Pareto Archived Evolution Strategy Research Articles

A Novel Multiobjective Genetic Programming Approach to High-Dimensional Data Classification.

The development of data sensing technology has generated a vast amount of high-dimensional data, posing great challenges for machine learning models. Over the past decades, despite demonstrating its effectiveness in data classification, genetic programming (GP) has still encountered three major challenges when dealing with high-dimensional data: 1) solution diversity; 2) multiclass imbalance; and 3) large feature space. In this article, we have developed a problem-specific multiobjective GP framework (PS-MOGP) for handling classification tasks with high-dimensional data. To reduce the large solution space caused by high dimensionality, we incorporate the recursive feature elimination strategy based on mining the archive of evolved GP solutions. A progressive domination Pareto archive evolution strategy (PD-PAES), which optimizes the objectives in a specific order according to their objectives, is proposed to evaluate the GP individuals and maintain a better diversity of solutions. Besides, to address the seriously imbalanced class issue caused by traditional binary decomposition (BD) one versus rest (OVR) for multiclass classification problems, we design a method named BD with a similar positive and negative class size (BD-SPNCS) to generate a set of auxiliary classifiers. Experimental results on benchmark and real-world datasets demonstrate that our proposed PS-MOGP outperforms state-of-the-art traditional and evolutionary classification methods in the context of high-dimensional data classification.

Intelligent Optimization Approaches for a Secured Dynamic Partial Reconfigurable Architecture-Based Health Monitoring System

In this work, an intelligent multi-objective optimization technique is proposed to optimize various parameters such as power consumption ([Formula: see text]), computation time ([Formula: see text]) and area ([Formula: see text]) for a health monitoring system designed using the Secured Dynamic Partial Reconfiguration (SDPR) architecture. The cost-efficient Dynamic Partial Reconfiguration (DPR)-based field-programmable gate array (FPGA) is very useful for analyzing many applications such as automation and data processing. The novelty of this paper is to design a new intelligent SDPR (i-SDPR) module in order to achieve better performance in a health monitoring system by considering various performance parameters. The SDPR architecture is incorporated with two reconfigurable modules such as Encrypt and Authenticate, which results in an increase in the core power consumption ([Formula: see text]), computation time ([Formula: see text]) and area ([Formula: see text]). So, to improve the performance of the SDPR-based health monitoring system, there is a necessity to optimize the performance parameters and it is achieved through intelligent multi-objective evolutionary (MOEA) techniques. The intelligent multi-objective evolutionary techniques such as Niched-Pareto Genetic Algorithm (NPGA), Pareto Archived Evolution Strategy (PAES) and Pareto Envelope-based Selection Algorithm (PESA) have been considered for better optimization in the performance parameters. For the study, the free-to-use MIMIC-III dataset is taken, which contains critically admitted various intensive care unit patient data. The dataset is processed through any one of the multi-objective evolutionary operators till satisfying the conditions and then forwarded to implementation. The proposed architecture has been implemented and tested using Cyclone[Formula: see text] V SX SoC Development Kit. The comparative analysis of various performance parameters was done for the proposed i-SDPR with the existing techniques such as the DPR and SDPR approach to show the improvement. The results declare that the proposed techniques obtain better performance compared to the existing techniques.

Near-Optimal Covering Solution for USV Coastal Monitoring using PAES

This paper addresses a multi-objective optimization problem for marine monitoring using USV. The objectives are to cover the maximum area with the lowest energy cost while avoiding collisions. The problem is solved using an exact and heuristic methods. First, a multi-objective Mixed Integer Programming formulation is proposed to model the USV monitoring problem. It consists of a combination of the Covering Salesman Problem (CSP) and Travelling Salesman Problem with Profit (TSPP). Then, we use CPLEX software to provide exact solutions. On the other hand, a customized chromosome-size algorithm is used to find heuristic solution. The latter is a multi-objective evolutionary algorithm known as Pareto Archived Evolution Strategy (PAES). The obtained results showed that the exact solving of the USV monitoring mission problem with mixed-integer programming (MIP) methods needs extensive computational costs. However, the customized PAES was able to provide Near-optimal solutions for large-size graphs in much faster time as compared to the exact one.

