A Multioperator Search Strategy Based on Cheap Surrogate Models for Evolutionary Optimization

Surrogate-assisted evolutionary framework with an ensemble of teaching-learning and differential evolution for expensive optimization

Surrogate-assisted evolutionary algorithms (SAEAs) have shown great potential to solve computationally expensive optimization problems (EOPs). Their two key components, i.e., the optimizer and the surrogate model, both need to select solutions to promote further evolution and to update the model, respectively. However, the corresponding selection strategies are designed independently and mainly consider the predicted fitness of candidate solutions. Consequently, they can hardly complement each other well and are much likely to mislead the population evolution since the surrogate model necessarily has some prediction errors. Directing against this issue, this study proposes a unified dual-space-driven selection (DSDS) strategy and develops a new SAEA by taking differential evolution and radial basis function as the optimizer and the surrogate model, respectively. Besides the predicted fitness in objective space of candidate solutions, DSDS also considers their distribution in decision space by measuring how close they are to the geometric centers of their respective neighborhoods with a new indicator called neighborhood centrality (NC). It tries to select the solutions with good fitness and small NC values under a multi-objective sample selection framework and thus helps the resulting SAEA steadily search in multiple neighborhoods of excellent solutions. The performance of the new SAEA was extensively tested on six commonly used benchmark functions with five different dimensions from 20 to 200 as well as two typical real-word traffic signal optimization cases. Experimental results demonstrate that it possesses more competitive performance and stronger robustness than state-of-the-art SAEAs.

This study proposes a new surrogate-assisted evolutionary algorithm, CHDE+ELDR, that combines CHDE, a constraint-handling evolutionary algorithm, and ELDR, a pairwise ranking surrogate model. The experiment compares CHDE+ELDR with CHDE without a surrogate model on 13 constrained optimization benchmark problems. The experimental results show that CHDE+ELDR significantly outperforms CHDE without a surrogate model on all benchmark problems.

In recent years, various methods from the evolutionary computation (EC) field have been applied to electromagnetic (EM) design problems and have shown promising results. However, due to the high computational cost of the EM simulations, the efficiency of directly using evolutionary algorithms is often very low (e.g., several weeks' optimization time), which limits the application of these methods for many industrial applications. To address this problem, a new method, called surrogate model assisted differential evolution for antenna synthesis (SADEA), is presented in this paper. The key ideas are: (1) A Gaussian Process (GP) surrogate model is constructed on-line to predict the performances of the candidate designs, saving a lot of computationally expensive EM simulations. (2) A novel surrogate model-aware evolutionary search mechanism is proposed, directing effective global search even when a traditional high-quality surrogate model is not available. Three complex antennas and two mathematical benchmark problems are selected as examples. Compared with the widely used differential evolution and particle swarm optimization, SADEA can obtain comparable results, but achieves a 3 to 7 times speed enhancement for antenna design optimization.

Many real-world applications can be formulated as expensive multimodal optimization problems (EMMOPs). When surrogate-assisted evolutionary algorithms (SAEAs) are employed to tackle these problems, they not only face the problem of selecting surrogate models but also need to tackle the problem of discovering and updating multiple modalities. Different optimization problems and different stages of evolutionary algorithms (EAs) generally require different types of surrogate models. To address this issue, in this article, we present a multisurrogate-assisted multitasking particle swarm optimization algorithm to seek multiple optimal solutions of EMMOPs at a low computational cost. The proposed algorithm first transforms an EMMOP into a multitasking optimization problem by integrating various surrogate models, and designs a multitasking niche particle swarm algorithm to solve it. Following that, a surrogate model management strategy based on the skill factor and clustering is developed to effectively balance the number of real function evaluations and the prediction accuracy of candidate optimal solutions. In addition, an adaptive local search strategy based on the trust region is proposed to enhance the capability of swarm in exploiting potential optimal modalities. We compare the proposed algorithm with five state-of-the-art SAEAs and seven multimodal EAs on 19 benchmark functions and the building energy conservation problem and experimental results show that the proposed algorithm can obtain multiple highly competitive optimal solutions.

