Multi-Objective Evolutionary Optimization

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Overview

The field studies how to find sets of solutions that capture trade-offs among competing goals, rather than a single best answer. Common approaches include NSGA-II and NSGA-III, SPEA2, MOEA/D, and differential evolution, with diversity preservation and constraint-handling methods to guide the search. Current work tackles large-scale, dynamic, uncertain, and expensive problems using techniques such as variable grouping, surrogates, adaptive operators, and learned guidance, across applications from engineering design to scheduling and machine learning. A central challenge is balancing convergence, diversity, feasibility, and evaluation cost; performance remains problem-dependent, while runtime theory and reliable algorithm selection are active concerns.

Latest papers

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88 papers8 papers in the last four weeks, level with the four weeks before. 0.0% of all new papers.

Apr 20, 2026

On Scalability of Multi-Objective Evolutionary Algorithms on Combinatorial Optimisation Problems

Scalability of evolutionary algorithms refers to assessing how their performance changes as problem size increases. In the area of multi-objective optimisation, research on the scalability of multi-objective evolutionary algorithms (MOEAs) has predominantly focussed on continuous problems. However, multi-objective combinatorial optimisation problems (MOCOPs) differ from continuous ones. Their discrete and rigid structure often brings rugged landscape, numerous local optimal solutions and disjoint global optimal regions. This leads to different behaviour of MOEAs. For example, SEMO, a simple MOEA without mating selection and diversity maintenance mechanisms, has been shown to be highly competitive, and in many cases to outperform more sophisticated MOEAs on MOCOPs. Yet, it remains unclear whether such findings hold for large-scale cases. In this paper, we conduct an empirical investigation into the scalability of MOEAs on combinatorial problems, with problem size from 50 to 5,000. Our results show that SEMO experiences a decline in convergence speed as dimensionality increases, compared to other MOEAs such as NSGA-II, SMS-EMOA and MOEA/D. We further demonstrate that the absence of crossover is a major contributor to SEMO's underperformance in large-scale problems, and that incorporating crossover into SEMO can substantially accelerate convergence in general, despite being detrimental in spreading solutions over the Pareto front.

Menghao Tang, Zimin Liang, Miqing Li

University of Birmingham Birmingham, United Kingdom

Evolutionary OptimizationMulti-Objective Evolutionary OptimizationCombinatorial OptimizationMulti-Objective OptimizationGenetic Algorithms
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Apr 17, 2026

Optimising Urban Flood Resilience

Due to the increasing frequency and severity of storm events, driven by the escalation of anthropogenic climate change and urban expansion, there is a requirement for increasingly efficient flood risk management strategies. While Blue-Green Infrastructure (BGI) offers a sustainable solution for managing flood risk, optimal implementation is challenging. To help overcome this challenge, this study presents a novel multi-objective optimisation tool that couples a state-of-the-art hydrodynamic model with a bespoke evolutionary algorithm. The use of a fully dynamic hydrodynamic model enables the tool to accurately evaluate the effectiveness of proposed BGI features with respect to property scale flood vulnerability and hazard analysis. This contrasts with alternative approaches which utilise simplified models, which can only reliably predict inundation extents, thus the proposed optimisation tool provides greater certainty regarding the optimality of the solutions. As a hydrodynamic simulation is required to evaluate each candidate solution, the bespoke evolutionary algorithm is specifically designed to minimise the number of simulations required, ensuring the tool is computationally practical. The effectiveness of the tool in this regard is validated via the derivation of exact convergence measures, for a tractable search space, and via comparisons with benchmark algorithms, for an intractable search space. Compared with traditional design practices, the proposed tool offers an automated approach capable of efficiently exploring a wide range of solutions, providing decision-makers with a set of optimal solutions from which they can make informed investment decisions. The presented methods provide a robust framework for optimising a variety of BGI features in complex urban environments.

James Mckenna, Christos Iliadis, Vassilis Glenis

School of Engineering, Newcastle University, Newcastle upon Tyne, United Kingdom

Multi-Objective Evolutionary Optimization
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Apr 16, 2026

Analysis of Multitasking Pareto Optimization for Monotone Submodular Problems

Pareto optimization via evolutionary multi-objective algorithms has been shown to efficiently solve constrained monotone submodular functions. Traditionally when solving multiple problems, the algorithm is run for each problem separately. We introduce multitasking formulations of these problems that are an effective way to solve multiple related problems with a single run. In our setting the given problems share a monotone submodular function ff but have different knapsack constraints. We examine the case where elements within a constraint have the same cost and show that our multitasking formulations result in small Pareto fronts. This allows the population to share solutions between all problems leading to significant improvements compared to running several classical approaches independently. Using rigorous runtime analysis, we analyze the expected time until the introduced multitasking approaches obtain a (1−1/e)(1-1/e)-approximation for each of the given problems. Our experimental investigations for the maximum coverage problem give further insight into the dynamics behind how the approach works and doesn't work in practice for problems where elements within a constraint also have varied costs.

Liam Wigney, Frank Neumann

Optimisation and Logistics School of Computer Science and Information Technology Adelaide University Adelaide, Australia

Submodular OptimizationEvolutionary OptimizationMulti-Objective Evolutionary OptimizationRuntime Analysis of Evolutionary AlgorithmsMulti-Task OptimizationEvolutionary Multitask Optimization
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Apr 16, 2026

COEVO: Co-Evolutionary Framework for Joint Functional Correctness and PPA Optimization in LLM-Based RTL Generation

LLM-based RTL code generation methods increasingly target both functional correctness and PPA quality, yet existing approaches universally decouple the two objectives, optimizing PPA only after correctness is fully achieved. Whether through sequential multi-agent pipelines, evolutionary search with binary correctness gates, or hierarchical reward dependencies, partially correct but architecturally promising candidates are systematically discarded. Moreover, existing methods reduce the multi-objective PPA space to a single scalar fitness, obscuring the trade-offs among area, delay, and power. To address these limitations, we propose COEVO, a co-evolutionary framework that unifies correctness and PPA optimization within a single evolutionary loop. COEVO formulates correctness as a continuous co-optimization dimension alongside area, delay, and power, enabled by an enhanced testbench that provides fine-grained scoring and detailed diagnostic feedback. An adaptive correctness gate with annealing allows PPA-promising but partially correct candidates to guide the search toward jointly optimal solutions. To preserve the full PPA trade-off structure, COEVO employs four-dimensional Pareto-based non-dominated sorting with configurable intra-level sorting, replacing scalar fitness without manual weight tuning. Evaluated on VerilogEval 2.0 and RTLLM 2.0, COEVO achieves 97.5% and 94.5% Pass@1 with GPT-5.4-mini, surpassing all agentic baselines across four LLM backbones, while attaining the best PPA on 43 out of 49 synthesizable RTLLM designs.