Energy-based USV maritime monitoring using multi-objective evolutionary algorithms

This study addresses the monitoring mission problem using an USV equipped with an on-board LiDAR allowing to monitor regions inside its coverage radius. The problem is formulated as a bi-objective coverage path planning with two conflicting objectives : minimization of the consumed energy and maximization of the coverage rate. To solve the problem, we use two popular multi-objective evolutionary algorithms : Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and Pareto Archived Evolution Strategy (PAES). First, we compare the efficiency of these two algorithms and show that PAES allows to find solutions allowing to save more energy as compared to those provided by NSGA-II. Then, we propose a new method which improves the performance of evolutionary algorithms when solving covering path planning problems by reducing the chromosome size. We have applied this method on the used algorithms and simulation results shows a significant performance enhancement both PAES and NSGA-II.

A Multicriteria Simheuristic Approach for Solving a Stochastic Permutation Flow Shop Scheduling Problem

This paper proposes a hybridized simheuristic approach that couples a greedy randomized adaptive search procedure (GRASP), a Monte Carlo simulation, a Pareto archived evolution strategy (PAES), and an analytic hierarchy process (AHP), in order to solve a multicriteria stochastic permutation flow shop problem with stochastic processing times and stochastic sequence-dependent setup times. For the decisional criteria, the proposed approach considers four objective functions, including two quantitative and two qualitative criteria. While the expected value and the standard deviation of the earliness/tardiness of jobs are included in the quantitative criteria to address a robust solution in a just-in-time environment, this approach also includes a qualitative assessment of the product and customer importance in order to appraise a weighted priority for each job. An experimental design was carried out in several study instances of the flow shop problem to test the effects of the processing times and sequence-dependent setup times, obtained through lognormal and uniform probability distributions with three levels of coefficients of variation, settled as 0.3, 0.4, and 0.5. The results show that both probability distributions and coefficients of variation have a significant effect on the four decision criteria selected. In addition, the analytical hierarchical process makes it possible to choose the best sequence exhibited by the Pareto frontier that adjusts more adequately to the decision-makers’ objectives.

CBGA-ES+: A Cluster-Based Genetic Algorithm with Non-Dominated Elitist Selection for Supporting Multi-Objective Test Optimization

Many real-world test optimization problems (e.g., test case prioritization) are multi-objective intrinsically and can be tackled using various multi-objective search algorithms (e.g., Non-dominated Sorting Genetic Algorithm (NSGA-II)). However, existing multi-objective search algorithms have certain randomness when selecting parent solutions for producing offspring solutions. In a worse case, suboptimal parent solutions may result in offspring solutions with bad quality, and thus affect the overall quality of the solutions in the next generation. To address such a challenge, we propose CBGA-ES+, a novel cluster-based genetic algorithm with non-dominated elitist selection to reduce the randomness when selecting the parent solutions to support multi-objective test optimization. We empirically compared CBGA-ES+ with random search and greedy (as baselines), four commonly used multi-objective search algorithms (i.e., Multi-objective Cellular genetic algorithm (MOCell), NSGA-II, Pareto Archived Evolution Strategy (PAES), and Strength Pareto Evolutionary Algorithm (SPEA2)), and the predecessor of CBGA-ES+ (named CBGA-ES) using five multi-objective test optimization problems with eight subjects (two industrial, one real world, and five open source). The results showed that CBGA-ES+ managed to significantly outperform the selected search algorithms for a majority of the experiments. Moreover, for the solutions in the same search space, CBGA-ES+ managed to perform better than CBGA-ES, MOCell, NSGA-II, PAES, and SPEA2 for 2.2, 13.6, 14.5, 17.4, and 9.9 percent, respectively. Regarding the running time of the algorithm, CBGA-ES+ was faster than CBGA-ES for all the experiments.

