Evolutionary Multiobjective Optimization Algorithms Research Articles

Two-stage species conservation for multimodal multi-objective optimization with local Pareto sets

Compared to general multi-objective optimization problems, multimodal multi-objective optimization problems (MMOPs) with local Pareto sets (PSs) must determine multiple global and local PSs simultaneously. Therefore, MMOPs with local PSs are challenging. To resolve this issue, this study proposes a multimodal multi-objective optimization evolutionary algorithm based on two-stage species conservation (MMOEA/TSC). MMOEA/TSC divides the evolutionary process into two stages: diversity-oriented species conservation and convergence-oriented species conservation. The former is aimed at locating promising regions in which global and local PSs may exist. To balance the distribution of solutions, a Gaussian variation strategy is used to iteratively generate diverse offspring in regions that contain the smallest number of solutions. The latter mainly focused on obtaining one PS with good convergence in each promising region. To help the solutions converge to the global and local PSs uniformly, a species stratification strategy was adopted according to the Pareto level of the well-converged solution for each species. The proposed algorithm was compared with seven state-of-the-art algorithms. For the CEC 2020 MMOP test problem set, the experimental results show that MMOEA/TSC has the capacity to find global and local PSs.

Multi-spatial information joint guidance evolutionary algorithm for dynamic multi-objective optimization with a changing number of objectives

Multi-spatial information joint guidance evolutionary algorithm for dynamic multi-objective optimization with a changing number of objectives

A Survey on Search Strategy of Evolutionary Multi-Objective Optimization Algorithms

The multi-objective optimization problem is difficult to solve with conventional optimization methods and algorithms because there are conflicts among several optimization objectives and functions. Through the efforts of researchers and experts from different fields for the last 30 years, the research and application of multi-objective evolutionary algorithms (MOEA) have made excellent progress in solving such problems. MOEA has become one of the primary used methods and technologies in the realm of multi-objective optimization. It is also a hotspot in the evolutionary computation research community. This survey provides a comprehensive investigation of MOEA algorithms that have emerged in recent decades and summarizes and classifies the classical MOEAs by evolutionary mechanism from the viewpoint of the search strategy. This paper divides them into three categories considering the search strategy of MOEA, i.e., decomposition-based MOEA algorithms, dominant relation-based MOEA algorithms, and evaluation index-based MOEA algorithms. This paper selects the relevant representative algorithms for a detailed summary and analysis. As a prospective research direction, we propose to combine the chaotic evolution algorithm with these representative search strategies for improving the search capability of multi-objective optimization algorithms. The capability of the new multi-objective evolutionary algorithm has been discussed, which further proposes the future research direction of MOEA. It also lays a foundation for the application and development of MOEA with these prospective works in the future.

A regularity augmented evolutionary algorithm with dual-space search for multiobjective optimization

The well-known regularity property allows the Pareto optimal solutions of a multiobjective optimization problem (MOP) to be embedded in some latent spaces by the manifold structure of the Pareto optimal set. This paper proposes an efficient regularity augmented evolutionary algorithm (RAEA) for multiobjective optimization, which aims to adopt such latent spaces for use with offspring generations. In this algorithm, a singular value decomposition method is adopted at each iteration to extract such latent space from the population with the regularity property. The enhancements of regularity in RAEA include: (1) an acceleration of convergence by incrementally projecting the dominated solutions into the latent space built with elite solutions (i.e., the non-dominated solutions); and (2) a novel dual-space search strategy (DSS) is developed for the generation of promising offspring solutions by searching in both latent and decision space. The developed algorithm was empirically compared with five well-known multiobjective evolutionary algorithms on several complicated MOP test suites. Experimental results suggest that RAEA outperforms the compared algorithms on these test instances in terms of two commonly-used indicators. Both the effectiveness of the convergence acceleration scheme and the developed dual-space searching strategy are also empirically validated.

