An efficient surrogate-assisted hybrid optimization algorithm for expensive optimization problems

Progressive Learning Hill Climbing Algorithm with Energy-Map-Based Initialization for Image Reconstruction

Image reconstruction is an interesting yet challenging optimization problem that has several potential applications. The task is to reconstruct an image using a fixed number of transparent polygons. Traditional gradient-based algorithms cannot be applied to the problem since the optimization objective has no explicit expression and cannot be represented by computational graphs. Metaheuristic search algorithms are powerful optimization techniques for solving complex optimization problems, especially in the context of incomplete information or limited computational capability. In this paper, we developed a novel metaheuristic search algorithm named progressive learning hill climbing (ProHC) for image reconstruction. Instead of placing all the polygons on a blank canvas at once, ProHC starts from one polygon and gradually adds new polygons to the canvas until reaching the number limit. Furthermore, an energy-map-based initialization operator was designed to facilitate the generation of new solutions. To assess the performance of the proposed algorithm, we constructed a benchmark problem set containing four different types of images. The experimental results demonstrated that ProHC was able to produce visually pleasing reconstructions of the benchmark images. Moreover, the time consumed by ProHC was much shorter than that of the existing approach.

Two-Stage Data-Driven Evolutionary Optimization for High-Dimensional Expensive Problems

Surrogate-assisted evolutionary algorithms (SAEAs) have been widely used for solving complex and computationally expensive optimization problems. However, most of the existing algorithms converge slowly in the later stage. This article proposes a novel two-stage data-driven evolutionary optimization (TS-DDEO) that meets the requirements of early exploration and later exploitation. In the first stage, a surrogate-assisted hierarchical particle swarm optimization method is used to find a promising area from the entire search space. In the second stage, we propose a best-data-driven optimization (BDDO) method with a strong exploitation ability to accelerate the optimization process. BDDO has a real-time update mechanism for the surrogate model and population and uses a predefined number of ranking-top solutions to update population and surrogates. BDDO combines three surrogate-assisted evolutionary sampling strategies: 1) surrogate-assisted differential evolution sampling; 2) surrogate-assisted local search; and 3) a surrogate-assisted full-crossover (FC) strategy which is proposed to integrate existing best genotypes in the population. Experiments and analysis have validated the effectiveness of the two-stage framework, the BDDO method, and the FC strategy. Moreover, the proposed algorithm is compared with five state-of-the-art SAEAs on high-dimensional benchmark functions. The result shows that TS-DDEO performs better both in effectiveness and robustness.

Surrogate-Assisted Hybrid Meta-Heuristic Algorithm with an Add-Point Strategy for a Wireless Sensor Network

Meta-heuristic algorithms are widely used in complex problems that cannot be solved by traditional computing methods due to their powerful optimization capabilities. However, for high-complexity problems, the fitness function evaluation may take hours or even days to complete. The surrogate-assisted meta-heuristic algorithm effectively solves this kind of long solution time for the fitness function. Therefore, this paper proposes an efficient surrogate-assisted hybrid meta-heuristic algorithm by combining the surrogate-assisted model with gannet optimization algorithm (GOA) and the differential evolution (DE) algorithm, abbreviated as SAGD. We explicitly propose a new add-point strategy based on information from historical surrogate models, using information from historical surrogate models to allow the selection of better candidates for the evaluation of true fitness values and the local radial basis function (RBF) surrogate to model the landscape of the objective function. The control strategy selects two efficient meta-heuristic algorithms to predict the training model samples and perform updates. A generation-based optimal restart strategy is also incorporated in SAGD to select suitable samples to restart the meta-heuristic algorithm. We tested the SAGD algorithm using seven commonly used benchmark functions and the wireless sensor network (WSN) coverage problem. The results show that the SAGD algorithm performs well in solving expensive optimization problems.

