High-Performance Computing (HPC) job scheduling involves balancing conflicting objectives such as minimizing makespan, reducing wait times, optimizing resource use, and ensuring fairness. Traditional methods, including heuristic-based (e.g., First-Come-First-Served) or intensive optimization techniques, often lack adaptability to dynamic workloads and heterogeneous HPC systems. To address this, we propose a novel Large Language Model (LLM)-based scheduler using a ReAct-style framework (Reason + Act), enabling iterative, interpretable decision-making. The system incorporates a scratchpad memory to track scheduling history and refine decisions via natural language feedback, while a constraint enforcement module ensures feasibility and safety. We evaluate our approach using OpenAI's O4-Mini and Anthropic's Claude 3.7 across seven real-world HPC workload scenarios, including heterogeneous mixes, bursty patterns, and adversarial cases. Comparisons against FCFS, Shortest Job First, and Google OR-Tools (on 10 to 100 jobs) reveal that LLM-based scheduling effectively balances multiple objectives while offering transparent reasoning through natural language traces. The method excels in constraint satisfaction and adapts to diverse workloads without domain-specific training. However, a trade-off between reasoning quality and computational overhead challenges real-time deployment. This work presents the first comprehensive study of reasoning-capable LLMs for HPC scheduling, demonstrating their potential to handle multiobjective optimization while highlighting limitations in computational efficiency. The findings provide insights into leveraging advanced language models for complex scheduling problems in dynamic HPC environments.
High-Level Synthesis (HLS) serves as an agile hardware development tool that streamlines the circuit design by abstracting the register transfer level into behavioral descriptions, while allowing designers to customize the generated microarchitectures through optimization directives. However, the combinatorial explosion of possible directive configurations yields an intractable design space. Traditional design space exploration (DSE) methods, despite adopting heuristics or constructing predictive models to accelerate Pareto-optimal design acquisition, still suffer from prohibitive exploration costs and suboptimal results. Addressing these concerns, we introduce iDSE, the first LLM-aided DSE framework that leverages HLS design quality perception to effectively navigate the design space. iDSE intelligently pruns the design space to guide LLMs in calibrating representative initial sampling designs, expediting convergence toward the Pareto front. By exploiting the convergent and divergent thinking patterns inherent in LLMs for hardware optimization, iDSE achieves multi-path refinement of the design quality and diversity. Extensive experiments demonstrate that iDSE outperforms heuristic-based DSE methods by 5.1$\times$$\sim$16.6$\times$ in proximity to the reference Pareto front, matching NSGA-II with only 4.6% of the explored designs. Our work demonstrates the transformative potential of LLMs in scalable and efficient HLS design optimization, offering new insights into multiobjective optimization challenges.
Federated learning enables decentralized model training while preserving data privacy, yet it faces challenges in balancing communication efficiency, model performance, and privacy protection. To address these trade-offs, we formulate FL as a federated multiobjective optimization problem and propose FedMOEAC, a clustering-based evolutionary algorithm that efficiently navigates the Pareto-optimal solution space. Our approach integrates quantization, weight sparsification, and differential privacy to reduce communication overhead while ensuring model robustness and privacy. The clustering mechanism en-hances population diversity, preventing premature convergence and improving optimization efficiency. Experimental results on MNIST and CIFAR-10 demonstrate that FedMOEAC achieves 98.2% accuracy, reduces communication overhead by 45%, and maintains a privacy budget below 1.0, outperforming NSGA-II in convergence speed by 33%. This work provides a scalable and efficient FL framework, ensuring an optimal balance between accuracy, communication efficiency, and privacy in resource-constrained environments.
