Evolutionary Multi-objective Optimization Research Articles

Virtual Sound Image Reconstruction Method for Multi-objective Optimization of Folk Music Based on Evolutionary Algorithm

At present, the exchanges in various fields such as culture, economy, and politics are becoming more and more close in the world. From the perspective of the relationship between national music and cultural development, the development of national music has also received more and more attention, and it has become an inevitable trend in the development of today's era. The purpose of this paper was to perform virtual reconstruction of the sound image of folk music through multiple objective optimizations, and to model the virtual sound image of folk music as a multi-objective optimization problem. According to the research on sound image positioning, the relevant noise factors were removed, so as to achieve the playback of ethnic music that enhanced the surround effect and visual enjoyment. The evolutionary algorithm in this paper was mainly based on the multi-objective optimized sound image localization technology. For the music virtual sound image, an improved FCM algorithm and an evolutionary multi-objective optimization algorithm combining local and non-local information of the sound image were proposed, respectively. Through the analysis of the traditional sound image algorithm method, the accuracy of the sound image localization on the horizontal plane could be effectively improved. After the conversion, the audience could feel the better stereo image and surround feeling of the folk music. Through experimental analysis, it can be seen that the system can not only perform virtual conversion of audio-visual signals of different frequencies, but also provide data for different audio playback systems. The feature point registration error is low, and the reconstruction effect is good, especially the random delay processing in the range of 0∼20m, and the performance is better than the traditional method. Finally, virtual left and right surround sound image signals were obtained, which effectively improved the three-dimensional surround feeling of folk music.

Effective response strategies based on adaptive selection for dynamic multi-objective evolutionary optimization

Dynamic multiobjective optimization problems (DMOPs) change over time, which require Evolutionary algorithms (EA) track Pareto-optimal solution (PS) or/and Pareto-optimal front (PF) in a constantly change environment. Prediction-based algorithms are the most common method to solve DMOPs. However, a single elaborate predictor is not always suitable for extracting changing pattern of different DMOPs, and not to mention DMOPs with unpredictable changes. To overcome these limitations, a simple yet effective algorithm, response strategies based on adaptive selection (RSAS), are proposed in this paper. When a change occurs, RSAS provides diversified solutions by different proposed strategies, that is, a center-guided self-correcting prediction, an individual-based prediction, and a precision-controllable mutation. Based on the quality of their generated solution set, an adaptive selection mechanism can adjust the selection probability of these three strategies. Since RSAS consists of not merely two different prediction strategies but also a mutation strategy, which can be more responsive to predictable and unpredictable changes. To validate the performance of RSAS, DMOP benchmarks in CEC2018 with recommended configurations are adopted. Compared to four state-of-the-art algorithms, the experimental results show that RSAS is effective and efficient.

Multitask Computation Offloading Based on Evolutionary Multiobjective Optimization in Industrial Internet of Things

Multitask Computation Offloading Based on Evolutionary Multiobjective Optimization in Industrial Internet of Things

On the investigation of the aerodynamics performance and associated flow physics of the optimized tubercle airfoil

In the present study, the evolutionary multi-objective optimization is employed to design the optimum amplitude and wavelength of sinusoidal leading-edge tubercles for the NACA0012 (National Advisory Committee for Aeronautics) airfoil to improve its aerodynamic performance at Reynolds number of 5.0 × 104 than that of the NACA0012 smooth leading-edge or baseline airfoil. Here, the optimum tubercle is found to have an amplitude of 11.71% and a wavelength of 25% of the baseline airfoil chord, respectively. Through a combination of in-house water tunnel experiments and numerical simulations, it is additionally established that the optimized tubercle airfoil exhibits superior lift and reduced drag characteristics compared to the baseline airfoil, particularly in the post-stall high angle of attack regime. Furthermore, it is noticed that the optimized tubercle design enhances the gap between large separation regions or stall cells along the tubercle airfoil span during the post-stall regime. Consequently, a more pronounced attached flow regime is developed between the consecutive stall cells, contributing to the tubercle airfoil's improved aerodynamic characteristics compared to the baseline airfoil. Our investigations also revealed that the formation and arrangement of the stall cells on the tubercle airfoil span are associated with a biased wake mechanism similar to the one observed in the wake of side-by-side arranged circular cylinders.