Data-driven Harris Hawks constrained optimization for computationally expensive constrained problems

Aiming at the constrained optimization problem where function evaluation is time-consuming, this paper proposed a novel algorithm called data-driven Harris Hawks constrained optimization (DHHCO). In DHHCO, Kriging models are utilized to prospect potentially optimal areas by leveraging computationally expensive historical data during optimization. Three powerful strategies are, respectively, embedded into different phases of conventional Harris Hawks optimization (HHO) to generate diverse candidate sample data for exploiting around the existing sample data and exploring uncharted region. Moreover, a Kriging-based data-driven strategy composed of data-driven population construction and individual selection strategy is presented, which fully mines and utilizes the potential available information in the existing sample data. DHHCO inherits and develops HHO's offspring updating mechanism, and meanwhile exerts the prediction ability of Kriging, reduces the number of expensive function evaluations, and provides new ideas for data-driven constraint optimization. Comprehensive experiments have been conducted on 13 benchmark functions and a real-world expensive optimization problem. The experimental results suggest that the proposed DHHCO can achieve quite competitive performance compared with six representative algorithms and can find the near global optimum with 200 function evaluations for most examples. Moreover, DHHCO is applied to the structural optimization of the internal components of the real underwater vehicle, and the final satisfactory weight reduction effect is more than 18%.

Variable surrogate model-based particle swarm optimization for high-dimensional expensive problems

Many industrial applications require time-consuming and resource-intensive evaluations of suitable solutions within very limited time frames. Therefore, many surrogate-assisted evaluation algorithms (SAEAs) have been widely used to optimize expensive problems. However, due to the curse of dimensionality and its implications, scaling SAEAs to high-dimensional expensive problems is still challenging. This paper proposes a variable surrogate model-based particle swarm optimization (called VSMPSO) to meet this challenge and extends it to solve 200-dimensional problems. Specifically, a single surrogate model constructed by simple random sampling is taken to explore different promising areas in different iterations. Moreover, a variable model management strategy is used to better utilize the current global model and accelerate the convergence rate of the optimizer. In addition, the strategy can be applied to any SAEA irrespective of the surrogate model used. To control the trade-off between optimization results and optimization time consumption of SAEAs, we consider fitness value and running time as a bi-objective problem. Applying the proposed approach to a benchmark test suite of dimensions ranging from 30 to 200 and comparisons with four state-of-the-art algorithms show that the proposed VSMPSO achieves high-quality solutions and computational efficiency for high-dimensional problems.

A survey on binary metaheuristic algorithms and their engineering applications

This article presents a comprehensively state-of-the-art investigation of the engineering applications utilized by binary metaheuristic algorithms. Surveyed work is categorized based on application scenarios and solution encoding, and describes these algorithms in detail to help researchers choose appropriate methods to solve related applications. It is seen that transfer function is the main binary coding of metaheuristic algorithms, which usually adopts Sigmoid function. Among the contributions presented, there were different implementations and applications of metaheuristic algorithms, or the study of engineering applications by different objective functions such as the single- and multi-objective problems of feature selection, scheduling, layout and engineering structure optimization. The article identifies current troubles and challenges by the conducted review, and discusses that novel binary algorithm, transfer function, benchmark function, time-consuming problem and application integration are need to be resolved in future.

An Analysis of the Operation Factors of Three PSO-GA-ED Meta-Heuristic Search Methods for Solving a Single-Objective Optimization Problem

In this study, we evaluate several nongradient (evolutionary) search strategies for minimizing mathematical function expressions. We developed and tested the genetic algorithms, particle swarm optimization, and differential evolution in order to assess their general efficacy in optimization of mathematical equations. A comparison is then made between the results and the efficiency, which is determined by the number of iterations, the observed accuracy, and the overall run time. Additionally, the optimization employs 12 functions from Easom, Holder table, Michalewicz, Ackley, Rastrigin, Rosen, Rosen Brock, Shubert, Sphere, Schaffer, Himmelblau's, and Spring Force Vanderplaats. Furthermore, the crossover rate, mutation rate, and scaling factor are evaluated to determine the effectiveness of the following algorithms. According to the results of the comparison of optimization algorithms, the DE algorithm has the lowest time complexity of the others. Furthermore, GA demonstrated the greatest degree of temporal complexity. As a result, using the PSO method produces different results when repeating the same algorithm with low reliability in terms of locating the optimal location.