Dynamic multi-objective evolutionary optimization algorithm based on two-stage prediction strategy

Tracking pareto-optimal set or pareto-optimal front in limited time is an important problem of dynamic multi-objective optimization evolutionary algorithms (DMOEAs). However, the current DMOEAs suffer from some deficiencies. In the early optimization process, the algorithms may suffer from random search. In the late optimization process, the knowledge which can accelerate the convergence rate is not fully utilized. To address the above issue, a DMOEA based on the two-stage prediction strategy (TSPS) is proposed. TSPS divides the optimization progress into two stages. At the first stage, multi-region knee points are selected to capture the pareto-optimal front shape, which can accelerate the convergence and maintaining good diversity at the same time. At the second stage, improved inverse modeling is applied to search the representative individuals, which can improve the diversity of the population and is beneficial to predicting the moving location of the pareto-optimal front. Experimental results on dynamic multi-objective optimization test suites show that TSPS is superior to the other six DMOEAs. In addition, the experimental results also show that the proposed method has the ability to respond quickly to environmental changes.

An Interview with Kalyanmoy Deb 2022 ACM Fellow

Prof. Kalyanmoy Deb has been named one of the 2022 ACM Fellows for "Outstanding Contributions That Propel Technology Today", in particular for his "technical contributions in evolutionary multi-objective optimization algorithms and multi-criterion decision support." Kalyanmoy kindly agreed to answer all our questions, ranging from his seminal contributions to his views and perspectives on evolutionary computation and its role within computing science and artificial Intelligence.

An adaptive two-stage evolutionary algorithm for large-scale continuous multi-objective optimization

An adaptive two-stage evolutionary algorithm for large-scale continuous multi-objective optimization

An In-depth Benchmarking of Evolutionary and Swarm Intelligence Algorithms for Autoscaling Parameter Sweep Applications on Public Clouds

Many important computational applications in science, engineering, industry, and technology are represented by PSE (parameter sweep experiment) applications. These applications involve a large number of resource-intensive and independent computational tasks. Because of this, cloud autoscaling approaches have been proposed to execute PSE applications on public cloud environments that offer instances of different VM (virtual machine) types, under a pay-per-use scheme, to execute diverse applications. One of the most recent approaches is the autoscaler MOEA (multiobjective evolutive algorithm), which is based on the multiobjective evolutionary algorithm NSGA-II (nondominated sorting genetic algorithm II). MOEA considers on-demand and spot VM instances and three optimization objectives relevant for users: minimizing the computing time, monetary cost, and spot instance interruptions of the application’s execution. However, MOEA’s performance regarding these optimization objectives depends significantly on the optimization algorithm used. It has been shown recently that MOEA’s performance improves considerably when NSGA-II is replaced by a more recent algorithm named NSGA-III. In this paper, we analyze the incorporation of other multiobjective optimization algorithms into MOEA to enhance the performance of this autoscaler. First, we consider three multiobjective optimization algorithms named E-NSGA-III (extreme NSGA-III), SMS-EMOA (S-metric selection evolutionary multiobjective optimization algorithm), and SMPSO (speed-constrained multiobjective particle swarm optimization), which have behavioral differences with NSGA-III. Then, we evaluate the performance of MOEA with each of these algorithms, considering the three optimization objectives, on four real-world PSE applications from the meteorology and molecular dynamics areas, considering different application sizes. To do that, we use the well-known CloudSim simulator and consider different VM types available in Amazon EC2. Finally, we analyze the obtained performance results, which show that MOEA with E-NSGA-III arises as the best alternative, reaching better and significant savings in terms of computing time (10%–17%), monetary cost (10%–40%), and spot instance interruptions (33%–100%).