Heng Ping, Peiyu Zhang, Shixuan Li +5

University of Southern California United States

Multi-Objective Evolutionary OptimizationCode GenerationLLM-Based Program SynthesisRTL Code GenerationCode Language Models
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Apr 15, 2026

On the use of evolutionary optimization for the dynamic chance constrained open-pit mine scheduling problem

Open-pit mine scheduling is a complex real-world optimization problem that involves uncertain economic values and dynamically changing resource capacities. Evolutionary algorithms are particularly effective in these scenarios, as they can easily adapt to uncertain and changing environments. However, uncertainty and dynamic changes are often studied in isolation in real-world problems. In this paper, we study a dynamic chance-constrained open-pit mine scheduling problem in which block economic values are stochastic and mining and processing capacities vary over time. We adopt a bi-objective evolutionary formulation that simultaneously maximizes expected discounted profit and minimizes its standard deviation. To address dynamic changes, we propose a diversity-based change response mechanism that repairs a subset of infeasible solutions and introduces additional feasible solutions whenever a change is detected. We evaluate the effectiveness of this mechanism across four multi-objective evolutionary algorithms and compare it with a baseline re-evaluation-based change-response strategy. Experimental results on six mining instances demonstrate that the proposed approach consistently outperforms the baseline methods across different uncertainty levels and change frequencies.

Ishara Hewa Pathiranage, Aneta Neumann

Machine Learning and Optimisation, School of Computer Science and Information Technology, Adelaide University, Adelaide, Australia

Stochastic OptimizationChance-Constrained OptimizationMulti-Objective Evolutionary Optimization
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Apr 13, 2026

On the Use of Bi-Objective Evolutionary Algorithms for the Stochastic MKP under Dynamic Constraints

The multiple knapsack problem (MKP) generalizes the classical knapsack problem by assigning items to multiple knapsacks subject to capacity constraints. It is used to model many real-world resource allocation and scheduling problems. In practice, these optimization problems often involve stochastic and dynamic components. Evolutionary algorithms provide a flexible framework for addressing such problems under uncertainty and dynamic changes. In this paper, we investigate a stochastic and dynamic variant of MKP with chance constraints, where the item weights are modeled as independent normally distributed random variables and knapsack capacities change during the optimization process. We formulate the problem as a bi-objective optimization formulation that balances profit maximization and probabilistic capacity satisfaction at a given confidence level. We conduct an empirical comparison of four widely used multi-objective evolutionary algorithms (MOEAs), representing both decomposition- and dominance-based search paradigms. The algorithms are evaluated under varying uncertainty levels, confidence thresholds, and dynamic change settings. The results provide comparative insights into the behavior of decomposition-based and dominance-based MOEAs for stochastic MKP under dynamic constraints.

Ishara Hewa Pathiranage, Aneta Neumann

Machine Learning and Optimisation, School of Computer Science and Information Technology, Adelaide University, Adelaide, Australia

Combinatorial OptimizationConstrained OptimizationMulti-Objective OptimizationMulti-Objective Evolutionary OptimizationChance-Constrained Optimization
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Apr 12, 2026

Reinforcement Learning-Guided NSGA-II Enhanced with Gray Relational Coefficient for Multi-Objective Optimization: Application to NASDAQ Portfolio Optimization

In modern financial markets, decision-makers increasingly rely on quantitative methods to navigate complex trade-offs among multiple, often conflicting objectives. This paper addresses constrained multi-objective optimization (MOO) with an application to portfolio optimization for minimizing risk and maximizing return. To address existing gaps, we propose a novel reinforcement learning (RL)-guided non-dominated sorting genetic algorithm II (NSGA-II) enhanced with gray relational coefficients (GRC), termed RL-NSGA-II-GRC, which combines an RL agent controller and GRC-based selection to improve convergence and diversity of Pareto fronts. The agent adapts evolutionary parameters online using metrics of hypervolume, feasibility, and diversity, while the GRC tournament operator ranks parents via a unified score considering dominance rank, crowding distance, and proximity to ideal reference. We evaluate the framework on the Kursawe and CONSTR benchmarks and a NASDAQ portfolio application. On the benchmarks, RL-NSGA-II-GRC achieves convergence improvements of about 5.8% and 4.4% over NSGA-II, while preserving well-distributed non-dominated solutions. In the portfolio application, it produces a smooth, densely populated efficient frontier supporting identification of the maximum Sharpe ratio portfolio (annualized Sharpe =1.92) and utility-optimal portfolios for different risk-aversion levels. The main contributions are three-fold: 1) we propose an RL-NSGA-II-GRC method integrating an RL agent into the evolutionary framework to adaptively control parameters via generational feedback; 2) we design a GRC-enhanced binary tournament operator providing a comprehensive indicator to guide the search toward the Pareto front; 3) we demonstrate, on benchmark MOO and a NASDAQ case study, that the method delivers improved convergence and well-populated frontiers supporting actionable insights.