A novel Whale Optimization Algorithm integrated with Nelder–Mead simplex for multi-objective optimization problems

Recently, several meta-heuristics and evolutionary algorithms have been proposed for tackling optimization problems. Such methods tend to suffer from degraded performance when solving multi-objective optimization problems due to addressing the conflicting goals of finding accurate estimation of Pareto optimal solutions and increasing their distribution across all objectives. In this paper, the Whale Optimization Algorithm (WOA) is improved and extended to solve such multi-objective optimization problems with the purpose of alleviating these drawbacks. The improvements include: (1) modifying the distance control factor of the standard WOA to contain values generated dynamically instead of a fixed one, (2) the trade-off between moving toward the opposite of the best solution and its original values based on a certain probability to prevent stuck into local minima, and (3) accelerating the convergence and coverage using Nelder–Mead method and the Pareto Archived Evolution Strategy (PAES). The proposed algorithm is tested on three benchmark multi-objective test functions (DTLZ, CEC 2009, and GLT), including 25 test functions, to verify its effectiveness by comparing with nine robust multi-objective algorithms. The experiments demonstrate the superiority of the proposed algorithm compared to some of the existing multi-objective algorithms in the literature.

A new bi-objective vehicle routing-scheduling problem with cross-docking: Mathematical model and algorithms

This paper addresses a vehicle routing problem with cross-docking (VRPCD) that considers truck scheduling, splitting pickup and delivery orders with time-windows at supplier and retailer locations, while optimizing two conflicting objectives (i.e., cost efficiency and responsiveness). The objectives are to minimize the total operational cost and the sum of the maximum earliness and tardiness. A new bi-objective mixed-integer linear programming model is presented and a multi-objective meta-heuristic evolutionary algorithm is proposed for solving the problem. Numerical results indicate the effectiveness of our proposed algorithm comparing with two multi-objective meta-heuristic algorithms (i.e., non-dominated sorting genetic algorithm (NSGA-II) and Pareto archived evolution strategy (PAES)). Also, we report findings from a hypothetical case study in a retail chain in Houston, Texas.

Multi-objective resource allocation in mobile edge computing using PAES for Internet of Things

In recent years, mobile edge computing (MEC), as a powerful computing paradigm, provides sufficient computing resources for Internet of Things (IoT). Generally, the deployment of MEC servers closer to mobile users has effectively reduced access delays and the cost of using cloud services. However, the multi-objective resource allocation for IoT applications to meet service requirements (i.e., the shortest completion time of IoT applications, the load balance and lower energy consumption of MEC servers, etc.) still faces severe challenges. To address this challenge, a multi-objective resource allocation method, named MRAM, is proposed in this paper for IoT. Technically, the pareto archived evolution strategy is leveraged to optimize the time cost of IoT applications, load balance and energy consumption of MEC servers. Furthermore, the multiple criteria decision making and the technique for order preference by similarity to ideal solution are utilized to obtain the optimal multi-objective resource allocation strategy. Ultimately, the comprehensive analysis of MRAM is introduced in detail.

Modified Pareto archived evolution strategy for the multi-skill project scheduling problem with generalized precedence relations

In this research, we study the multi-skill resource-constrained project scheduling problem, where there are generalized precedence relations between project activities. Workforces are able to perform one or several skills, and their efficiency improves by repeating their skills. For this problem, a mathematical formulation has been proposed that aims to optimize project completion time, reworking risks of activities, and costs of processing the activities, simultaneously. A modified version of the Pareto Archived Evolution Strategy (MV-PAES) is developed to solve the problem. Contrary to the basic PAES, this algorithm operates based on a population of solutions. For the proposed method, we devised crossover and mutation operators, which strengthen this algorithm in exploring solution space. Comprehensive numerical tests have been conducted to evaluate the performance of the MV-PAES in comparison with two other meta-heuristics. The outputs show the excellence of the MV-PAES in comparison with other methods. A real-world software development project has been studied to demonstrate the practicality of the proposed model for real-world environment. The influence of competency evolution has been investigated in this case study. The results imply that the competency evolution has a considerable impact on the objective function values.