Optimizing cleaner productions of sustainable energies: A co-design framework for complementary operations of offshore wind and pumped hydro-storages

There has been a constant evolution in developing clean energy technologies to reduce environmental concerns. In this context, wind energy technology is an ingenious option to make the energy sector more sustainable. However, the growing penetration of wind energy pose challenges to the power system reliability. An integrated system including offshore wind farms (OWFs) and pumped hydroelectric storages (PHSs) emerges as a promising solution to this issue. However, the current wind farm layout optimization (WFLO) always neglect the optimal designs of the PHSs, and also is not based on the optimal OWF controls. Therefore, this paper develops a co-design optimization framework to jointly optimize the wind farm layout and the PHSs’ configurations. The operation principle of the integrated system is first described and two optimization objectives are proposed. An evolutionary trained adaptive neuro-fuzzy inference system (ANFIS) is constructed to forecast OWF power output. The co-design optimization is then formulated as a constrained multi-objective optimization problem and evolutionary algorithms are adopted to find the optimal solutions. Two design cases considering the optimal/non-optimal OWF controls are proposed for the validations. The test results indicate that the trained ANFIS can efficiently identify the characteristics of OWF power generations. In the co-design optimization, the averaged power mismatch is lower than 5 MW, and there are several points that have zero power mismatch. The maximum OWF powers are around 30 MW in the optimal OWF control case, but are lower than 25 MW without using the optimal control. There also exist obvious differences between the optimal PHS parameters in the two cases due to the optimal OWF control.

Investigation and multi-objective optimization of friction stir welding of AA7075-T651 plates

The present study investigates and comparatively evaluates different evolutionary algorithms for multi-objective optimization of friction stir welding (FSW) of AA7075-T651 plates. The FSW parameters are optimized for obtaining the joint with higher tensile strength, microhardness and lower surface roughness using particle swarm optimization, strength Pareto-based evolutionary algorithm II, differential evolution and teaching learning-based optimization techniques. The validation experiments showed better prediction accuracy with the SPEA II technique. This study finds maximum tensile strength and microhardness of 187.45 MPa and 142.47 HV, respectively, and minimum surface roughness of 15.93 µm for FSW joint when using a welding speed and tool rotation, of 40 mm/min and 1923 rpm, respectively. The FSW joint obtained at these optimized parameters showed the homogeneous material mixing with the equiaxed fine-grain distribution at the weld nugget with fewer voids, as confirmed by the scanning electron microscopic images with energy-dispersive X-ray spectroscopic analysis.

Multi-Objective Optimization Strategy Applied in Data Centers Electrical Subsystems

Data center infrastructures must have high availability, low cost, and high energy efficiency. However, these objectives are often conflicting. For instance, an additional Uninterruptible Power Supply (UPS) improves the system availability but may jeopardize the total cost and the energy consumption. This paper presents a strategy based on the Non-dominated Sorting Genetic Algorithm II (NSGA-II), a multi-objective evolutionary optimization algorithm, to improve the design of electrical data center architectures. To show the applicability of the proposed strategy, we present a comparative study between the brute force algorithm and proposed strategy based on NSGA-II, as it has shown promising results in multi-objective problems 1, 2 and 3. When setting complex electrical infrastructure data center models, the results showed that applying the proposed strategy reduces the runtime 961 times and achieves Pareto optimal curvature with a difference of approximately 1%.

Batched Data-Driven Evolutionary Multiobjective Optimization Based on Manifold Interpolation

Multiobjective optimization problems are ubiquitous in real-world science, engineering, and design optimization problems. It is not uncommon that the objective functions are as a black box, the evaluation of which usually involve time-consuming and/or costly physical experiments. Data-driven evolutionary optimization can be used to search for a set of nondominated tradeoff solutions, where the expensive objective functions are approximated as a surrogate model. In this article, we propose a framework for implementing batched data-driven evolutionary multiobjective optimization (EMO). It is so general that any off-the-shelf EMO algorithms can be applied in a plug-in manner. There are two unique components: 1) based on the Karush–Kuhn–Tucker conditions, a manifold interpolation approach that explores more diversified solutions with a convergence guarantee along the manifold of the approximated Pareto-optimal set and 2) a batch recommendation approach that reduces the computational time of the data-driven evolutionary optimization process by evaluating multiple samples at a time in parallel. Comparing against seven state-of-the-art surrogate-assisted evolutionary algorithms, experiments on 168 benchmark test problem instances with various properties and a real-world application on hyper-parameter optimization fully demonstrate the effectiveness and superiority of our proposed framework, which is featured with a faster convergence and a stronger resilience to various Pareto-optimal front shapes.