Evolutionary multiobjective optimization (EMO) has made significant strides over the past two decades. However, as problem scales and complexities increase, traditional EMO algorithms face substantial performance limitations due to insufficient parallelism and scalability. While most work has focused on algorithm design to address these challenges, little attention has been given to hardware acceleration, thereby leaving a clear gap between EMO algorithms and advanced computing devices, such as GPUs. To bridge the gap, we propose to parallelize EMO algorithms on GPUs via the tensorization methodology. By employing tensorization, the data structures and operations of EMO algorithms are transformed into concise tensor representations, which seamlessly enables automatic utilization of GPU computing. We demonstrate the effectiveness of our approach by applying it to three representative EMO algorithms: NSGA-III, MOEA/D, and HypE. To comprehensively assess our methodology, we introduce a multiobjective robot control benchmark using a GPU-accelerated physics engine. Our experiments show that the tensorized EMO algorithms achieve speedups of up to 1113x compared to their CPU-based counterparts, while maintaining solution quality and effectively scaling population sizes to hundreds of thousands. Furthermore, the tensorized EMO algorithms efficiently tackle complex multiobjective robot control tasks, producing high-quality solutions with diverse behaviors. Source codes are available at https://github.com/EMI-Group/evomo.
In scenarios where multiple decision-makers operate within a common decision space, each focusing on their own multi-objective optimization problem (e.g., bargaining games), the problem can be modeled as a multi-party multi-objective optimization problem (MPMOP). While numerous evolutionary algorithms have been proposed to solve MPMOPs, most results remain empirical. This paper presents the first theoretical analysis of the expected runtime of evolutionary algorithms on bi-party multi-objective optimization problems (BPMOPs). Our findings demonstrate that employing traditional multi-objective optimization algorithms to solve MPMOPs is both time-consuming and inefficient, as the resulting population contains many solutions that fail to achieve consensus among decision-makers. An alternative approach involves decision-makers individually solving their respective optimization problems and seeking consensus only in the final stage. While feasible for pseudo-Boolean optimization problems, this method may fail to guarantee approximate performance for one party in NP-hard problems. Finally, We propose coevolutionary multi-party multi-objective optimizers (CoEMPMO) for pseudo-Boolean optimization and shortest path problems within a multi-party multi-objective context, which maintains a common solution set among all parties through coevolution. Theoretical and experimental results demonstrate that the proposed \( \text{CoEMPMO}_{\text{random}} \) outperforms previous algorithms in terms of the expected lower bound on runtime for pseudo-Boolean optimization problems. Additionally, \( \text{CoEMPMO}_{\text{cons}}^{\text{SP}} \) achieves better efficiency and precision in solving shortest path problems compared to existing algorithms.
We consider the issue of intensification/diversification balance in the context of a memetic algorithm for the multiobjective optimization of investment portfolios with cardinality constraints. We approach this issue in this work by considering the selective application of knowledge-augmented operators (local search and a memory of elite solutions) based on the search epoch in which the algorithm finds itself, hence alternating between unbiased search (guided uniquely by the built-in search mechanics of the algorithm) and focused search (intensified by the use of the problem-aware operators). These operators exploit Sharpe index (a measure of the relationship between return and risk) as a source of problem knowledge. We have conducted a sensibility analysis to determine in which phases of the search the application of these operators leads to better results. Our findings indicate that the resulting algorithm is quite robust in terms of parameterization from the point of view of this problem-specific indicator. Furthermore, it is shown that not only can other non-memetic counterparts be outperformed, but that there is a range of parameters in which the MA is also competitive when not better in terms of standard multiobjective performance indicators.
In recent years, multimodal multiobjective optimization algorithms (MMOAs) based on evolutionary computation have been widely studied. However, existing MMOAs are mainly tested on benchmark function sets such as the 2019 IEEE Congress on Evolutionary Computation test suite (CEC 2019), and their performance on real-world problems is neglected. In this paper, two types of real-world multimodal multiobjective optimization problems in feature selection and location selection respectively are formulated. Moreover, four real-world datasets of Guangzhou, China are constructed for location selection. An investigation is conducted to evaluate the performance of seven existing MMOAs in solving these two types of real-world problems. An analysis of the experimental results explores the characteristics of the tested MMOAs, providing insights for selecting suitable MMOAs in real-world applications.
Constrained multiobjective optimization problems (CMOPs) are commonly found in real-world applications. CMOP is a complex problem that needs to satisfy a set of equality or inequality constraints. This paper proposes a variant of the bidirectional coevolution algorithm (BiCo) with differential evolution (DE). The novelties in the model include the DE differential mutation and crossover operators as the main search engine and a non-dominated sorting selection scheme. Experimental results on two benchmark test suites and eight real-world CMOPs suggested that the proposed model reached better overall performance than the original model.