Design of Human Resource Management System Based on Deep Learning

With the advent of the Internet era, the frequency and proportion of candidates obtaining recruitment information through the Internet is getting higher and higher, and the amount of human resources information such as talent information and postinformation has also increased unprecedentedly, which makes human resources services face the problem of information overload. At the same time, deep learning has achieved great success in a series of fields such as computer vision, natural language processing, and semantic recognition in recent years. However, there are few related works in the field of deep learning applied to human resource management system at present. Therefore, this paper studies and improves the recommendation algorithm based on deep learning and applies it to the field of human resources recommendation. In order to improve the traditional and single algorithm of the existing recommendation system, and improve the performance of the human resource management recommendation system.

Energy-Efficient Clustering Mechanism of Routing Protocol for Heterogeneous Wireless Sensor Network Based on Bamboo Forest Growth Optimizer

In wireless sensor networks (WSN), most sensor nodes are powered by batteries with limited power, meaning the quality of the network may deteriorate at any time. Therefore, to reduce the energy consumption of sensor nodes and extend the lifetime of the network, this study proposes a novel energy-efficient clustering mechanism of a routing protocol. First, a novel metaheuristic algorithm is proposed, based on differential equations of bamboo growth and the Gaussian mixture model, called the bamboo growth optimizer (BFGO). Second, based on the BFGO algorithm, a clustering mechanism of a routing protocol (BFGO-C) is proposed, in which the encoding method and fitness function are redesigned. It can maximize the energy efficiency and minimize the transmission distance. In addition, heterogeneous nodes are added to the WSN to distinguish tasks among nodes and extend the lifetime of the network. Finally, this paper compares the proposed BFGO-C with three classic clustering protocols. The results show that the protocol based on the BFGO-C can be successfully applied to the clustering routing protocol and can effectively reduce energy consumption and enhance network performance.

An adaptive dimension differential evolution algorithm based on ranking scheme for global optimization

In recent years, evolutionary algorithms based on swarm intelligence have drawn much attention from researchers. This kind of artificial intelligent algorithms can be utilized for various applications, including the ones of big data information processing in nowadays modern world with heterogeneous sensor and IoT systems. Differential evolution (DE) algorithm is one of the important algorithms in the field of optimization because of its powerful and simple characteristics. The DE has excellent development performance and can approach global optimal solution quickly. At the same time, it is also easy to get into local optimal, so it could converge prematurely. In the view of these shortcomings, this article focuses on the improvement of the algorithm of DE and proposes an adaptive dimension differential evolution (ADDE) algorithm that can adapt to dimension updating properly and balance the search and the development better. In addition, this article uses the elitism to improve the location update strategy to improve the efficiency and accuracy of the search. In order to verify the performance of the new ADDE, this study carried out experiments with other famous algorithms on the CEC2014 test suite. The comparison results show that the ADDE is more competitive.

Rotating behind Security: A Lightweight Authentication Protocol Based on IoT-Enabled Cloud Computing Environments

With the rapid development of technology based on the Internet of Things (IoT), numerous IoT devices are being used on a daily basis. The rise in cloud computing plays a crucial role in solving the resource constraints of IoT devices and in promoting resource sharing, whereby users can access IoT services provided in various environments. However, this complex and open wireless network environment poses security and privacy challenges. Therefore, designing a secure authentication protocol is crucial to protecting user privacy in IoT services. In this paper, a lightweight authentication protocol was designed for IoT-enabled cloud computing environments. A real or random model, and the automatic verification tool ProVerif were used to conduct a formal security analysis. Its security was further proved through an informal analysis. Finally, through security and performance comparisons, our protocol was confirmed to be relatively secure and to display a good performance.

