High-dimensional Multi-modal Optimization Research Articles

Surrogate and Autoencoder-Assisted Multitask Particle Swarm Optimization for High-Dimensional Expensive Multimodal Problems

In practice, some optimization problems require expensive calculation and exhibit multimodal characteristics simultaneously. These problems are called high-dimensional expensive multimodal optimization problems. When addressing such problems, existing surrogate-assisted evolutionary algorithms (SAEAs) encounter the “curse of dimensionality," which severely affects their capability to search optimal solutions. Therefore, this study proposed a surrogate and autoencoder-assisted multitask particle swarm optimization algorithm. First, an autoencoder-embedded multitask evolutionary framework was established to transform a high-dimensional multimodal optimization problem into multiple low-dimensional subproblems or subtasks. Further, a multi-level surrogate model management mechanism combining mirror learning was proposed. An appropriate local surrogate model can be rapidly generated for each modality of the problem. Moreover, a dual-mode local exploitation strategy was developed to improve the capability of swarm to exploit each subtask. The proposed algorithm was compared with seven existing SAEAs on 33 benchmark functions and the aeroengine aerodynamic design optimization problem. Experimental results revealed that the proposed algorithm can obtain multiple highly competitive optimal solutions, including global optimal solutions.

Improved Driving Training-Based Optimization Algorithm Using Levy Flight and Crowding Distance Techniques

This study presents an improved version of the Driving Training-Based Optimization (DTBO) algorithm, the Improved Driving Training-Based Optimization (IDTBO). The work addresses fundamental issues in selecting drivers and learners for the conventional DTBO, which substantially impact the algorithm's accuracy and convergence speed. Two significant improvements are proposed: including the crowding distance technique for more diverse driver and learner selection and incorporating the Levy Flight distribution for better exploration and local optima avoidance. The IDTBO's performance is evaluated using twelve benchmark functions, including unimodal and high-dimensional multimodal optimization functions. The results indicate that IDTBO performs exceptionally well, with more extraordinary exploitation ability on unimodal functions and consistent achievement of the global optima. The proposed IDTBO demonstrated exceptional exploration capabilities on high-dimensional multimodal functions and performed competitively with other algorithms in the literature. From six functions, the IDTBO obtained zero optimal values. Again, the rate of convergence analysis demonstrates that IDTBO finds optimal solutions in fewer iterations, demonstrating its capacity to balance exploration and exploitation. To assess the strength of the IDTBO in solving real-world problems, the improved DTBO is further tested on two practical benchmark engineering problems. The IDTBO again produced a competitive performance against other algorithms in the literature. The study shows that IDTBO is a valuable metaheuristic algorithm that can tackle various real-world optimization problems.

Subject-Specific Human Modeling for Human Pose Estimation

3-D human pose estimation or human tracking has always been the focus of research in the human–computer interaction community. As the calibration step of human pose estimation, subject-specific modeling is crucially important to the subsequent pose estimation process. It not only provides a priori knowledge but also clearly defines the tracking target. This article presents a fully automatic subject modeling framework to reconstruct human pose, shape, as well as the body texture in a challenging optimization scenario. By integrating powerful differentiable rendering into the subject-specific modeling pipeline, the proposed method transforms the texture reconstruction problem into analysis by synthesis minimization and solves it efficiently by a gradient-based method. Furthermore, a novel covariance matrix adaptation annealing algorithm is proposed to attack the high-dimensional multimodal optimization problem in an adaptive manner. The domain knowledge of hierarchical human anatomy is seamlessly injected to the annealing optimization process by using a soft covariance matrix mask. All together contributes to the novel algorithm robust to the temptation of local minima. Experiments on the Human3.6 M dataset and the People-Snapshot dataset demonstrate the competitive results to the state of the art both qualitatively and quantitatively.

Three-dimensional UCAV path planning using a novel modified artificial ecosystem optimizer