Zhiyuan Wang, Qinxu Ding, Ding Ding +4

School of Business, Singapore University of Social Sciences, Singapore 599494, Singapore

Multi-Objective Evolutionary OptimizationMulti-Objective OptimizationPortfolio Optimization
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Apr 10, 2026

SkillMOO: Multi-Objective Optimization of Agent Skills for Software Engineering

Agent skills are increasingly used to configure coding agents for software engineering (SE) tasks, yet current practice treats them as static, hand-crafted assets, or evolved on pass rate alone. This is insufficient: a skill can improve task success while substantially raising token cost, or introducing misleading guidance. We argue that SE agent skill bundles can be treated as multi-objective search objects and present SkillMOO, a framework that evolves skill bundles through LLM-proposed edits and NSGA-II Pareto selection on pass rate and inference cost. Evaluated across all 16 SkillsBench SE tasks, SkillMOO achieves the top pass rate rank on 11 of 12 non-zero-pass tasks while achieving cost reductions of up to 31.7% over static bundles, with pass rate gains up to 21 percentage points. Analysis of 38 skill edits shows that pruning and substitution dominate successful operations, offering actionable principles for skill bundle design. Thereby, the current practice of deploying skills without cost-aware validation leaves better skill configurations unexplored, motivating a new class of cost-aware, search-based skill engineering.

Jingzhi Gong, Ruizhen Gu, Zhiwei Fei +7

King’s College London, London, United Kingdom · Queen’s University Belfast, Belfast, United Kingdom · Nanjing University, Nanjing, China +3

Software Engineering AgentsMulti-Objective Evolutionary Optimization
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Apr 9, 2026

Robust Multi-Objective Optimization for Bicycle Rebalancing in Shared Mobility Systems

Dock-based bike-sharing systems exhibit spatial imbalances between bicycle supply and user demand, often addressed through overnight truck-based rebalancing. This work studies static overnight rebalancing under demand uncertainty modeled as a tri-objective optimization problem. The objectives minimize total travel distance, expected unmet demand, and a robustness-oriented unmet demand measure over high-demand scenarios. Route plans are evaluated via a recourse simulation that enforces truck loads and station capacity constraints across multiple demand realizations. The robustness objective supports selecting plans that reduce peak-demand service degradation. Trade-off solutions are approximated with Non-dominated Sorting Genetic Algorithm II using a permutation--partition encoding and domain-specific relocation operators, including a biased best-improvement move for station relocation. Experiments on the real Barcelona Bicing system with 460 stations show well-distributed Pareto sets and substantial contributions to the reference non-dominated set. Greedy constructive baselines mainly yield extreme solutions and are often dominated.

Diego Daniel Pedroza-Perez, Gabriel Luque, Sergio Nesmachnow +1

ITIS Software, University of Malaga, Spain · Universidad de la República, Uruguay

Multi-Objective OptimizationRobust OptimizationVehicle RoutingMulti-Objective Evolutionary Optimization
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Apr 6, 2026

Ranking Constraints via Topological Dual-Directional Search in Evolutionary Multi-Objective Optimization

Existing evolutionary algorithms for Constrained Multi-objective Optimization Problems (CMOPs) typically treat all constraints uniformly, overlooking their distinct geometric relationships with the true Constrained Pareto Front (CPF). In reality, constraints play different roles: some directly shape the final CPF, some create infeasible obstacles, while others are irrelevant. To exploit this insight, we propose a novel algorithm named RCCMO, which sequentially performs unconstrained exploration, single-constraint exploitation, and full-constraint refinement. The core innovation of RCCMO lies in a constraint prioritization method derived from these geometric insights, seamlessly coupled with a unique dual-directional search mechanism. Specifically, RCCMO first prioritizes constraints that constitute the final CPF, approaching them from the evolutionary direction (optimizing objectives) to locate the CPF directly shaped by single-constraint boundaries. Subsequently, for constraints that merely hinder the population's progress, RCCMO searches from the anti-evolutionary direction (targeting the infeasible boundaries where hindering constraints intersect with the CPF) to effectively discover how these constraints obstruct and form the final CPF. Meanwhile, irrelevant constraints are intentionally bypassed. Furthermore, a series of specialized mechanisms are proposed to accelerate the algorithm's execution, reduce heuristic misjudgments, and dynamically adjust search directions in real time. Extensive experiments on 5 benchmark test suites and 29 real-world CMOPs demonstrate that RCCMO significantly outperforms seven state-of-the-art algorithms.

Ruiqing Sun, Dawei Feng, Sheng Qi +6

National Key Laboratory of Parallel and Distributed Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410000, P.R. China · College of System Engineering, National University of Defense Technology, Changsha 410000, P.R. China · College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, P.R. China +1

Multi-Objective Evolutionary OptimizationEvolutionary OptimizationMulti-Objective Optimization
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Apr 4, 2026

RDEx-CMOP: Feasibility-Aware Indicator-Guided Differential Evolution for Fixed-Budget Constrained Multiobjective Optimization

Constrained multiobjective optimisation requires fast feasibility attainment together with stable convergence and diversity preservation under strict evaluation budgets. This report documents RDEx-CMOP, the differential evolution variant used in the IEEE CEC 2025 numerical optimisation competition (C06 special session) constrained multiobjective track. RDEx-CMOP integrates an ε-level feasibility schedule, a SPEA2-style indicator-driven fitness assignment, and a fitness-oriented current-to-pbest/1 mutation operator. We evaluate RDEx-CMOP on the official CEC 2025 CMOP benchmark using the median-target U-score framework and the released trace data. Experimental results show that RDEx-CMOP achieves the highest total score and the best overall average rank among all released comparison algorithms, with strong target-attainment behaviour and near-zero final violation on most problems.

