based multiobjective change detection method based on superpixel-wise feature representation and self-adaptive neighborhood-based binary difference evolution. During the clustering for feature analysis, a multiobjective optimization problem (MOP) is modeled which take the likelihood and Bhattacharyya distance between changed and unchanged classes as two objective functions. To solve the MOP, this paper firstly applies the superpixel binary representation technique into the encoding process of multiobjective evolutionary algorithm so that the dimension of pixel coding space can be substantially reduced. Then a self-adaptive neighborhood-based binary differential evolution strategy is proposed to explore the optimal change detection strategy, where a novel mutation operator integrating neighborhood information is designed for the improvement of change detection performance. Experimental results on three real SAR datasets confirm that the proposed method can make a better performance on change detection and the metaheuristic algorithm has good convergence and stability. • Change detection of synthetic aperture radar images. • Superpixel-based difference feature representation strategy. • Difference analysis in a form of evolutionary multi-objective optimization. • A self-adaptive neighborhood-based binary difference evolution framework. 

Superpixel-based multiobjective change detection based on self-adaptive neighborhood-based binary differential evolution

Many evolutionary multi-objective optimization (EMOs) methodologies have been proposed and shown a great potential in approximating the entire Pareto front. While in real world, what decision makers (DMs) want is one or several solutions to satisfy their requirements. It has become a hot problem that dynamically using preference information provided by DMs during the optimization process guides the search of EMO algorithms. An interactive reference region-based evolutionary algorithm through decomposition is proposed, denoted as RR-MOEA/D in this paper, which focuses the search on the desire of DMs to save computational resources. MOEA/D, as a well-known multi-objective optimization algorithm, is used as a basic framework here. In MOEA/D, by dealing with the sub-problems in the preference region and ignoring uninterested ones, the solutions obtained can converge to the regions which the DM prefers on the Pareto front and the computational complexity can be saved to a great extent. At each interaction, a humanized and simple interactive condition is adopted so that the reference region can be changed in a very intuitive way if the DM is unsatisfied the results in the interactive process. A rapid interaction is designed and a set of rough solutions can be obtained quickly whenever the preference information is changed. The proposed algorithm is tested on several benchmark problems and the experimental results show that the proposed algorithm can take full use of preference information and successfully converge to the reference region due to its reasonable and simple interaction mechanism.

Interactive Reference Region Based Multi-Objective Evolutionary Algorithm Through Decomposition

This letter puts forward a new algorithm, ensemble strategy multiobjective fuzzy clustering method (ESMOFCM). To fully combine the gray information and spatial information of neighbor pixels, a new dividing fluctuant parameter is proposed for producing a difference image. Then, we use a frame based on multiobjective fuzzy clustering to alleviate the contradiction between removing noise and preserving details in images. Ensemble strategy is adopted to integrate all Pareto optimal solutions. The experimental results show that the proposed algorithm is superior to comparison algorithms.

Change Detection in SAR Images Using Multiobjective Optimization and Ensemble Strategy

The invention discloses an SAR image change detection method based on fluctuation parameter classification, and mainly solves the problems of relatively large speckle noise, failure to retain local information of an SAR image and low classification accuracy. A technical scheme is as follows: on the basis of a ratio operator of a neighborhood, measuring an approaching degree between pixels at a position x and the pixels of the neighborhood omega by employing two new indexes f1 and f2; determining a gray value of a differential image D at the position x by comparing the two new indexes f1 and f2 with a magnitude of a fluctuation parameter h to obtain the differential image D; carrying out clustering on the differential image D to obtain a binary image Q; and updating the binary image Q to obtain the binary image R which is finally detected out. According to the SAR image change detection method disclosed by the invention, the speckle noise is reduced, the image local information is retained and the classification accuracy is improved. And the SAR image change detection method can be applied to remote sensing, medical diagnosis and video monitoring.

SAR image change detection method based on fluctuation parameter classification

The invention discloses a multi-objective optimization SAR image change detection method based on a high-reliability network, and mainly solves the problem in the prior art that speckle noise is relatively large, SAR image local information cannot be kept and classification accuracy is low. The technical scheme is that a fluctuation parameter division method is applied to input two SAR images Y and Y to generate an original difference chart D ; then denoising is performed on the original difference chart to obtain a denoised difference chart D ; using the original difference chart D and the denoised difference chart D to construct two objective functions, calculating to obtain a solution set when function values of the two target functions are minimum at the same time, and then obtaining a plurality of binary images Q ; and using the binary images Q and a trained high-reliaiblity network to obtain a final change detection image R . The multi-objective optimization SAR image change detection method based on the high-reliability network reduces speckle noise, keeps image local information, improves the degree of accuracy of classification, and can be applied to remote sensing, medical diagnosis and video monitoring.

Multi-objective optimization SAR image change detection method based on high-reliability network

The invention discloses a multi-target optimization SAR image change detection method based on integrated learning and mainly solves problems of large spot noise, incapability in keeping the local information of SAR images and low classification accuracy in the prior art. The method comprises steps that a fluctuation parameter division method is employed to generate an original difference graph D1 for two inputted SAR images Y1 and Y2; de-noising of the original difference graph D1 is carried out to acquire a de-noising difference graph D2; two target functions are constructed based on the original difference graphs D1 and the de-noising difference graph D2, a solution set of the two target functions having the smallest function values is acquired through calculation, and multiple binary images are acquired; an integrated learning method is further utilized to acquire a final change detection image R based on the multiple binary images. The method is advantaged in that spot noise is reduced, the image local information is kept, classification accuracy is improved, and the method can be applied to remote sensing, medical diagnosis and video monitoring.

Multi-target optimization SAR image change detection method based on integrated learning

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