Evolutionary Multi-objective Optimization Research Articles

A Many-Objective Evolutionary Algorithm Based on Indicator and Decomposition

In the field of many-objective evolutionary optimization algorithms (MaOEAs), how to maintain the balance between convergence and diversity has been a significant research problem. With the increase of the number of objectives, the number of mutually nondominated solutions increases rapidly, and multi-objective evolutionary optimization algorithms, based on Pareto-dominated relations, become invalid because of the loss of selection pressure in environmental selection. In order to solve this problem, indicator-based many-objective evolutionary algorithms have been proposed; however, they are not good enough at maintaining diversity. Decomposition-based methods have achieved promising performance in keeping diversity. In this paper, we propose a MaOEA based on indicator and decomposition (IDEA) to keep the convergence and diversity simultaneously. Moreover, decomposition-based algorithms do not work well on irregular PFs. To tackle this problem, this paper develops a reference-points adjustment method based on the learning population. Experimental studies of several well-known benchmark problems show that IDEA is very effective compared to ten state-of-the-art many-objective algorithms.

Multi-objective optimal scheduling of laminar cooling water supply system for hot rolling mills driven by digital twin for energy-saving

As a result of the complex structure of laminar cooling water supply systems, both facets of strict process requirements and various intermittent running conditions could cause challenges of energy-saving and equipment upkeep. Given the energy wastage issue of the laminar cooling system of hot rolling, this paper develops an optimal scheduling system according to digital twin using Online Sequential Extreme Learning Machine (OS-ELM) and multi-objective evolutionary optimization using Improved Sparrow Search Algorithm (ISSA). The optimal scheduling system according to digital twins can accurately predict the water consumption trend of the water supply system and optimize the scheduling instructions and operation scheme through dynamic information interaction and mapping of process constraints, intermittent operating conditions, rolling rhythm, measured data, etc. between physical space and virtual space. Experimental results reveal that the proposed method can lessen power usage by 13.60% and water consumption by 10.54% regarding the premise of ensuring what is needed of cooling procedures. In addition, the water pump can maintain high effectiveness during operation to guarantee the security and stability of laminar cooling water supply systems.

Editorial: Evolutionary multi-objective optimization algorithms in microgrid power dispatching

Editorial: Evolutionary multi-objective optimization algorithms in microgrid power dispatching

Crowding distance development for ranking efficient units in DEA

Data Envelopment Analysis models have proven ability to classify decision making units into two efficient and inefficient sets. Although inefficient ones can be sorted by the value of efficiency score, ranking the efficient units has always been a challenging subject in DEA. Various methods, in terms of implementation and nature, have been proposed to rank efficient DMUs. A novel method based on diversity and variety of units on the efficient frontier is presented in this study. Firstly, the crowding distance definition from the multi-objective evolutionary optimization is developed and then a linear programming model is introduced to detect and rank the efficient units at the same time. This means that by solving the proposed model for each DMU separately, ranking efficient units is fulfilled meaning there is no prior need to detect efficient ones. Furthermore, this model can be applied to rank inefficient units with the same logic of the efficient ones which leads to a homogenous ranking of all DMUs. To check the validity and compatibility of this method, it is analyzed through its application on a case study.

A Reference Point-Based Evolutionary Algorithm Solves Multi and Many-Objective Optimization Problems: Method and Validation.

The integration of a decision maker's preferences in evolutionary multi-objective optimization (EMO) has been a common research scope over the last decade. In the published literature, several preference-based evolutionary approaches have been proposed. The reference point-based non-dominated sorting genetic (R-NSGA-II) algorithm represents one of the well-known preference-based evolutionary approaches. This method mainly aims to find a set of the Pareto-optimal solutions in the region of interest (ROI) rather than obtaining the entire Pareto-optimal set. This approach uses Euclidean distance as a metric to calculate the distance between each candidate solution and the reference point. However, this metric may not produce desired solutions because the final minimal Euclidean distance value is unknown. Thus, determining whether the true Pareto-optimal solution is achieved at the end of optimization run becomes difficult. In this study, R-NSGA-II method is modified using the recently proposed simplified Karush-Kuhn-Tucker proximity measure (S-KKTPM) metric instead of the Euclidean distance metric, where S-KKTPM-based distance measure can predict the convergence behavior of a point from the Pareto-optimal front without prior knowledge of the optimum solution. Experimental results show that the algorithm proposed herein is highly competitive compared with several state-of-the-art preference-based EMO methods. Extensive experiments were conducted with 2 to 10 objectives on various standard problems. Results show the effectiveness of our algorithm in obtaining the preferred solutions in the ROI and its ability to control the size of each preferred region separately at the same time.