Investigating normalization in preference-based evolutionary multi-objective optimization using a reference point

Normalization of objectives plays a crucial role in evolutionary multi-objective optimization (EMO) to handle objective functions with different scales, which can be found in real-world problems. Although the effect of normalization methods on the performance of EMO algorithms has been investigated in the literature, that of preference-based EMO (PBEMO) algorithms is poorly understood. Since PBEMO aims to approximate a region of interest, its population generally does not cover the Pareto front in the objective space. This property may make normalization of objectives in PBEMO difficult. This paper investigates the effectiveness of three normalization methods in three representative PBEMO algorithms. We present a bounded archive-based method for approximating the nadir point. First, we demonstrate that the normalization methods in PBEMO perform significantly worse than that in conventional EMO in terms of approximating the ideal point, nadir point, and range of the PF. Then, we show that PBEMO requires normalization of objectives on problems with differently scaled objectives. Our results show that there is no clear “best normalization method” in PBEMO, but an external archive-based method performs relatively well.

A Systematic Review of Multi-Objective Evolutionary Algorithms Optimization Frameworks

The study of evolutionary algorithms (EAs) has witnessed an impressive increase during the last decades. The need to explore this area is determined by the growing request for design and the optimization of more and more engineering problems in society, such as highway construction processes, food and agri-technologies processes, resource allocation problems, logistics and transportation systems, microarchitectures, suspension systems optimal design, etc. All of these matters refer to specific highly computational problems with a huge design space, hence the obvious need for evolutionary algorithms and frameworks, or platforms that allow for the implementing and testing of such algorithms and methods. This paper aims to comparatively analyze the existing software platforms and state-of-the-art multi-objective optimization algorithms and make a review of what features exist and what features might be included next as further developments in such tools, from a researcher’s perspective. Additionally, it is essential for a framework to be easily extendable with new types of problems and optimization algorithms, metrics and quality indicators, genetic operators or specific solution representations and results analysis and comparison features. After presenting the most relevant existing features in these types of platforms, we suggest some future steps and the developments we have been working on.

Evolutionary multi-objective high-order tetrahedral mesh optimization

High-order mesh optimization has many goals, such as improving smoothness, reducing approximation error, and improving mesh quality. The previous methods do not optimize these objectives together, resulting in suboptimal results. To this end, we propose a multi-objective optimization method for high-order meshes. Central to our algorithm is using the multi-objective genetic algorithm (MOGA) to adapt to the multiple optimization objectives. Specifically, we optimize each control point one by one, where the MOGA is applied. We demonstrate the feasibility and effectiveness of our method over various models. Compared to other state-of-the-art methods, our method achieves a favorable trade-off between multiple objectives.

A Hydrodynamic Model and Data-Driven Evolutionary Multi-Objective Optimization Algorithm Based Optimal Operation Method for Multi-barrage Flood Control

A Hydrodynamic Model and Data-Driven Evolutionary Multi-Objective Optimization Algorithm Based Optimal Operation Method for Multi-barrage Flood Control

Multi-objective path planning for multi-UAV connectivity and area coverage

In this paper, we assume that a team of drones equipped with sensing and networking capabilities explore an unknown area via onboard sensors for surveillance, monitoring, target search or data collection purposes and deliver the sensed data to a ground control station (GCS) over multi-hop links. We propose a multi-drone path planner that jointly optimizes area coverage time and connectivity among the drones. We propose a novel connectivity metric that includes not only percentage connectivity of the drones to GCS, but also the maximum duration of consecutive time that the drones are disconnected from the GCS. To solve this optimization formulation, we propose a multi-objective evolutionary algorithm with novel operations. We use our solver to test single, two and many objective path planning problems and compare our Pareto-optimal solutions to benchmark weighted-sum based solutions. We show that as opposed to the single solution that weighted-sum methods provide based on prior information from the user, the proposed evolutionary multi-objective optimizers can provide a diverse set of solutions that cover a range of mission time and connectivity performance illustrating the trade-off between these conflicting objectives. The end-user can then choose the best path solution based on the mission priorities during operation.