Indicator-based (multiobjective) diversity optimization aims at finding a set of near (Pareto-)optimal solutions that maximizes a diversity indicator, where diversity is typically interpreted as the number of essentially different solutions. Whereas, in the first diversity-oriented evolutionary multiobjective optimization algorithm, the NOAH algorithm by Ulrich and Thiele, the Solow Polasky Diversity (also related to Magnitude) served as a metric, other diversity indicators might be considered, such as the parameter-free Max-Min Diversity, and the Riesz s-Energy, which features uniformly distributed solution sets. In this paper, focusing on multiobjective diversity optimization, we discuss different diversity indicators from the perspective of indicator-based evolutionary algorithms (IBEA) with multiple objectives. We examine theoretical, computational, and practical properties of these indicators, such as monotonicity in species, twinning, monotonicity in distance, strict monotonicity in distance, uniformity of maximizing point sets, computational effort for a set of size~n, single-point contributions, subset selection, and submodularity. We present new theorems -- including a proof of the NP-hardness of the Riesz s-Energy Subset Selection Problem -- and consolidate existing results from the literature. In the second part, we apply these indicators in the NOAH algorithm and analyze search dynamics through an example. We examine how optimizing with one indicator affects the performance of others and propose NOAH adaptations specific to the Max-Min indicator.
Representation learning is a pivotal area in the field of machine learning, focusing on the development of methods to automatically discover the representations or features needed for a given task from raw data. Unlike traditional feature engineering, which requires manual crafting of features, representation learning aims to learn features that are more useful and relevant for tasks such as classification, prediction, and clustering. We introduce Principal Orthogonal Latent Components Analysis Network (POLCA Net), an approach to mimic and extend PCA and LDA capabilities to non-linear domains. POLCA Net combines an autoencoder framework with a set of specialized loss functions to achieve effective dimensionality reduction, orthogonality, variance-based feature sorting, high-fidelity reconstructions, and additionally, when used with classification labels, a latent representation well suited for linear classifiers and low dimensional visualization of class distribution as well.
This letter investigates a movable antenna (MA)-aided full-duplex (FD) satellite communication system, where the satellite, equipped with both transmit and receive MAs, serves multiple uplink (UL) and downlink (DL) user terminals (UTs) in FD mode. Specifically, we formulate a multiobjective optimization problem to minimize the UL and DL transmit powers under imperfect channel state information (CSI). To jointly optimize the MA positions and transmit powers, we propose a two-loop particle swarm optimization (PSO) algorithm based on a multiobjective optimization framework. Simulation results show that flexible adjustments of MA positions can effectively reduce the total UL and DL transmit powers, while also alleviating the burden on self-interference (SI) cancellation modules.
Multiobjective optimization problems (MOPs) are prevalent in machine learning, with applications in multi-task learning, learning under fairness or robustness constraints, etc. Instead of reducing multiple objective functions into a scalar objective, MOPs aim to optimize for the so-called Pareto optimality or Pareto set learning, which involves optimizing more than one objective function simultaneously, over models with thousands / millions of parameters. Existing benchmark libraries for MOPs mainly focus on evolutionary algorithms, most of which are zeroth-order / meta-heuristic methods that do not effectively utilize higher-order information from objectives and cannot scale to large-scale models with thousands / millions of parameters. In light of the above gap, this paper introduces LibMOON, the first multiobjective optimization library that supports state-of-the-art gradient-based methods, provides a fair benchmark, and is open-sourced for the community.
This paper addresses distributed constrained multiobjective resource allocation problems (DCMRAPs) within multi-agent networks, where each agent has multiple, potentially conflicting local objectives, constrained by both local and global constraints. By reformulating the DCMRAP as a single-objective weighted $L_p$ problem, a distributed solution is enabled, which eliminates the need for predetermined weighting factors or centralized decision-making in traditional methods. Leveraging prescribed-time control and dynamic event-triggered mechanisms (ETMs), novel distributed algorithms are proposed to achieve Pareto optimality within a prescribed settling time through sampled communication. Using generalized time-based generators (TBGs), these algorithms provide more flexibility in optimizing accuracy and control smoothness without the constraints of initial conditions. Novel dynamic ETMs are designed to work with generalized TBGs to promote communication efficiency, which adjusts to both local error metrics and network-based disagreements. The Zeno behavior is excluded. Validated by Lyapunov analysis and simulations, our method demonstrates superior control performance and efficiency compared to existing methods, advancing distributed optimization in complex environments.