Optimal driving based trip planning of electric vehicles using evolutionary algorithms: A driving assistance system

The existing driving assistance systems (DAS) are not capable to manage the electric vehicle (EV) problems namely insufficiency of charging stations and inadequate range. A novel DAS is presented here to extend the range and overcome other EV drawbacks by suggesting the driver an optimal driving strategy (ODS) continuously throughout trip performing. ODS is decided by solving a multi-objective optimization problem (MOOP), subsequently adopting a multi-criterion decision making technique. Implementation of the DAS in real application requires both better optimization results and low computational time. A study was carried out to investigate the DAS performance with four contending evolutionary algorithms (EAs), NSGAII (a non-dominated sorting multi-objective genetic algorithm), PESA (Pareto envelope-based selection algorithm), PAES (Pareto archived evolution strategy), and SPEA 2 (Strength Pareto evolutionary algorithm). After an initial investigation of EA performances based on different matrices, NSGAII and PESA were found to be most suitable. The natures of decision variables in the Pareto-optimal solutions were analyzed. After an extensive analysis based on different micro-trip structures, it was found that without considering the computational time, PESA solutions possess better convergence and diversity properties than NSGAII solutions. Various approaches were adopted to minimize DAS computation time considering both NSGAII and PESA without significantly compromising the solution’s optimality.

Selective ensemble learning method for belief-rule-base classification system based on PAES

Traditional Belief-Rule-Based (BRB) ensemble learning methods integrate all of the trained sub-BRB systems to obtain better results than a single belief-rule-based system. However, as the number of BRB systems participating in ensemble learning increases, a large amount of redundant sub-BRB systems are generated because of the diminishing difference between subsystems. This drastically decreases the prediction speed and increases the storage requirements for BRB systems. In order to solve these problems, this paper proposes BRBCS-PAES: a selective ensemble learning approach for BRB Classification Systems (BRBCS) based on Pareto-Archived Evolutionary Strategy (PAES) multi-objective optimization. This system employs the improved Bagging algorithm to train the base classifier. For the purpose of increasing the degree of difference in the integration of the base classifier, the training set is constructed by the repeated sampling of data. In the base classifier selection stage, the trained base classifier is binary coded, and the number of base classifiers participating in integration and generalization error of the base classifier is used as the objective function for multi-objective optimization. Finally, the elite retention strategy and the adaptive mesh algorithm are adopted to produce the PAES optimal solution set. Three experimental studies on classification problems are performed to verify the effectiveness of the proposed method. The comparison results demonstrate that the proposed method can effectively reduce the number of base classifiers participating in the integration and improve the accuracy of BRBCS.

Robust solutions in multi-objective stochastic permutation flow shop problem

The aim of this paper is to present a simheuristic approach that obtains robust schedules for a multi-objective permutation flow shop problem with stochastic processing times. In fact, this approach minimizes the expected tardiness and standard deviation of tardiness, as a efficiency and a robustness measure for the stated problem. The simheuristic algorithm hybridize the Tabu Search metaheuristic and the Pareto Archived Evolution Strategy algorithm with a Monte Carlo Simulation process. At first, this approach is tested in 540 benchmarked instances for the deterministic case. It uses a zero-standard-deviation strategy to show the competitiveness compared with other implemented tabu search algorithms. Afterwards, two experimental designs are carried out, with the same 540 instances, where two factors of interest are considered, such as the probability distribution and coefficient of variation of processing times. The probability distributions used were the lognormal and uniform distributions, and three coefficients of variation (0.3, 0.4, and 0.5). Results show that both probability distributions and coefficients of variation have a significant effect in the objective functions, showing the importance of an accurate fitting of probability distributions of the parameter under uncertainty. In addition, these results evidence that the usage of deterministic methods in presence of random events are not desirable or recommended. Finally, the simheuristic was implemented to solve the scheduling problem in an optical laboratory showing better results for expected tardiness and standard deviation of tardiness in comparison with company schedules.