Sichen Tao, Yifei Yang, Ruihan Zhao +3

Department of Engineering, University of Toyama, Toyama-shi 930-8555, Japan · Cyberscience Center, Tohoku University, Sendai-shi 980-8578, Japan · Faculty of Science and Technology, Hirosaki University, Hirosaki-shi 036-8560, Japan +5

Multi-Objective Evolutionary OptimizationMulti-Objective OptimizationDifferential Evolution
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Apr 1, 2026

A Hierarchical Importance-Guided Multi-objective Evolutionary Framework for Deep Neural Network Pruning

The optimization of over-parameterized deep neural networks represents a large-scale, high-dimensional, and strongly non-convex decision problem that challenges existing optimization frameworks. Current evolutionary and gradient-based pruning methods often struggle to scale to such dimensionalities, as they rely on flat search spaces, scalarized objectives, or repeated retraining, leading to premature convergence and prohibitive computational cost. This paper introduces a hierarchical importance-guided evolutionary framework that reformulates convolutional network pruning as a tractable large-scale multi-objective optimization problem. In the first phase, a continuous evolutionary search performs coarse exploration of weight-wise pruning thresholds to shrink the search space and identify promising regions of the Pareto set. The second phase applies a fine-grained binary evolutionary optimization constrained to the surviving weights, where importance-aware sampling and adaptive variation operators refine local search in the sparse region of the Pareto set. This hierarchical design combines global exploration and localized exploitation to achieve a well-distributed Pareto set of networks balancing compactness and accuracy. Empirical results on CIFAR-10 and CIFAR-100 using ResNet-56 and ResNet-110 confirm the method's effectiveness compared to existing evolutionary approaches: pruning achieves up to 51.9% and 38.9% parameter reductions with almost no accuracy loss compared to state-of-the-art evolutionary DNN pruning methods. The proposed method contributes a scalable evolutionary approach for solving very-large-scale multi-objective optimization problems, offering a general paradigm extendable to other domains where the decision space is exponentially large, objective functions are conflicting, and efficient trade-off discovery is essential.

Zak Khan, Azam Asilian Bidgoli

Department of Computer Science and Physics, Wilfrid Laurier University, Waterloo, N2L 3C5, Ontario, Canada

Neural Network PruningNeural Network CompressionMulti-Objective Evolutionary Optimization
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Apr 1, 2026

A Decoupled Basis-Vector-Driven Generative Framework for Dynamic Multi-Objective Optimization

Dynamic multi-objective optimization requires continuous tracking of moving Pareto fronts. Existing methods struggle with irregular mutations and data sparsity, primarily facing three challenges: the non-linear coupling of dynamic modes, negative transfer from outdated historical data, and the cold-start problem during environmental switches. To address these issues, this paper proposes a decoupled basis-vector-driven generative framework (DB-GEN). First, to resolve non-linear coupling, the framework employs the discrete wavelet transform to separate evolutionary trajectories into low-frequency trends and high-frequency details. Second, to mitigate negative transfer, it learns transferable basis vectors via sparse dictionary learning rather than directly memorizing historical instances. Recomposing these bases under a topology-aware contrastive constraint constructs a structured latent manifold. Finally, to overcome the cold-start problem, a surrogate-assisted search paradigm samples initial populations from this manifold. Pre-trained on 120 million solutions, DB-GEN performs direct online inference without retraining or fine-tuning. This zero-shot generation process executes in milliseconds, requiring approximately 0.2 seconds per environmental change. Experimental results demonstrate that DB-GEN improves tracking accuracy across various dynamic benchmarks compared to existing algorithms.

Yaoming Yang, Shuai Wang, Bingdong Li +2

Multi-Party Multi-Objective OptimizationMulti-Objective OptimizationMulti-Objective Evolutionary Optimization
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Mar 31, 2026

Genetic algorithms for multi-omic feature selection: a comparative study in cancer survival analysis

Multi-omic datasets offer opportunities for improved biomarker discovery in cancer research, but their high dimensionality and limited sample sizes make identifying compact and effective biomarker panels challenging. Feature selection in large-scale omics can be efficiently addressed by combining machine learning with genetic algorithms, which naturally support multi-objective optimization of predictive accuracy and biomarker set size. However, genetic algorithms remain relatively underexplored for multi-omic feature selection, where most approaches concatenate all layers into a single feature space. To address this limitation, we introduce Sweeping*, a multi-view, multi-objective algorithm alternating between single- and multi-view optimization. It employs a nested single-view multi-objective optimizer, and for this study we use the genetic algorithm NSGA3-CHS. It first identifies informative biomarkers within each layer, then jointly evaluates cross-layer interactions; these multi-omic solutions guide the next single-view search. Through repeated sweeps, the algorithm progressively identifies compact biomarker panels capturing cross-modal complementary signals. We benchmark five Sweeping* strategies, including hierarchical and concatenation-based variants, using survival prediction on three TCGA cohorts. Each strategy jointly optimizes predictive accuracy and set size, measured via the concordance index and root-leanness. Overall performance and estimation error are assessed through cross hypervolume and Pareto delta under 5-fold cross-validation. Our results show that Sweeping* can improve the accuracy-complexity trade-off when sufficient survival signal is present and that integrating omic layers can enhance survival prediction beyond clinical-only models, although benefits remain cohort-dependent.

Luca Cattelani, Vittorio Fortino

Institute of Biomedicine, School of Medicine, University of Eastern Finland, Yliopistonranta 8, 70210, Finland

Feature SelectionGenetic AlgorithmsMulti-Omics Data IntegrationMulti-Objective Evolutionary OptimizationCancer Survival Prediction
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Mar 29, 2026

A Novel Immune Algorithm for Multiparty Multiobjective Optimization

Traditional multiobjective optimization problems (MOPs) are insufficiently equipped for scenarios involving multiple decision makers (DMs), which are prevalent in many practical applications. These scenarios are categorized as multiparty multiobjective optimization problems (MPMOPs). For MPMOPs, the goal is to find a solution set that is as close to the Pareto front of each DM as much as possible. This poses challenges for evolutionary algorithms in terms of searching and selecting. To better solve MPMOPs, this paper proposes a novel approach called the multiparty immune algorithm (MPIA). The MPIA incorporates an inter-party guided crossover strategy based on the individual's non-dominated sorting ranks from different DM perspectives and an adaptive activation strategy based on the proposed multiparty cover metric (MCM). These strategies enable MPIA to activate suitable individuals for the next operations, maintain population diversity from different DM perspectives, and enhance the algorithm's search capability. To evaluate the performance of MPIA, we compare it with ordinary multiobjective evolutionary algorithms (MOEAs) and state-of-the-art multiparty multiobjective optimization evolutionary algorithms (MPMOEAs) by solving synthetic multiparty multiobjective problems and real-world biparty multiobjective unmanned aerial vehicle path planning (BPUAV-PP) problems involving multiple DMs. Experimental results demonstrate that MPIA outperforms other algorithms.