A Comparative Visual Analytics Framework for Evaluating Evolutionary Processes in Multi-Objective Optimization.

Evolutionary multi-objective optimization (EMO) algorithms have been demonstrated to be effective in solving multi-criteria decision-making problems. In real-world applications, analysts often employ several algorithms concurrently and compare their solution sets to gain insight into the characteristics of different algorithms and explore a broader range of feasible solutions. However, EMO algorithms are typically treated as black boxes, leading to difficulties in performing detailed analysis and comparisons between the internal evolutionary processes. Inspired by the successful application of visual analytics tools in explainable AI, we argue that interactive visualization can significantly enhance the comparative analysis between multiple EMO algorithms. In this paper, we present a visual analytics framework that enables the exploration and comparison of evolutionary processes in EMO algorithms. Guided by a literature review and expert interviews, the proposed framework addresses various analytical tasks and establishes a multi-faceted visualization design to support the comparative analysis of intermediate generations in the evolution as well as solution sets. We demonstrate the effectiveness of our framework through case studies on benchmarking and real-world multi-objective optimization problems to elucidate how analysts can leverage our framework to inspect and compare diverse algorithms.

Cooperative Deployment Multi-Objective Optimization Approach for High-Resolution Multi-Airship Earth-Observation Coverage Network

As a platform for Near space-based Earth-observation network, stratospheric airship has attracted a lot of attention in recent years, because of its advantages in endurance, coverage, cost, and durability. However, the airship has low conversion speed and large vehicle inertia, so it is significant to deploy Multi-airship Earth-observation Coverage Network (MAEON) collaboratively. To this end, this paper proposes an Earth-observation model with considerations of loading devices side-swing characteristics and field of view (FOV), and establishes a collaborative deployment model of MAEON to realize objectives of observation coverage, target point statistics, observation resolution, multi-airship community profit. To obtain the solution set of cooperative deployment problem efficiently and widely, a multi-objective evolutionary optimization algorithm (MOEA) with associated bi-criterion is proposed. Then, weight vector distribution control with dynamic adjustment is introduced to ensure that the solution set spreads more uniform and extensive. By embedding improved evolution factors, Non-Pareto criterion (NPC) and Pareto criterion (PC) based parts co-evolve and exchange information, which is effective in diversity and convergence. The normalized weight sum method is modified by adding the moderators, which are controlled by the population outcome in the iterative process. The experiment is repeated in 8 groups of data, and compared with 4 popular MOEAs. Through simulation experiments, it can be seen that the proposed algorithm has advantages in performance, universality, and stability.

Evolutionary multi-objective optimisation for large-scale portfolio selection with both random and uncertain returns

Evolutionary multi-objective optimisation for large-scale portfolio selection with both random and uncertain returns

A systematic framework for evolutionary multi-objective optimization to complex building design problems at the early design stage

As in biology, multi-objective evolutionary algorithms cross-reference various design parameters in the search to maximize or minimize one or more specific objectives, thus finding the best solution for the specified purposes. In addition, it is possible to perform the appendment of many variables simultaneously and make numerous real-time simulations. This paper proposes a systematic framework for evolutionary multi-objective optimization to complex building design problems at the early stage. The framework is demonstrated by optimizing the courtyard geometry as a case study. The methods include generating courtyard geometry (i.e., height/width ratios and orientations) as design variables according to solar geometry. Simulations are explored, providing recommendations to maximize solar access in winter and filled shade during summer. The outcomes are a framework resumed systematically to address the contrasting objectives of the given building problems. The framework’s application can adapt to each case’s architectural, environmental, and technical criteria.

Dynamic Neighborhood Adjustment Strategy for Multi-Objective Evolutionary Algorithm Based on Decomposition

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) has achieved great success in the field of evolutionary multi-objective optimization. It decomposes a multi-objective optimization problem into a number of scalar optimization sub-problems. Each sub-problem is optimized by using information from its neighboring sub-problems. Therefore, the neighborhood size of each sub-problem plays an important role in MOEA/D. Different neighborhood sizes are tested in this paper. Experimental results demonstrate that larger neighborhood size helps achieve better convergence and diversity with more CPU time and vice versa. MOEA/D uses constant neighborhood size during the whole process, and it is difficult to balance the convergence, diversity and running time. Therefore, this paper propose an algorithm based on MOEA/D. The algorithm adjusts the neighborhood size dynamically in different generations and different sub-problems to reduce the running time while the convergence and diversity of this algorithm are similar or better than other state-of-the-art algorithms. Compared to the original MOEA/D, experimental results show that adjusting the neighborhood size dynamically is a good way to reduce the running time significantly while maintaining the convergence and diversity. Furthermore, the algorithm proposed in this paper is compared with five state-of-the-art algorithms based on MOEA/D. The experimental results show that the proposed algorithm outperforms the others in efficiency while performs similarly in convergence and diversity.