NSGA-III Performance in Multi-objective Tour Guide Assignment Problem

Optimization of a multi-objective tour guide assignment problem considering total guiding time, total assignment cost, and service quality is conducted. Several multi-objective evolutionary algorithms (MOEAs), such as the Non-dominated Sorting Genetic Algorithm III (NSGA-III), ε -NSGA-II, the epsilon MOEA (ε -MOEA), NSGA-II, the Pareto archived evolution strategy (PAES), and the Pareto Envelope-based Selection Algorithm II (PESA-II), have been used to solve and evaluate the problem in the MOEA framework. Based on the results, we found that NSGA-III gives better performance than the other algorithms in terms of solution quality and running time.

Belief Rule Base Inference Algorithm Based on Mixed Pareto Archived Evolutionary Strategy

Most of the existing methods for belief rule based (BRB) focus on single objective optimization for parameter or structure. However, according to the existing research, improving reasoning accuracy and reducing the complexity of BRB system usually conflict each other. Thus, designing a suitable algorithm to find right trade-off for the two goals is necessary. For this purpose, an algorithm named M-PAES-BRB (belief rule base inference method based on multi-objective optimization) is proposed to determine an approximation of the optimal Pareto front by concurrently minimizing the root mean squared error and the complexity. The algorithm adopts an improved mixed pareto archived evolutionary strategy (M-PAES) to build a multi-objective optimization model, M-PAES use recombination operator and mutation operator to generate candidate solutions. In the experiment, we select two standard time series, Mackey-Glass and Box-Jenkins as the experimental datasets, to test the feasibility and effectiveness of M-PAES-BRB. Compared to fuzzy rule base multi-objective evolutionary algorithms (FRBSs), the experiment results show that M-PAES-BRB's reasoning accuracy is higher and the complexity is lower.

Multi-objective parallel robotic dispensing planogram optimisation using association rule mining and evolutionary algorithms

ABSTRACTThis research addresses a medication planogram optimisation problem for robotic dispensing systems (RDSs) in mail-order pharmacy automation (MOPA) facilities. A MOPA is used by a high-throughput fulfilment facility that processes a large volume of prescription orders. In MOPA facilities, each RDS unit integrates auto-dispenser devices and a robot arm to count and dispense medications automatically to complete high demand. An RDS planogram is the allocation of medications in one RDS unit and their distribution in different RDS units. A significant challenge in MOPA systems is to design an efficient planogram strategy. In this study, the RDS planogram is optimised to meet three objectives: association between medications, workload balance of RDSs, and robot arm travel distance. Association rule mining (ARM) is applied to explore the associations between medications, whereas a nonlinear mixed-integer programming (MIP) model is developed to optimise medication allocation based on ARM outputs. Four evolutionary algorithms, namely Non-dominated Sorting Genetic Algorithm (NSGA-II), knee-based NSGA-II (k-NSGA-II), Pareto Archived Evolution Strategy (PAES), and Strength Pareto Evolutionary Algorithm (SPEA-II), are applied to solve the proposed planogram optimisation model on eight experimental problems. Based on the different performance evaluation criteria, the best algorithm with higher performance is identified for each criterion.

Simulation-based model for the optimization of machining parameters in a metal-cutting operation

To achieve a certain measurable performance in cutting machines, the machine parameters need to be optimized. Several constraints determine the possible values that these parameters can take. Although parameters are usually assumed to be deterministic, in practice, it is common to find variations on the characteristics of the products or the processes. Modeling machining parameters as stochastic factors provides a more realistic representation of cutting operations. Moreover, multiple operational objectives are of interest, in many real situations, these multiple objectives are conflicting. Consequently, the problem of setting the parameters becomes a trade-off situation. This paper presents a novel Simulation-based Multi-Objective Optimization (SimMOpt) solution procedure. The procedure is divided into two phases: (1) finding initial solutions and, (2) using a simulated annealing-based method for finding neighboring solutions. In the first phase, non-linear goal programming is used for finding high quality initial solutions. The second phase incorporates Pareto Archive Evolution Strategy (PAES) and hypotheses testing for searching near-optimal solutions for a set of stochastic parameters (i.e., cutting speed, feed rate, and depth of cut) in metal cutting operations. Three objectives are optimized (i.e., operation time, operation cost, and quality of the product). The results from implementing this procedure are analyzed and compared to a baseline methodology based on the Multi-Objective Simulated Annealing (MOSA) algorithm. The analysis demonstrates that the proposed method outperforms the Genetic Algorithm (GA), which was the benchmark algorithm, in terms of the solution quality of all the objectives. More importantly, the solutions from using the SimMOpt procedure outperform those obtained from using an enhanced MOSA-based approach (i.e., 4.71% improvement in the hypervolume approximation).