As a challenging high-dimensional multimodal optimization problem, path planning for unmanned combat aerial vehicles (UCAVs) has evolved into a hard optimization problem with multiple objectives and types of constraints in complex operational environments. The traditional approaches lack good search capability in complex multimodal search spaces, resulting in difficulties in providing satisfactory flight paths under multiple constraints. Intelligent optimization algorithms have become the first choice for solving path planning problems because of their excellent global exploration capabilities. Artificial ecosystem optimizer (AEO) is an efficient and intelligent optimization algorithm that has remarkable effectiveness in handling optimization problems. However, it also has the disadvantage of slow convergence. In this work, a modified version of the AEO, named MAEO, is proposed to overcome its shortcomings and apply it to the UCAV path planning problem. In the MAEO algorithm, a new production model that focuses on the current optimal search area is proposed to improve the quality of the producer, thereby effectively guiding consumers to search for the optimal space. Then, an enhanced updating consumption mechanism inspired by animal predation behavior is designed, including two predation operations: one is the introduction of the dynamic elite individual in the original update method to simulate that consumers are also predated by their natural enemies during predation to enhance the convergence speed of the algorithm. The second is a unique spiral predation strategy adopted by the consumers to round up the prey. This mechanism not only effectively avoids the lack of population diversity but also improves the global exploration ability of the algorithm. Furthermore, an adaptive Cauchy mutation strategy is successfully hybridized with the AEO algorithm to boost the ability of the algorithm to escape from the local optimum. Simulation experiments of path planning in a series of complex three-dimensional environments show that the algorithm can plan a path satisfying the constraints stably and efficiently, which proves the superiority of the algorithm.

Improved salp swarm algorithm based on gravitational search and multi-leader search strategies

<abstract> <p>The salp swarm algorithm (SSA) will converge prematurely and fall into local optimum when solving complex high-dimensional multimodal optimization tasks. This paper proposes an improved SSA (GMLSSA) based on gravitational search and multi-swarm search strategies. In the gravitational search strategy, using multiple salp individuals to guide the location update of search agents can get rid of the limitation of individual guidance and improve the exploration ability of the algorithm. In the multi-swarm leader strategy, the original population is divided into several independent subgroups to increase population diversity and avoid falling into local optimization. In the experiment, 20 benchmark functions (including the well-known CEC 2014 function) were used to test the performance of the proposed GMLSSA in different dimensions, and the results were compared with the most advanced search algorithm and SSA variants. The experimental results are evaluated through four different analysis methods: numerical, stability, high-dimensional performance, and statistics. These results conclude that GMLSSA has better solution quality, convergence accuracy, and stability. In addition, GMLSSA is used to solve the tension/compression spring design problem (TCSD). The proposed GMLSSA is superior to other competitors in terms of solution quality, convergence accuracy, and stability.</p> </abstract>

A New Method for Analyzing the Performance of the Harmony Search Algorithm

A harmony search (HS) algorithm for solving high-dimensional multimodal optimization problems (named DIHS) was proposed in 2015 and showed good performance, in which a dynamic-dimensionality-reduction strategy is employed to maintain a high update success rate of harmony memory (HM). However, an extreme assumption was adopted in the DIHS that is not reasonable, and its analysis for the update success rate is not sufficiently accurate. In this study, we reanalyzed the update success rate of HS and now present a more valid method for analyzing the update success rate of HS. In the new analysis, take-k and take-all strategies that are employed to generate new solutions are compared to the update success rate, and the average convergence rate of algorithms is also analyzed. The experimental results demonstrate that the HS based on the take-k strategy is efficient and effective at solving some complex high-dimensional optimization problems.

Adaptive Dynamic Disturbance Strategy for Differential Evolution Algorithm

To overcome the problems of slow convergence speed, premature convergence leading to local optimization and parameter constraints when solving high-dimensional multi-modal optimization problems, an adaptive dynamic disturbance strategy for differential evolution algorithm (ADDSDE) is proposed. Firstly, this entails using the chaos mapping strategy to initialize the population to increase population diversity, and secondly, a new weighted mutation operator is designed to weigh and combinemutation strategies of the standard differential evolution (DE). The scaling factor and crossover probability are adaptively adjusted to dynamically balance the global search ability and local exploration ability. Finally, a Gauss perturbation operator is introduced to generate a random disturbance variation, and to accelerate premature individuals to jump out of local optimization. The algorithm runs independently on five benchmark functions 20 times, and the results show that the ADDSDE algorithm has better global optimization search ability, faster convergence speed and higher accuracy and stability compared with other optimization algorithms, which provide assistance insolving high-dimensionaland complex problems in engineering and information science.

