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.

/pdf/differential-evolution-a-survey-of-the-state-of-the-art-3lz840pz2t.pdf

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.

/pdf/an-evolutionary-many-objective-optimization-algorithm-using-2bj8j4euce.pdf

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

In this paper, we propose a population-based implementation of simulated annealing to tackle multi-objective optimisation problems, in particular those of combinatorial nature. The proposed algorithm is called Evolutionary Multi-objective Simulated Annealing Algorithm (EMOSA), which combines local and evolutionary search by incorporating two distinctive features. The first feature is to tune the weight vectors of scalarizing functions (i.e., search directions) for selection during local search using a two-phase strategy. The second feature is the competition between members of the current population with similar weight vectors. We compare the proposed algorithm to three other multi-objective simulated annealing algorithms and also to the Pareto archived evolutionary strategy (PAES). Experiments are carried out on a set of bi-objective travelling salesman problem (TSP) instances with convex or nonconvex Pareto-optimal fronts. Our experimental results demonstrate that the two-phase tuning of weight vectors and the competition between individuals make a significant contribution to the improved performance of EMOSA.

/pdf/evolutionary-multi-objective-simulated-annealing-with-4ezqmuzqal.pdf

Evolutionary Multi-objective Simulated Annealing with adaptive and competitive search direction

Clustering based content and color adaptive tone mapping

Multi-exposure fusion (MEF) is a widely used approach to high dynamic range imaging The selection of features for fusion weight calculation is important to the performance of MEF In this paper, we investigate the effectiveness of convolutional neural network (CNN) features for MEF Considering the fact that there are no ground-truth images in MEF to train an end-to-end CNN, we adopt the pre-trained networks in other tasks to extract the feature Both the selection of network and the selection of convolution layer are studied With the extracted CNN feature map, we compute the local visibility and consistency maps to determine the weight map for MEF The proposed method works well for both static and dynamic scenes It exhibits competitive quantitative measures, and presents perceptually pleasing MEF outputs with little halo effects

Multi-Exposure Fusion with CNN Features

Iterative thresholding is a dominating strategy for sparse optimization problems. The main goal of iterative thresholding methods is to find a so-called $k$ -sparse solution. However, the setting of regularization parameters or the estimation of the true sparsity are nontrivial in iterative thresholding methods. To overcome this shortcoming, we propose a preference-based multiobjective evolutionary approach to solve sparse optimization problems in compressive sensing. Our basic strategy is to search the knee part of weakly Pareto front with preference on the true $k$ -sparse solution. In the noiseless case, it is easy to locate the exact position of the $k$ -sparse solution from the distribution of the solutions found by our proposed method. Therefore, our method has the ability to detect the true sparsity. Moreover, any iterative thresholding methods can be used as a local optimizer in our proposed method, and no prior estimation of sparsity is required. The proposed method can also be extended to solve sparse optimization problems with noise. Extensive experiments have been conducted to study its performance on artificial signals and magnetic resonance imaging signals. Our experimental results have shown that our proposed method is very effective for detecting sparsity and can improve the reconstruction ability of existing iterative thresholding methods.

A Preference-Based Multiobjective Evolutionary Approach for Sparse Optimization

We propose an elitist Greedy Randomized Adaptive Search Procedure (GRASP) metaheuristic algorithm, called mGRASP/MH, for approximating the Pareto-optimal front in the multi-objective quadratic assignment problem (mQAP). The proposed algorithm is characterized by three features: elite greedy randomized construction, adaptation of search directions and cooperation between solutions. The approach builds starting solutions in a greedy fashion by using problem-specific information and elite solutions found previously. Also, mGRASP/MH maintains a population of solutions, each associated with a search direction (i.e. weight vector). These search directions are adaptively changed during the search. Moreover, a cooperation mechanism is also implemented between the solutions found by different local search procedures in mGRASP/MH. Our experiments show that mGRASP/MH performs better or similarly to several other state-of-the-art multi-objective metaheuristic algorithms when solving benchmark mQAP instances.

/pdf/an-elitist-grasp-metaheuristic-for-the-multi-objective-11knjhhl7c.pdf

Hui Li

Papers

Evolutionary Multi-objective Simulated Annealing with adaptive and competitive search direction

Clustering based content and color adaptive tone mapping

Multi-Exposure Fusion with CNN Features

A Preference-Based Multiobjective Evolutionary Approach for Sparse Optimization

An Elitist GRASP Metaheuristic for the Multi-objective Quadratic Assignment Problem