Running time analysis of the Pareto archived evolution strategy on pseudo-Boolean functions

Evolutionary algorithms have long been quite successfully applied to solve multi-objective optimization problems. However, theoretical analysis of multi-objective evolutionary algorithms (MOEAs) is mainly restricted to the simple evolutionary multi-objective optimizer (SEMO). The Pareto archived evolution strategy (PAES) is a simple but important multi-objective evolutionary algorithm which is come from the study of telecommunication problems, and it has been successfully applied to many optimization problems, such as image processing and signal processing. In this paper, we make a first step toward studying the rigorous running time analysis for PAES. We show that the PAES outperforms the SEMO on function PATH when the PAES uses a simple mutation operator. However, it can not find the whole Pareto front with overwhelming probability on the well-studied function LOTZ. Additional experiments show that the experimental results are in agreement with the theoretical results.

Progressive preference articulation for decision making in multi-objective optimisation problems

This paper proposes a novel algorithm for addressing multi-objective optimisation problems, by employing a progressive preference articulation approach to decision making. This enables the interactive incorporation of problem knowledge and decision maker preferences during the optimisation process. A novel progressive preference articulation mechanism, derived from a statistical technique, is herein proposed and implemented within a multi-objective framework based on evolution strategy search and hypervolume indicator selection. The proposed algorithm is named the Weighted Z-score Covariance Matrix Adaptation Pareto Archived Evolution Strategy with Hypervolume-sorted Adaptive Grid Algorithm (WZ-HAGA). WZ-HAGA is based on a framework that makes use of evolution strategy logic with covariance matrix adaptation to perturb the solutions, and a hypervolume indicator driven algorithm to select successful solutions for the subsequent generation. In order to guide the search towards interesting regions, a preference articulation procedure composed of four phases and based on the weighted z-score approach is employed. The latter procedure cascades into the hypervolume driven algorithm to perform the selection of the solutions at each generation. Numerical results against five modern algorithms representing the state-of-the-art in multi-objective optimisation demonstrate that the proposed WZ-HAGA outperforms its competitors in terms of both the hypervolume indicator and pertinence to the regions of interest.

Covariance matrix adaptation pareto archived evolution strategy with hypervolume-sorted adaptive grid algorithm

Real-world problems often involve the optimisation of multiple conflicting objectives. These problems, referred to as multi-objective optimisation problems, are especially challenging when more than three objectives are considered simultaneously. This paper proposes an algorithm to address this class of problems. The proposed algorithm is an evolutionary algorithm based on an evolution strategy framework, and more specifically, on the Covariance Matrix Adaptation Pareto Archived Evolution Strategy (CMA-PAES). A novel selection mechanism is introduced and integrated within the framework. This selection mechanism makes use of an adaptive grid to perform a local approximation of the hypervolume indicator which is then used as a selection criterion. The proposed implementation, named Covariance Matrix Adaptation Pareto Archived Evolution Strategy with Hypervolume-sorted Adaptive Grid Algorithm (CMA-PAES-HAGA), overcomes the limitation of CMA-PAES in handling more than two objectives and displays a remarkably good performance on a scalable test suite in five, seven, and ten-objective problems. The performance of CMA-PAES-HAGA has been compared with that of a competition winning meta-heuristic, representing the state-of-the-art in this sub-field of multi-objective optimisation. The proposed algorithm has been tested in a seven-objective real-world application, i.e. the design of an aircraft lateral control system. In this optimisation problem, CMA-PAES-HAGA greatly outperformed its competitors.