Kesheng Chen, Wenjian Luo, Qi Zhou +3

Guangdong Provincial Key Laboratory of Novel Security Intelligence Technologies, School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen 518055, China. · Peng Cheng Laboratory, Shenzhen 518000, China. · School of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing 210044, China. +1

Multi-Party Multi-Objective OptimizationMulti-Objective OptimizationMulti-Objective Evolutionary Optimization
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Mar 28, 2026

RDEx-MOP: Indicator-Guided Reconstructed Differential Evolution for Fixed-Budget Multiobjective Optimization

Multiobjective optimisation in the CEC 2025 MOP track is evaluated not only by final IGD values but also by how quickly an algorithm reaches the target region under a fixed evaluation budget. This report documents RDEx-MOP, the reconstructed differential evolution variant used in the IEEE CEC 2025 numerical optimisation competition (C06 special session) bound-constrained multiobjective track. RDEx-MOP integrates indicator-based environmental selection, a niche-maintained Pareto-candidate set, and complementary differential evolution operators for exploration and exploitation. We evaluate RDEx-MOP on the official CEC 2025 MOP benchmark using the released checkpoint traces and the median-target U-score framework. Experimental results show that RDEx-MOP achieves the highest total score and the best average rank among all released comparison algorithms, including the earlier RDEx baseline.

Sichen Tao, Yifei Yang, Ruihan Zhao +3

Department of Engineering, University of Toyama, Toyama-shi 930-8555, Japan · Cyberscience Center, Tohoku University, Sendai-shi 980-8578, Japan · Faculty of Science and Technology, Hirosaki University, Hirosaki-shi 036-8560, Japan +5

Multi-Objective Evolutionary OptimizationEvolutionary OptimizationDifferential Evolution
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Mar 27, 2026

Efficient Disruption of Criminal Networks through Multi-Objective Genetic Algorithms

Criminal networks, such as the Sicilian Mafia, pose substantial threats to public safety, national security, and economic stability. Outdated disruption methods with a focus on removing influential individuals or key players have proven ineffective due to the covertness of the network. Thus, researchers have been trying to apply Social Network Analysis (SNA) techniques, such as centrality-based measures, to identify key players. However, removing individuals with high centrality often proves to be inefficient, as it does not mimic the real-world scenarios that Law Enforcement Agencies (LEAs) face. For instance, the operational costs limit the LEAs from exploiting the results of the centrality-based methods. This study proposes a multi-objective optimisation framework like the Weighted Sum Genetic Algorithm (WS-GA) and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to identify disruption strategies that balance two conflicting goals, maximising fragmentation and minimising operational cost which is captured by the spatial distance between nodes and the nearest LEA headquarters. The study utilises the "Montagna Operation" dataset for the experiments. The results demonstrate that although centrality-based approaches can fragment network effectively, they tend to incur higher operational costs. In contrast, the proposed algorithms achieve comparable disruption outcomes with significantly lower operational costs. The contribution of this work lies in incorporating operational costs in a form of spatial distance constraints into disruption strategy, which has been largely overlooked in prior studies. This research offers a scalable multi-objective capability that improves practical application of SNA in guiding LEAs in disrupting criminal networks more efficiently and strategically.

Yehezkiel Darmadi, Thanh Thi Nguyen, Campbell Wilson

Faculty of Information Technology, Monash University, Melbourne, Victoria, 3800, Australia · AiLECS Lab, Faculty of Information Technology, Monash University, Melbourne, Victoria, 3800, Australia

Multi-Objective OptimizationComputational Social ScienceMulti-Objective Evolutionary Optimization
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Mar 23, 2026

Training-Free Diffusion-Driven Modeling of Pareto Set Evolution for Dynamic Multiobjective Optimization

Dynamic multiobjective optimization problems (DMOPs) feature time-varying objectives, which cause the Pareto optimal solution (POS) set to drift over time and make it difficult to maintain both convergence and diversity under limited response time. Many existing prediction-based dynamic multiobjective evolutionary algorithms (DMOEAs) either depend on learned models with nontrivial training cost or employ one-step population mapping, which may overlook the gradual nature of POS evolution. This paper proposes DD-DMOEA, a training-free diffusion-based dynamic response mechanism for DMOPs. The key idea is to treat the POS obtained in the previous environment as a "noisy" sample set and to guide its evolution toward the current POS through an analytically constructed multi-step denoising process. A knee-point-based auxiliary strategy is used to specify the target region in the new environment, and an explicit probability-density formulation is derived to compute the denoising update without neural training. To reduce the risk of misleading guidance caused by knee-point prediction errors, an uncertainty-aware scheme adaptively adjusts the guidance strength according to the historical prediction deviation. Experiments on the CEC2018 dynamic multiobjective benchmarks show that DD-DMOEA achieves competitive or better convergence-diversity performance and provides faster dynamic response than several state-of-the-art DMOEAs.