Subset Selection for Evolutionary Multiobjective Optimization

Subset selection, which selects a subset of solutions according to certain criterion/indicator, is a topic closely related to evolutionary multi-objective optimization (EMO). The critical component of a multi-objective evolutionary algorithm (MOEA), environmental selection, is essentially a subset selection problem, i.e., selecting N solutions as the next-generation population from usually 2N candidates (where N denotes the size of the population). Another use of subset selection is the solution pre-processing procedure for decision-making, in which typically a few representatives are selected from the final population or a large-size archive, in order not to overwhelm the decision maker. Existing work for subset selection in EMO is focused on developing greedy algorithms, but may suffer from being trapped in local optima. In this paper, we approach the problem by providing a multi-objective evolutionary algorithmic framework. We consider several popular quality indicators for subset evaluation and present accelerated variants of a well-studied MOEA in the theoretical study area, Global Simple Evolutionary Multi-objective Optimizer (GSEMO), for each indicator. We conduct rigorous theoretical analyses of the acceleration procedure. Moreover, we prove that our algorithms can achieve the best-so-far approximation guarantee by the submodularity of the indicators. We finally empirically show the effectiveness and scalability of the proposed algorithms, in addition to the potentials to be further improved by introducing popular MOEAs (e.g., using NSGA-II and MOEA/D to replace GSEMO).

Improved Evolutionary Operators for Sparse Large-Scale Multiobjective Optimization Problems

Many critical science, societal, and engineering fields contain large-scale multiobjective optimization problems (LSMOPs), comprised of many decision variables. However, as the number of decision variables increases, optimization algorithms face exponentially large search spaces, thereby exhibiting a degraded performance. Nonetheless, LSMOPs whose optimal solutions correspond to sparse variable vectors can be solved more efficiently by evolutionary multiobjective optimization (EMO) algorithms. Despite the great recent strides in developing generic EMO algorithms for sparse LSMOPs, there is still room for improvement. Specifically, algorithms still struggle to find convergent and diverse Pareto fronts in an acceptable amount of time when solving sparse LSMOPs with thousands of decision variables. To better solve sparse LSMOPs, we propose a novel set of evolutionary operators to adapt small-scale EMO algorithms for sparse LSMOPs. These simple, novel, and effective operators include varied striped sparse population sampling (VSSPS), sparse simulated binary crossover (S-SBX), and sparse polynomial mutation (S-PM). These operators, combined with NSGA-II, make the proposed S-NSGA-II algorithm. S-NSGA-II runs near-universally faster than existing methods for problems containing up to 6,400 decision variables, while performing as well as or better than contemporary sparse LSMOP algorithms with respect to hypervolume, especially with problems with larger than 5,000 decision variables.

Neural Architecture Search as Multiobjective Optimization Benchmarks: Problem Formulation and Performance Assessment

The ongoing advancements in network architecture design have led to remarkable achievements in deep learning across various challenging computer vision tasks. Meanwhile, the development of neural architecture search (NAS) has provided promising approaches to automating the design of network architectures for lower prediction error. Recently, the emerging application scenarios of deep learning (e.g., autonomous driving) have raised higher demands for network architectures considering multiple design criteria: number of parameters/weights, number of floating-point operations, inference latency, among others. From an optimization point of view, the NAS tasks involving multiple design criteria are intrinsically multiobjective optimization problems; hence, it is reasonable to adopt evolutionary multiobjective optimization (EMO) algorithms for tackling them. Nonetheless, there is still a clear gap confining the related research along this pathway: on the one hand, there is a lack of a general problem formulation of NAS tasks from an optimization point of view; on the other hand, there are challenges in conducting benchmark assessments of EMO algorithms on NAS tasks. To bridge the gap: (i) we formulate NAS tasks into general multi-objective optimization problems and analyze the complex characteristics from an optimization point of view; (ii) we present an end-to-end pipeline, dubbed EvoXBench, to generate benchmark test problems for EMO algorithms to run efficiently -without the requirement of GPUs or Pytorch/Tensorflow; (iii) we instantiate two test suites comprehensively covering two datasets, seven search spaces, and three hardware devices, involving up to eight objectives. Based on the above, we validate the proposed test suites using six representative EMO algorithms and provide some empirical analyses. The code of EvoXBench is available at https://github.com/EMI-Group/EvoXBench.

