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

The classical algorithms based on regularization usually solve sparse optimization problems under the framework of single objective optimization, which combines the sparse term with the loss term. The majority of these algorithms suffer from the setting of regularization parameter or its estimation. To overcome this weakness, the extension of multiobjective evolutionary algorithm based on decomposition (MOEA/D) has been studied for sparse optimization. The major advantages of MOEA/D lie in two aspects: (1) free setting of regularization parameter and (2) detection of true sparsity. Due to the generational mode of MOEA/D, its efficiency for searching the knee region of the Pareto front is not very satisfactory. In this paper, we proposed a new steady-state MOEA/D with the preference to search the region of Pareto front near the true sparse solution. Within each iteration of our proposed algorithm, a local search step is performed to examine a number of solutions with similar sparsity levels in a neighborhood. Our experimental results have shown that the new MOEA/D clearly performs better than its previous version on reconstructing artificial sparse signals.

A New Steady-State MOEA/D for Sparse Optimization

The invention discloses a high bandwidth signal detection method for tracking the resonant frequency of an integrated optical waveguide gyro, and belongs to the technical field of integrated optical waveguide gyro. The method comprises the steps of: firstly, establishing a working circuit structure of a dual-tracking system, modulating a laser signal through an OSB modulator and an integrated optical modulator, and calculating the frequency of input light in a ring waveguide resonant cavity; meanwhile, demodulating output light into a low frequency component and a high frequency component, transmitting the low frequency component to a low frequency controller, and transmitting the low frequency component to a laser after feedback; outputting and converting the high frequency component intoa cosine signal after passing through a high frequency controller, and driving an MZI to lock the resonant frequency; and finally, controlling, by the low frequency controller, the laser frequency tochange within a wide range, quickly tracking, by the high frequency controller, the change of the resonant frequency within a small tracking range, and ensuring that a closed-loop error of resonant frequency tracking in a synchronization process is zero. According to the high bandwidth signal detection method disclosed by the invention, by means of the cooperative work of high and low frequency control loops, simultaneous detection and tracking control of the high and low frequency components are ensured, and high-precision detection is ensured while improving the measurement bandwidth.

High bandwidth signal detection method for tracking resonant frequency of integrated optical waveguide gyro

English courses are a compulsory course for non-English core courses. Studying English at university is an important part of studying at a non-English university. The purpose of a university education in English is to enhance the comprehensive language skills of students in English. In this way, they can communicate effectively in English during future work, study, and social interactions, while strengthening their ability to meet the needs of social development and international exchange. The functional improvement design of the college English network teaching system will help the system to provide technical support and services for college English teaching more effectively. It can more effectively cultivate students’ language communicative ability and autonomous learning ability. This article first improves the practical units of the education system and then adds the decision tree algorithm. It uses improved decision-making algorithms to evaluate student performance with an improved learning system. The number of leaf nodes of the improved decision tree algorithm on the three datasets is 19, 14, and 15, respectively, and the number of summary points is 27, 23, and 7, respectively.

Improvement Design of Functional Modules of College English Network Teaching System Based on Decision Tree Algorithm

This paper proposes a simple and practical reflective birefringent fiber interferometer sensor that consists of a polarization beam splitter, a polarization-maintaining transmission fiber, and a sensor unit comprising two segments of birefringent fibers and a thin-film reflector. This sensor could be used for dual parameter sensing. Experiments with different temperatures and lateral loads applied to the sensor unit demonstrated temperature and load sensitivity of ∼0.0010  nm/°C and 0.298 nm/N, respectively. Further study showed that temperature-insensitive lateral load measurement can be achieved by using equal length of birefringent fibers and performing differential wavelength measurement. The sensor is robust against environmental disturbance on the transmission fiber, making it potentially attractive for practical field applications.

Practical reflective birefringent fiber interferometer sensor.

Information literacy assessment is extremely important for the evaluation of the information literacy skills of college students. Intelligent optimization technique is an effective strategy to optimize the weight parameters of the information literacy assessment index system (ILAIS). In this paper, a new version of differential evolution algorithm (DE), named hybrid differential evolution with model-based reinitialization (HDEMR), is proposed to accurately fit the weight parameters of ILAIS. The main contributions of this paper are as follows: firstly, an improved contraction criterion which is based on the population entropy in objective space and the maximum distance in decision space is employed to decide when the local search starts. Secondly, a modified model-based population reinitialization strategy is designed to enhance the global search ability of HDEMR to handle complex problems. Two types of experiments are designed to assess the performance of HDEMR. In the first type of experiments, HDEMR is tested and compared with seven well-known DE variants on CEC2005 and CEC2014 benchmark functions. In the second type of experiments, HDEMR is compared with the well-known and widely used deterministic algorithm DIRECT on GKLS test classes. The experimental results demonstrate the effectiveness of HDEMR for global numerical optimization and show better performance. Furthermore, HDEMR is applied to optimize the weight parameters of ILAIS at China University of Geosciences (CUG), and satisfactory results are obtained.

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Hui Li

Papers

A New Steady-State MOEA/D for Sparse Optimization

High bandwidth signal detection method for tracking resonant frequency of integrated optical waveguide gyro

Improvement Design of Functional Modules of College English Network Teaching System Based on Decision Tree Algorithm

Practical reflective birefringent fiber interferometer sensor.

Information Literacy Assessment with a Modified Hybrid Differential Evolution with Model-Based Reinitialization