Jian Guan, Huolong Wu, Zhenzhong Wang +2

Institute of Artificial Intelligence, Xiamen University, Xiamen, 361005, China · Department of Artificial Intelligence, School of Informatics, Xiamen University; the Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education; and the Key Laboratory of Digital Protection and Intelligent Processing of Intangible Cultural Heritage of Fujian and Taiwan, Ministry of Culture and Tourism, Xiamen, 361005, China · Department of Artificial Intelligence, Sichuan University, Chengdu, 610065, China

Multi-Objective OptimizationMulti-Objective Evolutionary Optimization
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Mar 23, 2026

Evolutionary Biparty Multiobjective UAV Path Planning: Problems and Empirical Comparisons

Unmanned aerial vehicles (UAVs) have been widely used in urban missions, and proper planning of UAV paths can improve mission efficiency while reducing the risk of potential third-party impact. Existing work has considered all efficiency and safety objectives for a single decision-maker (DM) and regarded this as a multiobjective optimization problem (MOP). However, there is usually not a single DM but two DMs, i.e., an efficiency DM and a safety DM, and the DMs are only concerned with their respective objectives. The final decision is made based on the solutions of both DMs. In this paper, for the first time, biparty multiobjective UAV path planning (BPMO-UAVPP) problems involving both efficiency and safety departments are modeled. The existing multiobjective immune algorithm with nondominated neighbor-based selection (NNIA), the hybrid evolutionary framework for the multiobjective immune algorithm (HEIA), and the adaptive immune-inspired multiobjective algorithm (AIMA) are modified for solving the BPMO-UAVPP problem, and then biparty multiobjective optimization algorithms, including the BPNNIA, BPHEIA, and BPAIMA, are proposed and comprehensively compared with traditional multiobjective evolutionary algorithms and typical multiparty multiobjective evolutionary algorithms (i.e., OptMPNDS and OptMPNDS2). The experimental results show that BPAIMA performs better than ordinary multiobjective evolutionary algorithms such as NSGA-II and multiparty multiobjective evolutionary algorithms such as OptMPNDS, OptMPNDS2, BPNNIA and BPHEIA.

Kesheng Chen, Wenjian Luo, Xin Lin +2

Guangdong Provincial Key Laboratory of Novel Security Intelligence Technologies, School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen 518055, China · Peng Cheng Laboratory, Shenzhen 518055, China · School of Artificial Intelligence/School of Future Technology, Nanjing University of Information Science and Technology, Nanjing 210044, China

UAV Trajectory OptimizationMulti-Objective Motion PlanningMulti-Objective OptimizationMulti-Objective Evolutionary OptimizationMetaheuristic Optimization
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Mar 21, 2026

MOELIGA: a multi-objective evolutionary approach for feature selection with local improvement

Selecting the most relevant or informative features is a key issue in actual machine learning problems. Since an exhaustive search is not feasible even for a moderate number of features, an intelligent search strategy must be employed for finding an optimal subset, which implies considering how features interact with each other in promoting class separability. Balancing feature subset size and classification accuracy constitutes a multi-objective optimization challenge. Here we propose MOELIGA, a multi-objective genetic algorithm incorporating an evolutionary local improvement strategy that evolves subordinate populations to refine feature subsets. MOELIGA employs a crowding-based fitness sharing mechanism and a sigmoid transformation to enhance diversity and guide compactness, alongside a geometry-based objective promoting classifier independence. Experimental evaluation on 14 diverse datasets demonstrates MOELIGA's ability to identify smaller feature subsets with superior or comparable classification performance relative to 11 state-of-the-art methods. These findings suggest MOELIGA effectively addresses the accuracy-dimensionality trade-off, offering a robust and adaptable approach for multi-objective feature selection in complex, high-dimensional scenarios.

Leandro Vignolo, Matias Gerard

Research Institute for Signals, Systems and Computational Intelligence (sınc(i)), FICH–UNL/CONICET, Ciudad Universitaria UNL, Santa Fe, Argentina.

Feature SelectionGenetic AlgorithmsMulti-Objective Evolutionary OptimizationMetaheuristic Optimization
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Mar 17, 2026

Deep Reinforcement Learning-Assisted Automated Operator Portfolio for Constrained Multi-objective Optimization

Constrained multi-objective optimization problems (CMOPs) are of great significance in the context of practical applications, ranging from scientific to engineering domains. Most existing constrained multi-objective evolutionary algorithms (CMOEAs) usually employ fixed operators all the time, which exhibit poor versatility in handling various CMOPs. Therefore, some recent studies have focused on adaptively selecting the best operators for the current population states during the search process. The evolutionary algorithms proposed in these studies learn the value of each operator and recommend the operator with the highest value for the current population, resulting in only a single operator being recommended at each generation, which can potentially lead to local optima and inefficient utilization of function evaluations. To address the dilemma in operator adaptation, this paper proposes a reinforcement learning-based automated operator portfolio approach to learn an allocation scheme of operators at each generation. This approach considers the optimization-related and constraint-related features of the current population as states, the overall improvement in population convergence and diversity as rewards, and different operator portfolios as actions. By utilizing deep neural networks to establish a mapping model between the population states and the expected cumulative rewards, the proposed approach determines the optimal operator portfolio during the evolutionary process. By embedding the proposed approach into existing CMOEAs, a deep reinforcement learning-assisted automated operator portfolio based evolutionary algorithm for solving CMOPs, abbreviated as CMOEA-AOP, is developed. Empirical studies on 33 benchmark problems demonstrate that the proposed algorithm significantly enhances the performance of CMOEAs and exhibits more stable performance across different CMOPs.