Large-Scale Evolutionary Multi-Objective Optimization Based on Direction Vector Sampling

Large-Scale Evolutionary Multi-Objective Optimization Based on Direction Vector Sampling

A dual decomposition strategy for large-scale multiobjective evolutionary optimization

A dual decomposition strategy for large-scale multiobjective evolutionary optimization

MCDM, EMO and Hybrid Approaches: Tutorial and Review

Most of the practical applications that require optimization often involve multiple objectives. These objectives, when conflicting in nature, pose both optimization as well as decision-making challenges. An optimization procedure for such a multi-objective problem requires computing (computer-based search) and decision making to identify the most preferred solution. Researchers and practitioners working in various domains have integrated computing and decision-making tasks in several ways, giving rise to a variety of algorithms to handle multi-objective optimization problems. For instance, an a priori approach requires formulating (or eliciting) a decision maker’s value function and then performing a one-shot optimization of the value function, whereas an a posteriori decision-making approach requires a large number of diverse Pareto-optimal solutions to be available before a final decision is made. Alternatively, an interactive approach involves interactions with the decision maker to guide the search towards better solutions (or the most preferred solution). In our tutorial and survey paper, we first review the fundamental concepts of multi-objective optimization. Second, we discuss the classic interactive approaches from the field of Multi-Criteria Decision Making (MCDM), followed by the underlying idea and methods in the field of Evolutionary Multi-Objective Optimization (EMO). Third, we consider several promising MCDM and EMO hybrid approaches that aim to capitalize on the strengths of the two domains. We conclude with discussions on important behavioral considerations related to the use of such approaches and future work.

Genotype-Phenotype Mapping for Applied Evolutionary Multi-Objective and Multi-Physics Topology Optimization

We present a multi-objective topology optimization method based on the Non-Sorting Genetic Algorithm II (NSGA-II). The presented approach is a tool for early-stage engineering applications capable of providing insights into the complex relationship between structural features and the performance of a design without a priori assumptions about objective space. Mass reduction, linear elastic deformation, and stationary thermal conduction are considered simultaneously with three additional constraints. The specifically developed genotype-phenotype mapping ensures the practical benefit of obtained design propositions and significantly reduces computational effort to generate a dense set of Pareto solutions. The mapping procedure smooths probabilistically generated structures, removes unconnected material, and refines the spatial discretization for the subsequently used finite element solver. We present sets of Pareto optimal solutions to large three-dimensional design problems with multiple objectives and multiple near-application constraints that are feasible design propositions for engineering design. Geometrical features present in the obtained Pareto set are discussed.

Intrusion Detection in Internet of Things With MQTT Protocol—An Accurate and Interpretable Genetic-Fuzzy Rule-Based Solution

This article addresses the problem of an accurate and interpretable intrusion detection in Internet of Things (IoT) systems using the knowledge-discovery data-mining/machine-learning approach proposed by us. This approach—implemented as a fuzzy rule-based classifier—employs our generalization of the well-known multiobjective evolutionary optimization algorithm to optimize the accuracy-interpretability tradeoff of the IoT intrusion detection systems (IoT IDSs). The main contribution of this work is the design of accurate and interpretable IoT IDSs from the most recently published data—referred to as MQTT-IOT-IDS2020 data sets—describing the behavior of an MQTT-protocol-based IoT system. A comparison with seven available alternative approaches was also performed demonstrating that the approach proposed by us significantly outperforms alternative methods in terms of interpretability of intrusion-detection decisions made while remaining competitive or superior in terms of the accuracy of those decisions.

EMSOA based application mapping framework for power optimisation in 3D-NoC

ABSTRACT Application mapping is a difficult and crucial topic of research in Networks on Chip (NoC). Mapping of NoC is an NP-hard issue and various types of heuristics have been adopted to deal these issues. Therefore, in this research, Hesitant Fuzzy Linguistic Bi-objective Clustering Method (HFLBCM) with Evolutionary Multi-objective Seagull Optimisation Algorithm (EMSOA) is proposed for application mapping in 3D-NoC. The robustness of proposed method is confirmed by experiments conducted on certain benchmarks, like VOPD and MPEG-4 in NoC. At first, the HFLBCM approach selects the core and calculates the weight of each core. Subsequently, EMSOA method performs the application mapping with standard topologies, like mesh and torus. The implementation of the proposed method is done in Python and the parameters, like power, delay and computation time for VOPD and MPEG-4 benchmarks. The proposed approach has attained 45.175%, 65.319%, 71.226% lower power consumption for mesh topology and 30.141%, 19.211%, 32.727% lower power consumption for torus topology in VOPD benchmark than existing methods, like Knowledge-base multiple objective application mapping approach (AM-3D NoC-KBMA), self-adaptive mapping approach for NoC with low power consumption (AM-3D NoC-SKNNCM-SACSOA) and Ant lion optimised buffer less routing design for low power application specific NoC (AM-3D NoC-ALOA), respectively.