Particle Swarm Optimization or Differential Evolution—A comparison

Accelerating surrogate assisted evolutionary algorithms for expensive multi-objective optimization via explainable machine learning

A surrogate-assisted multi-objective evolutionary algorithm with dimension-reduction for production optimization

In artificial intelligence, evolutionary algorithms (EAs) have shown to be effective and robust in solving difficult optimization problems. EAs are generic populationbased metaheuristic optimization algorithms. The mechanisms used in EAs are inspired by biological evolution: reproduction, mutation, recombination, and selection. The development of EAs can be classified into two categories: single objective and multi-objective optimization. In this thesis, both single objective and multi-objective evolutionary algorithms have been studied. For single objective optimization, various niching techniques are integrated with differential evolution (DE) and particle swarm optimization (PSO) for multi-modal optimization. Multi-modal optimization deals with optimization tasks that involve finding all or most of the global/local peaks in one single run. EAs in their original forms are usually designed for locating one single global solution. To promote and maintain formation of multiple stable subpopulations within a single population, we introduced a neighborhood mutation technique to enhance DE with ability of handling multi-modal problems. We also proposed a locally informed PSO to tackle multi-modal optimization. Beside these, several existing niching techniques from the literature were modified and improved by us.

Optimization of operating schedule of machines in granite industry using evolutionary algorithms

The practical economic dispatch (ED) problems have many non-convex characteristics, which makes the searching of the global optimum difficult when using traditional mathematical methods. This paper presents a novel hybrid algorithm (HA) to the ED problems based on the particle swarm optimization (PSO) technique and differential evolution (DE) algorithm. Since the standard PSO has the adversity of premature convergence, the mutation and crossover operators of the DE, as well as the chaotic sequences, are considered to be integrated into the PSO to improve the global searching ability. Moreover, the dynamic penalty function is applied to deal with the constraints. The proposed method is tested on a 15-unit system considering the ramp rate limits, operating zones, and network losses. Also, the results are compared with those of other optimization methods.

Although surrogate-assisted evolutionary algorithms have been widely utilized in the science and engineering fields, efficient management of surrogates is still a challenging task because of the complicated action mechanisms of surrogates. Trying to investigate how surrogates influence the convergence of evolutionary algorithms, this paper performs an analysis of a (1+1) surrogate-assisted evolutionary algorithm with Gaussian mutations, where a linear surrogate model is employed to approximately evaluate the candidate solutions. Numerical results demonstrate that the linear surrogate model greatly improves performance of evolutionary algorithms on a unimodal problem when the standard deviation of Gaussian mutation σ is small. However, when σ is set big, the improving functions of linear surrogate models are not significant. However, for a multi-modal problem, the positive function of the linear surrogate model is not significant, because the employed Gaussian mutation cannot keep a balance between exploration and exploitation.KeywordsCandidate SolutionSphere FunctionGaussian MutationMultimodal ProblemGaussian Random NumberThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This brief paper reports a hybrid algorithm we developed recently to solve the global optimization problems of multimodal functions, by combining the advantages of two powerful population-based metaheuristics—differential evolution (DE) and particle swarm optimization (PSO). In the hybrid denoted by DEPSO, each individual in one generation chooses its evolution method, DE or PSO, in a statistical learning way. The choice depends on the relative success ratio of the two methods in a previous learning period. The proposed DEPSO is compared with its PSO and DE parents, two advanced DE variants one of which is suggested by the originators of DE, two advanced PSO variants one of which is acknowledged as a recent standard by PSO community, and also a previous DEPSO. Benchmark tests demonstrate that the DEPSO is more competent for the global optimization of multimodal functions due to its high optimization quality.

Flow through open channels can contain solids. The deposition of solids occasionally occurs due to insufficient flow velocity to transfer the solid particles, causing many problems with transfer systems. Therefore, a method to determine the limiting velocity (i.e. Fr) is required. In this paper, three alternative, hybrid evolutionary algorithm methods, including differential evolution (DE), genetic algorithm (GA) and particle swarm optimization (PSO) based on the adaptive network-based fuzzy inference system are presented: ANFIS-GA, ANFIS-DE and ANFIS-PSO. In these methods, evolutionary algorithms optimize the membership functions, and ANFIS adjusts the premises and consequent parameters to optimize prediction performance. The performance of the proposed methods is compared with that of the general ANFIS using three different datasets comprising a wide range of data. The results show that the hybrid models (ANFIS-GA, ANFIS-DE and ANFIS-PSO) are more accurate than general ANFIS in training with a hybrid algorithm (hybrid of back propagation and least squares). Among the evolutionary algorithms, ANFIS-PSO performed the best (R2=0.976, RMSE=0.26, MARE=0.057, BIAS=-0.004 and SI=0.059).

A set of empirical potentials based upon two and three body interactions were constructed for the Li+-C system and structural optimizations for various assemblages containing Li+ ions and graphene sheets were conducted using some emerging evolutionary and genetic algorithms, differential evolution, and particle swarm optimization in particular. Some limited molecular dynamics calculations were also performed. The results are discussed and analyzed with reference to the lithium ion batteries, where the graphite-Li+ assemblages traditionally constitute the negative electrode, for which the present results are highly pertinent.