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

Silicon nitride waveguide (Si3N4), is used as the most important sensitive device because of its excellent high-polarizing characteristics. It has the potential to build the miniaturized, high-precision resonant integrated optical gyroscope (RIOG) in recent years. However, the back-reflection caused by the refractive index difference between the Si3N4 waveguide and the pigtail fiber has a non-negligible impact on the accuracy of the gyroscope. In this paper, we propose a method to suppress the back-reflection of the end face of the Si3N4 waveguide resonator. We use the Fimmprop module of the simulation software Photon Design to simulate the relationship between the back-reflection coefficient of Si3N4 waveguide and different tilt angles. The simulation result shows that when the end face of the Si3N4 waveguide is oblique cut by 15°, the back-reflection is the minimum, about −67 dB. The back-reflection obtained through the experiments are about −65 dB, consistent with the simulation result. Together, our data suggested that the back-reflection noise of the Si3N4 can be suppressed by the oblique cutting of the end face by 15°. The conclusion can lay a foundation for improving the performance of RIOG based on Si3N4 waveguide resonator.

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Suppression of Back-Reflection From the End Face of Si 3 N 4 Waveguide Resonator

With the development of global market integration, the demand for English professionals in various industries is growing, and the professional standards for English professionals are also getting higher and higher. Therefore, English education is also faced with many opportunities and challenges; especially, the comprehensive education quality of English majors is becoming more and more prominent. The traditional teaching method using test scores as the evaluation standard leads to boring courses, students are not very interested in learning, and they cannot appreciate the charm of disciplines and majors, resulting in prominent problems in teaching form. This paper ﬁ rst analyzes the idea of the English learning quality evaluation system and then analyzes the English learning quality evaluation system based on HS-HKRVM. This paper also analyzes the construction of the English learning quality evaluation system based on the analysis layer process and ﬁ nally studies the construction of the English learning quality evaluation system based on HS-HKRVM. Experiments show that HS-HKRVM can play a great role in the evaluation and improvement of English teaching quality.

Analysis of the Role of HS-HKRVM Analytic Hierarchy Process in the Evaluation of English Teaching Quality

The presence of polarization noise generated by the waveguide resonator limits the performance of a resonant integrated optical gyroscope (RIOG). Using silicon nitride ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m1"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>Si</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> <mml:msub> <mml:mi mathvariant="normal">N</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:mrow> </mml:math> ) to fabricate a waveguide with an ultralow-aspect-ratio can result in a resonator that only supports light transmission in a single-polarization state, suppressing polarization noise. We successfully fabricated a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m2"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>Si</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> <mml:msub> <mml:mi mathvariant="normal">N</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:mrow> </mml:math> resonator with a bending radius of 17.5 mm, a finesse ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m3"> <mml:mrow> <mml:mi>F</mml:mi> </mml:mrow> </mml:math> ) of 150, a quality factor ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m4"> <mml:mrow> <mml:mi>Q</mml:mi> </mml:mrow> </mml:math> ) of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m5"> <mml:mrow> <mml:mn>1.54</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mn>7</mml:mn> </mml:msup> </mml:mrow> </mml:math> , and a propagation loss of 1.2 dB/m. The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m6"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>Si</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> <mml:msub> <mml:mi mathvariant="normal">N</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:mrow> </mml:math> resonator was used to construct a double closed-loop RIOG that showed long-term bias stability (3600 s) of 13.2°/h at room temperature, 14.8°/h at 40°C, 21.2°/h at 50°C, and 23.6°/h at 60°C. We believe this to be the best performance reported to date for a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m7"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>Si</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> <mml:msub> <mml:mi mathvariant="normal">N</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:mrow> </mml:math> resonator-based RIOG. This advancement paves the way for the wider application of RIOGs. 

Integrated optical gyroscope employing high performance silicon nitride resonator

The standard particle swarm optimization algorithm (simply called PSO) has many advantages such as rapid convergence However, a major disadvantage confronting the PSO algorithm is that they often converge to some local optimization In order to avoid the occurrence of premature convergence and local optimization of the PSO algorithm, a particle swarm optimization algorithm based on genetic selection stra-tegy, simply called GSS-PSO, is singled out in this paper GSS-PSO not only retains the rapid convergence charactering of the standard PSO algorithms, but also scales up their global search ability At last, we experimentally tested the efficiency of our new GSS-PSO algorithm using eight classical functions The experimental results show that our new GSS-PSO algorithm is generally better than the PSO algorithm

A Particle Swarm Optimization Algorithm Based on Genetic Selection Strategy

The continuing growth in space debris has posed a great threat to on-orbit operations. It is urgent to implement reliable and lasting monitoring of space debris. Safety and diversity in monitoring devices and business demands makes scheduling system resources increasingly complicated. This article proposes a novel adaptive multipopulation differential evolutionary algorithm based on a theoretical model specialized in the scheduling of space debris monitoring resources. Using Q-learning, the proposed algorithm adapts self-learning and dynamic adjustment properties in population proportion parameters. Experiments are performed with practical batch tasks and monitoring data to verify the effectiveness and reliable utility of the proposed algorithm to ensure the safety of on-orbit operation.

Reliable Scheduling Algorithm for Space Debris Monitoring Resources Using Adaptive Multipopulation Differential Evolutionary Optimization With Reinforcement Learning

Hui Li

Papers

Suppression of Back-Reflection From the End Face of Si 3 N 4 Waveguide Resonator

Analysis of the Role of HS-HKRVM Analytic Hierarchy Process in the Evaluation of English Teaching Quality

Integrated optical gyroscope employing high performance silicon nitride resonator

A Particle Swarm Optimization Algorithm Based on Genetic Selection Strategy

Reliable Scheduling Algorithm for Space Debris Monitoring Resources Using Adaptive Multipopulation Differential Evolutionary Optimization With Reinforcement Learning