Shuai Shao, Ye Tian, Shangshang Yang +1

the School of Computer Science and Technology, Anhui University, Hefei 230601, China

Multi-Objective OptimizationMulti-Objective Evolutionary Optimization
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Mar 12, 2026

An Evolutionary Algorithm with Probabilistic Annealing for Large-scale Sparse Multi-objective Optimization

Large-scale sparse multi-objective optimization problems (LSMOPs) are prevalent in real-world applications, where optimal solutions typically contain only a few nonzero variables, such as in adversarial attacks, critical node detection, and sparse signal reconstruction. Since the function evaluation of LSMOPs often relies on large-scale datasets involving a large number of decision variables, the search space becomes extremely high-dimensional. The coexistence of sparsity and high dimensionality greatly intensifies the conflict between exploration and exploitation, making it difficult for existing multi-objective evolutionary algorithms (MOEAs) to identify the critical nonzero decision variables within limited function evaluations. To address this challenge, this paper proposes an evolutionary algorithm with probabilistic annealing for large-scale sparse multi-objective optimization. The algorithm is driven by two probability vectors with distinct entropy characteristics: a convergence-oriented probability vector with relatively low entropy ensures stable exploitation, whereas an annealed probability vector with gradually decreasing entropy enables an adaptive transition from global exploration to local refinement. By integrating these complementary search dynamics, the proposed algorithm achieves a dynamic equilibrium between exploration and exploitation. Experimental results on benchmark problems and real-world applications demonstrate that the proposed algorithm outperforms state-of-the-art evolutionary algorithms in terms of both convergence and diversity.

Shuai Shao, Yuhao Sun, Xing Chen +3

School of Computer Science and Technology, Anhui University, Hefei 230601, China · Sapient Intelligence, Singapore

Multi-Party Multi-Objective OptimizationMulti-Objective OptimizationMulti-Objective Evolutionary Optimization
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Mar 11, 2026

Multi-objective Genetic Programming with Multi-view Multi-level Feature for Enhanced Protein Secondary Structure Prediction

Predicting protein secondary structure is essential for understanding protein function and advancing drug discovery. However, the intricate sequence-structure relationship poses significant challenges for accurate modeling. To address these, we propose MOGP-MMF, a multi-objective genetic programming framework that reformulates PSSP as an automated optimization task focused on feature selection and fusion. Specifically, MOGP-MMF introduces a multi-view multi-level representation strategy that integrates evolutionary, semantic, and newly introduced structural views to capture the comprehensive protein folding logic. Leveraging an enriched operator set, the framework evolves both linear and nonlinear fusion functions, effectively capturing high-order feature interactions while reducing fusion complexity. To resolve the accuracy-complexity trade-off, an improved multi-objective GP algorithm is developed, incorporating a knowledge transfer mechanism that utilizes prior evolutionary experience to guide the population toward global optima. Extensive experiments across seven benchmark datasets demonstrate that MOGP-MMF surpasses state-of-the-art methods, particularly in Q8 accuracy and structural integrity. Furthermore, MOGP-MMF generates a diverse set of non-dominated solutions, offering flexible model selection schemes for various practical application scenarios. The source code is available on GitHub: https://github.com/qian-ann/MOGP-MMF/tree/main.

Yining Qian, Lijie Su, Meiling Xu +1

National Frontiers Science Center for Industrial Intelligence and Systems Optimization, Shenyang 110819, China · Key Laboratory of Data Analytics and Optimization for Smart Industry (Northeastern University), Ministry of Education, Shenyang 110819, China · Liaoning Engineering Laboratory of Data Analytics and Optimization for Smart Industry, Shenyang 110819, China +2

Multi-View Feature FusionProtein Structure PredictionGenetic ProgrammingMulti-Objective Evolutionary Optimization
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Mar 9, 2026

Multi-Objective Evolutionary Optimization of Chance-Constrained Multiple-Choice Knapsack Problems with Implicit Probability Distributions

The multiple-choice knapsack problem (MCKP) is a classic combinatorial optimization with wide practical applications. This paper investigates a significant yet underexplored extension of MCKP: the multi-objective chance-constrained MCKP (MO-CCMCKP) under implicit probability distributions. The goal of the problem is to simultaneously minimize the total cost and maximize the confidence level of satisfying the capacity constraint, capturing essential trade-offs in domains like 5G network configuration. To address the computational challenge of evaluating chance constraints under implicit distributions, we first propose an order-preserving efficient resource allocation Monte Carlo (OPERA-MC) method. This approach adaptively allocates sampling resources to preserve dominance relationships while reducing evaluation time significantly. Further, we develop NHILS, a hybrid evolutionary algorithm that integrates specialized initialization and local search into NSGA-II to navigate sparse feasible regions. Experiments on synthetic benchmarks and real-world 5G network configuration benchmarks demonstrate that NHILS consistently outperforms several state-of-the-art multi-objective optimizers in convergence, diversity, and feasibility. The benchmark instances and source code will be made publicly available to facilitate research in this area.

Xuanfeng Li, Shengcai Liu, Wenjie Chen +2

Guangdong Provincial Key Laboratory of Brain-Inspired Intelligent Computation, Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China · School of Information Management, Central China Normal University, Wuhan 430079, China · Centre for Frontier AI Research, Institute of High Performance Computing, Agency for Science Technology and Research, Singapore 138632 +1

Chance-Constrained OptimizationCombinatorial OptimizationStochastic OptimizationMulti-Objective Evolutionary Optimization
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Dec 30, 2025

Decoupling Constraints from Two Directions for Evolutionary Constrained Multi-objective Optimization

Real-world constrained multi-objective optimization problems (CMOPs) commonly involve multiple constraints, and understanding and exploiting their coupling relationships is crucial for efficient optimization. Recent constraint-decoupling methods handle individual constraints separately, but they generally search only in the evolutionary direction to approximate single-constraint Pareto fronts (SCPFs). In this study, we show that part or all of the constrained Pareto front (CPF) may be unrelated to any SCPF and instead be shaped by the boundaries of infeasible regions. We refer to such a portion as the independent CPF (ICPF) and introduce the reverse CPF (RCPF) to characterize its associated informative infeasible boundaries. Based on these observations, we propose a bidirectional constraint-decoupling coevolutionary algorithm named DCF2D. DCF2D dynamically identifies the constraints obstructing the main population and activates constraint-specific auxiliary populations. These populations adaptively search in the evolutionary direction for the corresponding SCPFs or in the reverse evolutionary direction for the corresponding RCPFs. Its three-stage framework integrates unconstrained global exploration, event-driven bidirectional coevolution, and final convergence refinement. Experiments on 87 benchmark instances from seven test suites and 28 real-world engineering CMOPs demonstrate that DCF2D achieves the best overall performance among nine algorithms. Code available at: https://github.com/RuiqingS/DCF2D.