Machine learning has driven an exponential increase in computational demand, leading to massive data centers that consume significant amounts of energy and contribute to climate change. This makes sustainable data center control a priority. In this paper, we introduce SustainDC, a set of Python environments for benchmarking multi-agent reinforcement learning (MARL) algorithms for data centers (DC). SustainDC supports custom DC configurations and tasks such as workload scheduling, cooling optimization, and auxiliary battery management, with multiple agents managing these operations while accounting for the effects of each other. We evaluate various MARL algorithms on SustainDC, showing their performance across diverse DC designs, locations, weather conditions, grid carbon intensity, and workload requirements. Our results highlight significant opportunities for improvement of data center operations using MARL algorithms. Given the increasing use of DC due to AI, SustainDC provides a crucial platform for the development and benchmarking of advanced algorithms essential for achieving sustainable computing and addressing other heterogeneous real-world challenges.
This paper proposes a weight-aware deep reinforcement learning (WADRL) approach designed to address the multiobjective vehicle routing problem with time windows (MOVRPTW), aiming to use a single deep reinforcement learning (DRL) model to solve the entire multiobjective optimization problem. The Non-dominated sorting genetic algorithm-II (NSGA-II) method is then employed to optimize the outcomes produced by the WADRL, thereby mitigating the limitations of both approaches. Firstly, we design an MOVRPTW model to balance the minimization of travel cost and the maximization of customer satisfaction. Subsequently, we present a novel DRL framework that incorporates a transformer-based policy network. This network is composed of an encoder module, a weight embedding module where the weights of the objective functions are incorporated, and a decoder module. NSGA-II is then utilized to optimize the solutions generated by WADRL. Finally, extensive experimental results demonstrate that our method outperforms the existing and traditional methods. Due to the numerous constraints in VRPTW, generating initial solutions of the NSGA-II algorithm can be time-consuming. However, using solutions generated by the WADRL as initial solutions for NSGA-II significantly reduces the time required for generating initial solutions. Meanwhile, the NSGA-II algorithm can enhance the quality of solutions generated by WADRL, resulting in solutions with better scalability. Notably, the weight-aware strategy significantly reduces the training time of DRL while achieving better results, enabling a single DRL model to solve the entire multiobjective optimization problem.
The dispatch optimization of coal mine integrated energy system is challenging due to high dimensionality, strong coupling constraints, and multiobjective. Existing constrained multiobjective evolutionary algorithms struggle with locating multiple small and irregular feasible regions, making them inaplicable to this problem. To address this issue, we here develop a multitask evolutionary algorithm framework that incorporates the dispatch correlated domain knowledge to effectively deal with strong constraints and multiobjective optimization. Possible evolutionary multitask construction strategy based on complex constraint relationship analysis and handling, i.e., constraint coupled spatial decomposition, constraint strength classification and constraint handling technique, is first explored. Within the multitask evolutionary optimization framework, two strategies, i.e., an elite guided knowledge transfer by designing a special crowding distance mechanism to select dominant individuals from each task, and an adaptive neighborhood technology based mutation to effectively balance the diversity and convergence of each optimized task for the differential evolution algorithm, are further developed. The performance of the proposed algorithm in feasibility, convergence, and diversity is demonstrated in a case study of a coal mine integrated energy system by comparing with CPLEX solver and seven constrained multiobjective evolutionary algorithms.