Multiobjective evolutionary discovery of equation-based analytical models for dynamical systems

In this article, an approach to modeling dynamical systems in case of unknown governing physical laws has been introduced. The systems of differential equations obtained by means of a data-driven algorithm are taken as the desired models. In this case, the problem of predicting the state of the process is solved by integrating the resulting differential equations. In contrast to classical data-driven approaches to dynamical systems representation, based on the general machine learning methods, the proposed approach is based on the principles, comparable to the analytical equation-based modeling. Models in forms of systems of differential equations, composed as combinations of elementary functions and operation with the structure, were determined by adapted multi-objective evolutionary optimization algorithm. Time-series describing the state of each element of the dynamic system are used as input data for the algorithm. To ensure the correct operation of the algorithm on data characterizing real-world processes, noise reduction mechanisms are introduced in the algorithm. The use of multicriteria optimization, held in the space of complexity and quality criteria for individual equations of the differential equation system, makes it possible to improve the diversity of proposed candidate solutions and, therefore, to improve the convergence of the algorithm to a model that best represents the dynamics of the process. The output of the algorithm is a set of Pareto-optimal solutions of the optimization problem where each individual of the set corresponds to one system of differential equations. In the course of the work, a library of data-driven modeling of dynamic systems based on differential equation systems was created. The behavior of the algorithm was studied on a synthetic validation dataset describing the state of the hunter-prey dynamic system given by the Lotka-Volterra equations. Finally, a toolset based on the solution of the generated equations was integrated into the algorithm for predicting future system states. The method is applicable to data-driven modeling of arbitrary dynamical systems (e.g. hydrometeorological systems) in cases where the processes can be described using differential equations. Models generated by the algorithm can be used as components of more complex composite models, or in an ensemble of methods as an interpretable component.

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.

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

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

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.

A Tractive Population Assisted Dual-Population and Two-Phase Evolutionary Algorithm for Constrained Multi-Objective Optimization

A Tractive Population Assisted Dual-Population and Two-Phase Evolutionary Algorithm for Constrained Multi-Objective Optimization

A comparison of evolutionary algorithms on a Large Scale Many-Objective Problem in Food–Energy–Water Nexus

Food, energy, and water resources form a complex system called Food–Energy–Water Nexus (FEWN) that is crucial for the survival of human beings. These resources interact with each other in a way that achieving the objectives of one can conflict with the objectives of the others. Therefore, there is a need to have approaches such as Multi-Objective Optimization Evolutionary Algorithms (MOEAs) to address the conflicting objectives in FEWN. However, MOEAs are inefficient in solving problems with more than 3 objectives and with at least 100 decision variables. In recent years Large-Scale Many-Objectives Optimization Evolutionary Algorithms (LSMaOEAs) have been developed to solve such problems. The performance of these algorithms has been tested on some real-world applications and benchmark problems. However, evaluation of their performance on the Food–Energy–Water Nexus (FEWN) rarely appears in existing literature. In this paper we propose a Large-Scale Many-Objectives Problem in Food–Energy–Water Nexus (LSMaOPFEWN) that consists of 5 objectives and 315 decision variables. This problem is formulated as a Leontief Input–Output model that promotes sustainable consumption and production of resources in FEWN. Thereafter, we report experiments that evaluated the performance of selected LSMaOEAs on LSMaOPFEWN. Experimental results demonstrate that Linear Combination-based Search Algorithm (LCSA) performs better than 4 other selected algorithms due to its enhanced exploration and exploitation capability. This paper demonstrates that an algorithm utilizing dimensionality reduction techniques can be effective in solving a real world LMaOPFEWN.

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.