Ruiqing Sun, Dawei Feng, Xing Zhou +6

College of Computer Science and Technology, National University of Defense Technology, Changsha 410000, P.R. China · College of Intelligence Science and Technology, National University of Defense Technology, Changsha, 410000, P.R. China · State Key Laboratory of Complex & Critical Software Environment, College of Information and Communication, National University of Defense Technology, Wuhan 430019, P.R. China +1

Evolutionary OptimizationMulti-Objective Evolutionary OptimizationConstrained OptimizationMulti-Objective Optimization
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Nov 21, 2025

PepEVOLVE: Position-Aware Dynamic Peptide Optimization via Group-Relative Advantage

Macrocyclic peptides are an emerging modality that combines biologics-like affinity with small-molecule-like developability, yet their vast combinatorial space and multi-parameter objectives make lead optimization slow and challenging. Prior generative approaches for peptide lead optimization (e.g., PepINVENT) require chemists to pre-specify mutable positions for optimization, choices that are not always known a priori, and rely on static pretraining and optimization algorithms that limit the model's ability to generalize and effectively optimize peptide sequences. We introduce PepEVOLVE, a position-aware, dynamic framework that learns both where to edit and how to dynamically optimize peptides for multi-parameter improvement. PepEVOLVE (i) augments pretraining with dynamic masking and CHUCKLES shifting to improve generalization, (ii) uses a context-free multi-armed-bandit router that discovers high-reward residues, and (iii) couples a novel evolving optimization algorithm with group-relative advantage to stabilize reinforcement updates. During in silico evaluations, the router policy reliably learns and concentrates probability on chemically tractable sites that influence the desired peptide's properties. On a therapeutically motivated Rev-binding macrocycle benchmark, PepEVOLVE outperformed PepINVENT by reaching higher averaged permeability-weighted optimization scores of approximately 0.8 vs. 0.6, achieving best candidates with score of 0.97 (vs. 0.89), and converging in fewer steps under the task of optimizing permeability and lipophilicity with structure constraints. Overall, PepEVOLVE offers a practical, reproducible path to linear and macrocyclic peptide lead optimization when optimal edit sites are unknown, enabling more efficient chemical space exploration and improving design quality across multiple objectives to accelerate the design cycles.

Trieu Nguyen, Hao-Wei Pang, Shasha Feng

Merck & Co., Inc., Rahway, NJ, USA · University of South Florida, FL, USA

Molecular OptimizationDrug DiscoveryEvolutionary OptimizationReinforcement LearningMulti-Objective Evolutionary Optimization
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Jun 6, 2025

Decomposability-Guided Cooperative Coevolution for Large-Scale Itinerary Planning

Large-scale itinerary planning is a variant of the traveling salesman problem, aiming to determine an optimal path that maximizes the collected point-of-interest (POI) scores while minimizing travel time and cost, subject to travel duration constraints. This paper analyzes inter-component dependence in large-scale itinerary planning and establishes sufficient conditions for weak decomposability, under which an optimal path can visit each cluster as a contiguous subpath. Guided by this weak decomposability, we propose a novel multi-objective cooperative coevolutionary algorithm for large-scale itinerary planning, addressing the challenges of component imbalance and interactions. Specifically, we design a dynamic decomposition strategy based on the normalized fitness within each component, define optimization potential considering component scale and contribution, and develop a computational resource allocation strategy. Finally, we evaluate the proposed algorithm on 18 real-world test cases, eight large-scale semi-synthetic test cases, and eight adapted public clustered orienteering problem benchmark cases. Comparative results show that the proposed algorithm achieves the highest mean hypervolume across all 34 test cases and significantly outperforms the compared algorithms. Ablation and optimizer-decoupling analyses further validate the effectiveness of its core mechanisms and the general applicability of the proposed framework, with particularly pronounced performance gains on large-scale benchmark instances.

Ziyu Zhang, Peilan Xu, Yuetong Sun +2

School of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing 210044, China. · Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China. · School of Computer Science and Technology, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, Guangdong, China. +1

Travel PlanningTraveling Salesperson ProblemEvolutionary OptimizationMulti-Objective Evolutionary Optimization
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May 16, 2025

Diffusion-based Evolutionary Optimization for 3D Multi-Objective Molecular Generation

De novo 3D molecular design with multiple properties and fragment-retention constraints is formulated as a constrained multi-objective optimization problem. Existing 3D diffusion models provide strong capabilities for generating novel molecules, but adapting them to new conditions and multi-objective optimization tasks remains difficult. We present Diffusion-based Evolutionary Molecular Optimization (DEMO), a framework that draws solely on the unconditional molecular prior of a frozen pretrained diffusion model to generate chemically valid 3D candidates, while evolutionary search handles conditional generation and constrained multi-objective optimization, without retraining or fine-tuning. DEMO performs crossover and mutation on intermediate diffusion states through an Evolutionary-Guided Diffusion (EGD) operator, combines 2D topology and 3D geometry in Structure-Aware Environmental Selection (SAES) to preserve structural diversity, and uses three cooperating populations to coordinate structural exploration, fragment-constraint satisfaction, and property optimization. Experimental results demonstrate that EGD outperforms task-specific conditional generators in property targeting; SAES preserves structural diversity while retaining competitive hypervolume in multi-objective optimization; and DEMO improves objective convergence and generates diverse feasible molecules under fragment constraints. These results show how evolutionary search can reuse existing diffusion models for diverse molecular design requirements.

Ruiqing Sun, Dawei Feng, Sen Yang +5

College of Computer Science and Technology, National University of Defense Technology, 410073, Changsha, China · Bioinformatics Center, Academy of Military Medical Sciences (AMMS), 100080, Beijing, China

3D Molecular GenerationConstrained Generative ModelingMulti-Objective Evolutionary OptimizationDiffusion ModelsDiffusion Guidance
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