Artificial Intelligence is poised to transform the design of complex, large-scale detectors like the ePIC at the future Electron Ion Collider. Featuring a central detector with additional detecting systems in the far forward and far backward regions, the ePIC experiment incorporates numerous design parameters and objectives, including performance, physics reach, and cost, constrained by mechanical and geometric limits. This project aims to develop a scalable, distributed AI-assisted detector design for the EIC (AID(2)E), employing state-of-the-art multiobjective optimization to tackle complex designs. Supported by the ePIC software stack and using Geant4 simulations, our approach benefits from transparent parameterization and advanced AI features. The workflow leverages the PanDA and iDDS systems, used in major experiments such as ATLAS at CERN LHC, the Rubin Observatory, and sPHENIX at RHIC, to manage the compute intensive demands of ePIC detector simulations. Tailored enhancements to the PanDA system focus on usability, scalability, automation, and monitoring. Ultimately, this project aims to establish a robust design capability, apply a distributed AI-assisted workflow to the ePIC detector, and extend its applications to the design of the second detector (Detector-2) in the EIC, as well as to calibration and alignment tasks. Additionally, we are developing advanced data science tools to efficiently navigate the complex, multidimensional trade-offs identified through this optimization process.
To solve real-world expensive constrained multi-objective optimization problems (ECMOPs), surrogate/approximation models are commonly incorporated in evolutionary algorithms to pre-select promising candidate solutions for evaluation. However, the performance of existing approaches are highly dependent on the relative position of unconstrained and constrained Pareto fronts (UPF and CPF, respectively). In addition, the uncertainty information of surrogate models is often ignored, which can misguide the search. To mitigate these key issues (among others), an efficient probabilistic selection based constrained multi-objective EA is proposed, referred to as PSCMOEA. It comprises novel elements such as (a) an adaptive search bound identification scheme based on the feasibility and convergence status of evaluated solutions (b) a probabilistic selection method backed by theoretical formulations of model mean and uncertainties to conduct search in the predicted space to identify promising solutions (c) an efficient single infill sampling approach to balance feasibility, convergence and diversity across different stages of the search and (d) an adaptive switch to unconstrained search based on certain search conditions. Numerical experiments are conducted on an extensive range of challenging constrained problems using low evaluation budgets to simulate ECMOPs. The performance of PSCMOEA is benchmarked against five competitive state-of-the-art algorithms, to demonstrate its competitive and consistent performance.
Evolutionary algorithms excel in solving complex optimization problems, especially those with multiple objectives. However, their stochastic nature can sometimes hinder rapid convergence to the global optima, particularly in scenarios involving constraints. In this study, we employ a large language model (LLM) to enhance evolutionary search for solving constrained multi-objective optimization problems. Our aim is to speed up the convergence of the evolutionary population. To achieve this, we finetune the LLM through tailored prompt engineering, integrating information concerning both objective values and constraint violations of solutions. This process enables the LLM to grasp the relationship between well-performing and poorly performing solutions based on the provided input data. Solution's quality is assessed based on their constraint violations and objective-based performance. By leveraging the refined LLM, it can be used as a search operator to generate superior-quality solutions. Experimental evaluations across various test benchmarks illustrate that LLM-aided evolutionary search can significantly accelerate the population's convergence speed and stands out competitively against cutting-edge evolutionary algorithms.
Recently, there has been an increasing interest in the application of multiobjective optimization (MOO) in machine learning (ML). This interest is driven by the numerous real-life situations where multiple objectives must be optimized simultaneously. A key aspect of MOO is the existence of a Pareto set, rather than a single optimal solution, which represents the optimal trade-offs between different objectives. Despite its potential, there is a noticeable lack of satisfactory literature serving as an entry-level guide for ML practitioners aiming to apply MOO effectively. In this paper, our goal is to provide such a resource and highlight pitfalls to avoid. We begin by establishing the groundwork for MOO, focusing on well-known approaches such as the weighted sum (WS) method, alongside more advanced techniques like the multiobjective gradient descent algorithm (MGDA). We critically review existing studies across various ML fields where MOO has been applied and identify challenges that can lead to incorrect interpretations. One of these fields is physics informed neural networks (PINNs), which we use as a guiding example to carefully construct experiments illustrating these pitfalls. By comparing WS and MGDA with one of the most common evolutionary algorithms, NSGA-II, we demonstrate that difficulties can arise regardless of the specific MOO method used. We emphasize the importance of understanding the specific problem, the objective space, and the selected MOO method, while also noting that neglecting factors such as convergence criteria can result in misleading experiments.