A two-stage infill strategy and surrogate-ensemble assisted expensive many-objective optimization

Many optimization problems are expensive in practical applications. The surrogate-assisted optimization methods have attracted extensive attention as they can get satisfyingly optimal solutions in a limited computing resource. In this paper, we propose a two-stage infill strategy and surrogate-ensemble assisted optimization algorithm for solving expensive many-objective optimization problems. In this method, the population is optimized by a surrogate ensemble. Then a two-stage infill strategy is proposed to select individuals for real evaluations. The infill strategy considers individuals with better convergence or greater uncertainty. To calculate the uncertainty, we consider two aspects. One is the approximate variance of the current surrogate ensemble and the other one is the approximate variance of the historical surrogate ensemble. Finally, the population is revised by the recently updated surrogate ensemble. In experiments, we testify our method on two sets of many-objective benchmark problems. The results demonstrate the superiority of our proposed algorithm compared with the state-of-the-art algorithms for solving computationally expensive many-objective optimization problems.

A Mahalanobis Surrogate-Assisted Ant Lion Optimization and Its Application in 3D Coverage of Wireless Sensor Networks

Metaheuristic algorithms are widely employed in modern engineering applications because they do not need to have the ability to study the objective function’s features. However, these algorithms may spend minutes to hours or even days to acquire one solution. This paper presents a novel efficient Mahalanobis sampling surrogate model assisting Ant Lion optimization algorithm to address this problem. For expensive calculation problems, the optimization effect goes even further by using MSAALO. This model includes three surrogate models: the global model, Mahalanobis sampling surrogate model, and local surrogate model. Mahalanobis distance can also exclude the interference correlations of variables. In the Mahalanobis distance sampling model, the distance between each ant and the others could be calculated. Additionally, the algorithm sorts the average length of all ants. Then, the algorithm selects some samples to train the model from these Mahalanobis distance samples. Seven benchmark functions with various characteristics are chosen to testify to the effectiveness of this algorithm. The validation results of seven benchmark functions demonstrate that the algorithm is more competitive than other algorithms. The simulation results based on different radii and nodes show that MSAALO improves the average coverage by 2.122% and 1.718%, respectively.

Multiple infill criterion-assisted hybrid evolutionary optimization for medium-dimensional computationally expensive problems

Surrogate-assisted evolutionary algorithms have been paid more and more attention to solve computationally expensive problems. However, model management still plays a significant importance in searching for the optimal solution. In this paper, a new method is proposed to measure the approximation uncertainty, in which the differences between the solution and its neighbour samples in the decision space, and the ruggedness of the objective space in its neighborhood are both considered. The proposed approximation uncertainty will be utilized in the surrogate-assisted global search to find a solution for exact objective evaluation to improve the exploration capability of the global search. On the other hand, the approximated fitness value is adopted as the infill criterion for the surrogate-assisted local search, which is utilized to improve the exploitation capability to find a solution close to the real optimal solution as much as possible. The surrogate-assisted global and local searches are conducted in sequence at each generation to balance the exploration and exploitation capabilities of the method. The performance of the proposed method is evaluated on seven benchmark problems with 10, 20, 30 and 50 dimensions, and one real-world application with 30 and 50 dimensions. The experimental results show that the proposed method is efficient for solving the low- and medium-dimensional expensive optimization problems by compared to the other six state-of-the-art surrogate-assisted evolutionary algorithms.

Amassing the Security: An Enhanced Authentication Protocol for Drone Communications over 5G Networks

At present, the great progress made by the Internet of Things (IoT) has led to the emergence of the Internet of Drones (IoD). IoD is an extension of the IoT, which is used to control and manipulate drones entering the flight area. Now, the fifth-generation mobile communication technology (5G) has been introduced into the IoD; it can transmit ultra-high-definition data, make the drones respond to ground commands faster and provide more secure data transmission in the IoD. However, because the drones communicate on the public channel, they are vulnerable to security attacks; furthermore, drones can be easily captured by attackers. Therefore, to solve the security problem of the IoD, Hussain et al. recently proposed a three-party authentication protocol in an IoD environment. The protocol is applied to the supervision of smart cities and collects real-time data about the smart city through drones. However, we find that the protocol is vulnerable to drone capture attacks, privileged insider attacks and session key disclosure attacks. Based on the security of the above protocol, we designed an improved protocol. Through informal analysis, we proved that the protocol could resist known security attacks. In addition, we used the real-oracle random model and ProVerif tool to prove the security and effectiveness of the protocol. Finally, through comparison, we conclude that the protocol is secure compared with recent protocols.