A decomposition-rotation dominance based evolutionary algorithm with reference point adaption for many-objective optimization

Evolutionary multi-objective optimization aims at obtaining a set of Pareto-optimal solutions among the multiple conflicting objectives. However, the ability of multi-objective evolutionary algorithm to converge towards the Pareto front and maintain population diversity often seriously decrease with the number of objectives increasing. To address this problem, we propose a decomposition-rotation dominance based evolutionary algorithm with reference point adaption for many-objective optimization, termed DREA. In the DREA, a dominance relation based on decomposition and rotation (DR-dominance) is proposed for increasing selection pressure and maintaining diversity simultaneously, which is achieved by decomposing the objective space and rotating the coordinate system. At the same time, a reference point adaption strategy is designed, which can adapt well to different types of Pareto fronts. In addition, an effective mating selection strategy is proposed for enhancing the probability of parents with good convergence and diversity combination. The experimental results on several commonly used benchmark test problems with objective numbers varying from 5 to 20 and two real-world engineering applications have demonstrated that the proposed DREA is highly competitive in solving many-objective optimization.

Benchmarking large-scale subset selection in evolutionary multi-objective optimization

In the field of evolutionary multi-objective optimization (EMO), the standard practice is to present the final population of an EMO algorithm as the output. However, it has been shown that the final population often includes solutions which are dominated by other solutions generated and discarded in previous generations. Recently, a novel EMO framework has been developed to solve this issue by storing all the non-dominated solutions generated during the evolution in an archive, and selecting a subset of solutions from the archive as the output. The key component of this framework is the subset selection from the archive, which typically stores a large number of candidate solutions. However, most relevant studies have focused on small candidate solution sets for environmental selection. There is no benchmark test suite for large-scale subset selection. This study aims to fill this research gap by proposing a benchmark test suite for large-scale subset selection, and providing a comparison between several representative subset selection algorithms using the proposed test suite. The proposed test suite together with the benchmarking studies provides a baseline for researchers to understand, use, compare, and develop large-scale subset selection algorithms in the EMO field.

Counterintuitive Experimental Results in Evolutionary Large-Scale Multiobjective Optimization

Recently, large-scale multiobjective optimization has received increasing attention from the evolutionary multiobjective optimization (EMO) community. This has led to the emergence of a specialized research area called evolutionary large-scale multiobjective optimization (ELMO). In general, it is believed that multiobjective optimization problems become more difficult as the number of decision variables increases. However, the following two counterintuitive observations are obtained from careful examinations of recent ELMO studies. One is that experimental results on some large-scale multiobjective test problems were improved by increasing the number of decision variables. The other is that better results were obtained for some other large-scale multiobjective test problems by conventional EMO algorithms (EMOAs) than state-of-the-art ELMO algorithms (ELMOAs). These observations suggest that ELMOAs have not always been evaluated on appropriate test problems. Moreover, their performance is not always better than the performance of conventional EMOAs. In this letter, we first re-examine the performance of ELMOAs and conventional EMOAs on a wide variety of scalable multiobjective test problems. Then, counterintuitive experimental results are analyzed using the anytime performance evaluation scheme and distributions of randomly generated initial solutions. Based on the analysis, suggestions on how to handle large-scale multiobjective test problems with counterintuitive results are proposed.

Offspring regeneration method based on bi-level sampling for large-scale evolutionary multi-objective optimization

In evolutionary multi-objective optimization, the size of search space exponentially expands as the number of decision variables increases, which makes the generation of promising candidate solutions more difficult. For this, in this paper, we propose a bi-level offspring generation architecture, together with a deep offspring sampling method. The offspring generation process is divided into two phases. The first phase uses the general genetic operators to generate the offspring, and then in the second phase, the selected non-dominated solutions are utilized by the proposed deep sampling method to produce offspring again. Specifically, the proposed deep sampling method makes use of the selected non-dominated solutions to establish search directions at first, then solutions are sampled on them. It is expected to take advantage of both offspring generation schemes, thereby balancing the diversity and convergence of the population. Existing large-scale evolutionary algorithms can easily be extended to our proposed bi-level architecture. The experimental results demonstrate the significant advantages of the proposed architecture and sampling method, in comparison with several state-of-the-art large-scale multi∖many-objective optimization problems in solving LSMOPs with up to 5000 decision variables.