Evolutionary Multi-Objective Optimization Algorithm for Resource Allocation Using Deep Neural Network in Ultra-Dense Networks

Evolutionary Multi-Objective Optimization Algorithm for Resource Allocation Using Deep Neural Network in Ultra-Dense Networks

Detecting Hidden and Irrelevant Objectives in Interactive Multiobjective Optimization

Evolutionary multi-objective optimization algorithms (EMOAs) typically assume that all objectives that are relevant to the decision-maker (DM) are optimized by the EMOA. In some scenarios, however, there are irrelevant objectives that are optimized by the EMOA but ignored by the DM, as well as, hidden objectives that the DM considers when judging the utility of solutions but are not optimized. This discrepancy between the EMOA and the DM’s preferences may impede the search for the most-preferred solution and waste resources evaluating irrelevant objectives. Research on objective reduction has focused so far on the structure of the problem and correlations between objectives and neglected the role of the DM. We formally define here the concepts of irrelevant and hidden objectives and propose methods for detecting them, based on uni-variate feature selection and recursive feature elimination, that use the preferences already elicited when a DM interacts with a ranking-based interactive EMOA (iEMOA). We incorporate the detection methods into an iEMOA capable of dynamically switching the objectives being optimized. Our experiments show that this approach can efficiently identify which objectives are relevant to the DM and reduce the number of objectives being optimized, while keeping and often improving the utility, according to the DM, of the best solution found.

Investigating data-driven approaches to optimize nitrogen recommendations for winter wheat

The optimal nitrogen (N) application rate is an important concept to guide the strategic/static N management of crops. However, there is still a knowledge gap on how to combine the optimal N application rate, crop growth status, meteorological, and soil multi-source information to make tactic/dynamic N recommendation. For investigating the data-driven approaches to optimize nitrogen recommendations for winter wheat, this study proposed the concept of optimal topdressing N rate that coupling ‘strategic’ with ‘tactic’ ideas. Then a direct N fertilizer recommendation algorithm based on the optimal topdressing N rate was constructed integrating multi-source data with Random Forest (RF). The agronomic, economic, and environmental benefits of the algorithm were further evaluated based on a large-scale field-level validation experiments, and compared with the indirect N recommendation algorithm of RF-based yield prediction, farmers’ conventional N application rate, and regional optimal N application rate. Finally, multi-objective evolutionary optimization was used to verify the reasonability of the N fertilizer recommendation algorithms. The results showed that the optimal topdressing N algorithm had good model performance (Random Forest prediction R2 = 0.59 ∼ 0.72, RMSE = 39.63 ∼ 40.48 kg/ha), and vegetation indices, maximum temperature, and solar radiation were important features. The validation experiment results showed that compared to conventional management measures, the optimal topdressing N algorithm could reduce N fertilizer application by 18.9 % ∼ 48.4 % with intelligent adjustment, improve partial factor productivity by 12.99 % to 46.09 %, and reduce reactive N losses and greenhouse gas emissions by 20.56 % ∼ 47.24 % and 16.34 % ∼ 40.45 %, respectively. The rationality verification of solving nitrogen topdressing rate through multi-objective evolutionary algorithm proved that both indirect and direct N recommendation algorithms could make decisions within a reasonable threshold. The study provided insights for the data-driven based N management, strategy selection, and benefit evaluation process of N recommendation.

Population Feasibility State Guided Autonomous Constrained Multi-Objective Evolutionary Optimization

Many practical problems can be classified as constrained multi-objective optimization problems. Although various methods have been proposed for solving constrained multi-objective optimization problems, there is still a lack of research considering the integration of multiple constraint handling techniques. Given this, this paper combines the objective and constraint separation method with the multi-operator method, proposing a population feasibility state guided autonomous constrained evolutionary optimization method. This method first defines the feasibility state of the population based on both feasibility and ε feasibility of the solutions. Subsequently, a reinforcement learning model is employed to construct a mapping model between the population state and reproduction operators. Finally, based on the real-time population state, the mapping model is utilized to recommend the promising reproduction operator for the next generation. This approach demonstrates significant performance improvement for ε constrained mechanisms in constrained multi-objective optimization algorithms, and shows considerable advantages in comparison with state-of-the-art constrained multi-objective optimization algorithms.

