Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms in current use. DE operates through similar computational steps as employed by a standard evolutionary algorithm (EA). However, unlike traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used for generating the offspring. Since its inception in 1995, DE has drawn the attention of many researchers all over the world resulting in a lot of variants of the basic algorithm with improved performance. This paper presents a detailed review of the basic concepts of DE and a survey of its major variants, its application to multiobjective, constrained, large scale, and uncertain optimization problems, and the theoretical studies conducted on DE so far. Also, it provides an overview of the significant engineering applications that have benefited from the powerful nature of DE.

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Differential Evolution: A Survey of the State-of-the-Art

Having developed multiobjective optimization algorithms using evolutionary optimization methods and demonstrated their niche on various practical problems involving mostly two and three objectives, there is now a growing need for developing evolutionary multiobjective optimization (EMO) algorithms for handling many-objective (having four or more objectives) optimization problems. In this paper, we recognize a few recent efforts and discuss a number of viable directions for developing a potential EMO algorithm for solving many-objective optimization problems. Thereafter, we suggest a reference-point-based many-objective evolutionary algorithm following NSGA-II framework (we call it NSGA-III) that emphasizes population members that are nondominated, yet close to a set of supplied reference points. The proposed NSGA-III is applied to a number of many-objective test problems with three to 15 objectives and compared with two versions of a recently suggested EMO algorithm (MOEA/D). While each of the two MOEA/D methods works well on different classes of problems, the proposed NSGA-III is found to produce satisfactory results on all problems considered in this paper. This paper presents results on unconstrained problems, and the sequel paper considers constrained and other specialties in handling many-objective optimization problems.

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An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints

This paper proposes a novel population-based optimization algorithm called Sine Cosine Algorithm (SCA) for solving optimization problems. The SCA creates multiple initial random candidate solutions and requires them to fluctuate outwards or towards the best solution using a mathematical model based on sine and cosine functions. Several random and adaptive variables also are integrated to this algorithm to emphasize exploration and exploitation of the search space in different milestones of optimization. The performance of SCA is benchmarked in three test phases. Firstly, a set of well-known test cases including unimodal, multi-modal, and composite functions are employed to test exploration, exploitation, local optima avoidance, and convergence of SCA. Secondly, several performance metrics (search history, trajectory, average fitness of solutions, and the best solution during optimization) are used to qualitatively observe and confirm the performance of SCA on shifted two-dimensional test functions. Finally, the cross-section of an aircraft's wing is optimized by SCA as a real challenging case study to verify and demonstrate the performance of this algorithm in practice. The results of test functions and performance metrics prove that the algorithm proposed is able to explore different regions of a search space, avoid local optima, converge towards the global optimum, and exploit promising regions of a search space during optimization effectively. The SCA algorithm obtains a smooth shape for the airfoil with a very low drag, which demonstrates that this algorithm can highly be effective in solving real problems with constrained and unknown search spaces. Note that the source codes of the SCA algorithm are publicly available at http://www.alimirjalili.com/SCA.html .

SCA: A Sine Cosine Algorithm for solving optimization problems

Salp Swarm Algorithm

Partly due to lack of test problems, the impact of the Pareto set (PS) shapes on the performance of evolutionary algorithms has not yet attracted much attention. This paper introduces a general class of continuous multiobjective optimization test instances with arbitrary prescribed PS shapes, which could be used for studying the ability of multiobjective evolutionary algorithms for dealing with complicated PS shapes. It also proposes a new version of MOEA/D based on differential evolution (DE), i.e., MOEA/D-DE, and compares the proposed algorithm with NSGA-II with the same reproduction operators on the test instances introduced in this paper. The experimental results indicate that MOEA/D could significantly outperform NSGA-II on these test instances. It suggests that decomposition based multiobjective evolutionary algorithms are very promising in dealing with complicated PS shapes.

Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II

Infrared and visible image fusion aims to generate a composite image with salient thermal targets and texture information from infrared image and visible image Existing advanced methods tend to consume high computational cost for a high-quality fusion result In this paper, a simple yet effective method is proposed based on structural patch decomposition A modified gamma function is proposed to weight the mean intensity component to keep the thermal target An enhanced power function is used to weight the mean-removed component to preserve the texture information Different from general patch level fusion implemented via a sliding window, we convert the explicit structural patch decomposition and fusion into an image level mean filtering via a detailed analysis on input images By this means, the computational cost of the proposed method can be largely reduced, which is independent of the patch size Furthermore, we analyze the relationship of our method with classic filtering based image decomposition methods Finally, a multi-scale implementation of the proposed method is developed to avoid the evident halo and spatial inconsistency artifacts Extensive experimental results on the public dataset demonstrate that the proposed method can obtain more texture information and outperform the state-of-the-art fusion method qualitatively and quantitatively The code can be downloaded from: https://githubcom/xiaohuiben/MSID-KBS 

Fast infrared and visible image fusion with structural decomposition

A novel approach to detect an infrared small target in the compressive domain is presented. First, the original infrared image is projected on a sensing matrix to obtain the measurement vector. Then the target and the background are recovered simultaneously from the measurements based on low-rank and sparse matrix decomposition. Experimental results indicate that the proposed method not only works well under different complex backgrounds with less data storage, but also outperforms some existing methods in both subjective and objective qualities.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/el.2014.0180

Infrared small target detection in compressive domain

MOEA/D is a decomposition-based multiobjective evolutionary algorithm that has attracted much attention in recent years. Its performance depends on the setting of weight vectors which are used for defining subproblems. In the case of irregular Pareto fronts (e.g, disconnected or degenerated), fixed setting of weight vectors in MOEA/D may not work well. In this paper, we propose an improved MOEA/D with both random and fixed weight vectors. Moreover, an external archive based on a modified e-dominance strategy is used for storing nondominated solutions found by the proposed algorithm and assisting the generation of random weight vectors. Some experiments have been conducted to verify the efficiency and effectiveness of the improved MOEA/D on benchmark multiobjective test problems with irregular Pareto fronts. The experimental results show that the overall performance of the proposed algorithm is better than baseline MOEA/D and NSGA-II.

On the use of random weights in MOEA/D

This paper proposes a new constraint handling method named Angle-based Constrained Dominance Principle (ACDP). Unlike the original Constrained Dominance Principle (CDP), this approach adopts the angle information of the objective functions to enhance the population's diversity in the infeasible region. To be more specific, given two infeasible solutions, if the angle of the solutions is greater than a given threshold, they are considered to be non-dominated by each other. For a feasible solution and an infeasible solution, if the angle of the solutions is less than a given threshold, the feasible solution is better, otherwise they are non-dominated. To verify the proposed constraint handling approach ACDP, eight test problems CMOP1 to CMOP8 are introduced. The suggested algorithm MOEA/D-ACDP is compared with MOEA/D-CDP and NSGA-II-CDP on CMOP1 to CMOP8. The experimental results demonstrate that ACDP performs better than CDP in the framework of MOEA/D, and MOEA/D-ACDP is significantly better than NSGA-II-CDP, especially on the test instances with the very low ratio of feasible region against the whole objective space.

Angle-based constrained dominance principle in MOEA/D for constrained multi-objective optimization problems

The multi-exposure fusion (MEF) methods have received much attention in recent years due to the importance of constructing high dynamic range images. Among most of the existing studies, multi-scale structural-patch-decomposition-based MEF (MSPD-MEF) has achieved state-of-the-art fusion quality and the fastest running time. However, this method still suffers from detail loss in the fused images. To tackle this issue, we first incorporate the edge-preserving factors into this method to preserve the details in the fused images in a single-scale setting. Then, we develop the novel and flexible bell curve function, which can further preserve the details in both bright and dark regions. After that, we also show that our method can seamlessly plug in to this multi-scale framework. Extensive experimental results indicate that the proposed method can produce pleasing fusion results with little artifacts and low computational cost in both static and dynamic scenes.

Hui Li

Papers

Fast infrared and visible image fusion with structural decomposition

Infrared small target detection in compressive domain

On the use of random weights in MOEA/D

Angle-based constrained dominance principle in MOEA/D for constrained multi-objective optimization problems

Detail-Preserving Multi-Exposure Fusion With Edge-Preserving Structural Patch Decomposition