Monkey King Evolution: an enhanced ebb-tide-fish algorithm for global optimization and its application in vehicle navigation under wireless sensor network environment

Optimization algorithms are proposed to maximize the desirable properties while simultaneously minimizing the undesirable characteristics. Particle Swarm Optimization (PSO) is a famous optimization algorithm, and it has undergone many variants since its inception in 1995. Though different topologies and relations among particles are used in some state-of-the-art PSO variants, the overall performance on high dimensional multimodal optimization problem is still not very good. In this paper, we present a new memetic optimization algorithm, named Monkey King Evolutionary (MKE) algorithm, and give a comparative view of the PSO variants, including the canonical PSO, Inertia Weighted PSO, Constriction Coefficients PSO, Fully-Informed Particle Sawrm, Cooperative PSO, Comprehensive Learning PSO and some variants proposed in recent years, such as Dynamic Neighborhood Learning PSO, Social Learning Particle Swarm Optimization etc. The proposed MKE algorithm is a further work of ebb-tide-fish algorithm and what's more it performs very well not only on unimodal benchmark functions but also on multimodal ones on high dimensions. Comparison results under CEC2013 test suite for real parameter optimization show that the proposed MKE algorithm outperforms state-of-the-art PSO variants significantly. An application of the vehicle navigation optimization is also discussed in the paper, and the conducted experiment shows that the proposed approach to path navigation optimization saves travel time of real-time traffic navigation in a micro-scope traffic networks.

A harmony search algorithm for high-dimensional multimodal optimization problems

Harmony search (HS) and its variants have been found successful applications, however with poor solution accuracy and convergence performance for high-dimensional (≥200) multimodal optimization problems. The reason is mainly huge search space and multiple local minima. To tackle the problem, we present a new HS algorithm called DIHS, which is based on Dynamic-Dimensionality-Reduction-Adjustment (DDRA) and dynamic fret width (fw) strategy. The former is for avoiding generating invalid solutions and the latter is to balance global exploration and local exploitation. Theoretical analysis on the DDRA strategy for success rate of update operation is given and influence of related parameters on solution accuracy is investigated. Our experiments include comparison on solution accuracy and CPU time with seven typical HS algorithms and four widely used evolutionary algorithms (SaDE, CoDE, CMAES and CLPSO) and statistical comparison by the Wilcoxon Signed-Rank Test with the seven HS algorithms and four evolutionary algorithms. The problems in experiments include twelve multimodal and four complex uni-modal functions with high-dimensionality.Experimental results indicate that the proposed approach can provide significant improvement on solution accuracy with less CPU time in solving high-dimensional multimodal optimization problems, and the more dimensionality that the optimization problem is, the more benefits it provides.

Hybrid orthogonal CMAES for solving global optimization problems

In order to overcome the shortcomings of Covariance Matrix Adaptation Evolution Strategy(CMAES),such as premature convergence and low precision,when it is used in high-dimensional multimodal optimization,a hybrid algorithm combined CMAES with Orthogonal Design with Quantization(OD/Q) was proposed.Firstly,the small population CMAES was used to realize a fast searching.When orthogonal CMAES algorithm trapped in local extremum,base vectors for OD/Q were selected dynamically based on the position of current best solution.Then the entire solution space,including the field around extreme value,was explored by trial vectors generated by OD/Q.The proposed algorithm was guided by this process jumping out of the local optimum.The new approach was tested on six high-dimensional multimodal benchmark functions.Compared with other algorithms,the new algorithm has better searching precision,convergence speed and capacity of global search.

Solution of Inverse Convection Heat Transfer Problem Using an Enhanced Particle Swarm Optimization Algorithm

The main objective of this paper is to solve the inverse convection heat transfer problems with particle swarm optimization method. An enhanced particle swarm optimization (EPSO) algorithm is proposed to overcome the shortcoming of earlier convergence of standard PSO algorithms. The performance of EPSO is tested by some benchmark functions; it is shown that EPSO has a strong antilocal trap capability especially for high dimensional multimodal optimization problems. At last, EPSO is used to identify the unknown boundary heat flux in a channel flow. According to the computational results of four test problems, it is clear that the proposed EPSO algorithm is able to estimate the unknown heat flux accurately even when the input data contain measurement error.

Self-adaptive differential evolution algorithm based on orthogonal and niche elite for high-dimensional multi-modal optimization

Traditional Differential Evolution(DE) algorithm has shortcomings,such as being trapped into local optimum easily,low convergence speed and solution precision.An Orthogonal Niche Differential Evolution(ONDE) algorithm was proposed to resolve these problems.Firstly,the orthogonal table was used to generate initial population;secondly,the niche elite selection strategy was utilized to produce Niche Population(NP),and update Elite Population(EP) with niche population;thirdly,trapping into local search was prevented by crowded cutting;finally,differential evolution operator was improved by using self-adaptive mutation operators.Simulations on seven benchmark functions were used to test the proposed algorithm.The experimental results illustrate that ONDE algorithm has some advantages in convergence velocity,solution precision and stability.