Adaptive operator selection with dueling deep Q-network for evolutionary multi-objective optimization

Adaptive operator selection is an online method that automatically adjusts the application rate of different operators based on their actual performance. This paper proposes an adaptive operator selection paradigm based on dueling deep Q-network (DDQN), aiming to improve the training efficiency of the Q-network for solving multi-objective optimization problems. The Q-network is decomposed into state value and action advantage networks, allowing the agent to learn state values more frequently and accurately. A novel state space and reward mechanism are designed to adapt to the characteristics of evolutionary multi-objective optimization. Combining adaptive operator selection with a multi-objective evolutionary algorithm with adaptive weights (AdaW), an AdaW-DDQN algorithm with high adaptability is proposed. Experimental results on three complex benchmark suites demonstrate that the proposed adaptive operator selection paradigm significantly improves the performance of multi-objective optimization algorithms. The AdaW-DDQN algorithm provides an effective and efficient solution for solving multi-objective optimization problems.

Multigranularity Surrogate Modeling for Evolutionary Multiobjective Optimization With Expensive Constraints.

Multiobjective optimization problems (MOPs) with expensive constraints pose stiff challenges to existing surrogate-assisted evolutionary algorithms (SAEAs) in a very limited computational cost, due to the fact that the number of expensive constraints for an MOP is often large. For existing SAEAs, they always approximate constraint functions in a single granularity, namely, approximating the constraint violation (CV, coarse-grained) or each constraint (fine-grained). However, the landscape of CV is often too complex to be accurately approximated by a surrogate model. Although the modeling of each constraint function may be simpler than that of CV, approximating all the constraint functions independently may result in tremendous cumulative errors and high computational costs. To address this issue, in this article, we develop a multigranularity surrogate modeling framework for evolutionary algorithms (EAs), where the approximation granularity of constraint surrogates is adaptively determined by the position of the population in the fitness landscape. Moreover, a dedicated model management strategy is also developed to reduce the impact resulting from the errors introduced by constraint surrogates and prevent the population from trapping into local optima. To evaluate the performance of the proposed framework, an implementation called K-MGSAEA is proposed, and the experimental results on a large number of test problems show that the proposed framework is superior to seven state-of-the-art competitors.

Crossover can guarantee exponential speed-ups in evolutionary multi-objective optimisation

Evolutionary algorithms are popular algorithms for multi-objective optimisation (also called Pareto optimisation) as they use a population to store trade-offs between different objectives. Despite their popularity, the theoretical foundation of multi-objective evolutionary optimisation (EMO) is still in its early development. Fundamental questions such as the benefits of the crossover operator are still not fully understood. We provide a theoretical analysis of the well-known EMO algorithms GSEMO and NSGA-II to showcase the possible advantages of crossover: we propose classes of “royal road” functions on which these algorithms cover the whole Pareto front in expected polynomial time if crossover is being used. But when disabling crossover, they require exponential time in expectation to cover the Pareto front. The latter even holds for a large class of black-box algorithms using any elitist selection and any unbiased mutation operator. Moreover, even the expected time to create a single Pareto-optimal search point is exponential. We provide two different function classes, one tailored for one-point crossover and another one tailored for uniform crossover, and we show that some immune-inspired hypermutations cannot avoid exponential optimisation times. Our work shows the first example of an exponential performance gap through the use of crossover for the widely used NSGA-II algorithm and contributes to a deeper understanding of its limitations and capabilities.

Exploring the Explainable Aspects and Performance of a Learnable Evolutionary Multiobjective Optimization Method

Multiobjective optimization problems have multiple conflicting objective functions to be optimized simultaneously. The solutions to these problems are known as Pareto optimal solutions, which are mathematically incomparable. Thus, a decision maker must be employed to provide preferences to find the most preferred solution. However, decision makers often lack support in providing preferences and insights in exploring the solutions available. We explore the combination of learnable evolutionary models with interactive indicator-based evolutionary multiobjective optimization to create a learnable evolutionary multiobjective optimization method. Furthermore, we leverage interpretable machine learning to provide decision makers with potential insights about the problem being solved in the form of rule-based explanations. In fact, we show that a learnable evolutionary multiobjective optimization method can offer advantages in the search for solutions to a multiobjective optimization problem. We also provide an open source software framework for other researchers to implement and explore our ideas in their own works. Our work is a step toward establishing a new paradigm in the field on multiobjective optimization: explainable and learnable multiobjective optimization . We take the first steps toward this new research direction and provide other researchers and practitioners with necessary tools and ideas to further contribute to this field.