As the number and complexity of constraints in constrained multi-objective optimization problems (CMOPs) increase, the performance of existing constrained multi-objective evolutionary algorithms (CMOEAs) declines significantly. A novel idea is to sequentially address each constraint based on priority, effectively reducing the complexity of CMOPs. However, in these algorithms, the constraint-handling priority is determined statically in the initial stage. This may lead to inappropriate determination of constraint-handling priority since accurately estimating the constraint landscape in the initial stage is quite challenging. Moreover, these algorithms tackle constraints separately, neglecting the potential for inter-constraint cooperation and thus compromising their efficiency in constraint handling. Thus, we propose a constrained multi-objective evolutionary algorithm based on dynamic priority and cooperative offspring generation called DPCMOEA. Firstly, the constraint-handling priority is determined dynamically by the estimated inconsistency degree (EID) between the Pareto fronts of the candidate constraints and the current population. Secondly, computational resources are automatically allocated to each constraint according to EID based constraint relationship analysis. Finally, a new offspring generation strategy based on constraint cooperation is designed to enhance the quality of new solutions. Experimental results on six CMOP test suites demonstrate that DPCMOEA outperforms six state-of-the-art algorithms.

In this paper, we introduce a novel approach for addressing the multi-objective optimization problem in large language model merging via black-box multi-objective optimization algorithms. The goal of model merging is to combine multiple models, each excelling in different tasks, into a single model that outperforms any of the individual source models. However, the effectiveness of conventional model merging methods is constrained by human intuition or domain knowledge. While existing optimization-based model merging methods can automatically search for model merging parameter configurations, they often struggle to find a satisfactory configuration within a limited evaluation budget. To address this challenge, we propose a novel and sample-efficient automated model merging method, named MM-MO. This method leverages multi-objective Bayesian optimization algorithms to autonomously search for great merging configurations across various tasks. In MMMO, we proposed an enhanced acquisition strategy and an auxiliary optimization objective to improve the search process. Our enhanced acquisition strategy integrates a weak-to-strong method to refine the acquisition function, enabling previously evaluated superior configurations to guide the search for new ones. Meanwhile, Fisher information is utilized to further filter these configurations, increasing the possibility of finding high-quality merging configurations. Additionally, we design a sparsity metric as an auxiliary optimization objective, further enhance the models generalization performance across different tasks. We conducted comprehensive experiments with other mainstream model merging methods, demonstrating that the proposed MMMO algorithm is competitive and effective in achieving high-quality model merging.

Multi-objective Bayesian optimization (MOBO) has shown promising performance on various expensive multi-objective optimization problems (EMOPs). However, effectively modeling complex distributions of the Pareto optimal solutions is difficult with limited function evaluations. Existing Pareto set learning algorithms may exhibit considerable instability in such expensive scenarios, leading to significant deviations between the obtained solution set and the Pareto set (PS). In this paper, we propose a novel Composite Diffusion Model based Pareto Set Learning algorithm (CDM-PSL) for expensive MOBO. CDM-PSL includes both unconditional and conditional diffusion model for generating high-quality samples efficiently. Besides, we introduce a weighting method based on information entropy to balance different objectives. This method is integrated with a guiding strategy to appropriately balancing different objectives during the optimization process. Experimental results on both synthetic and real-world problems demonstrates that CDM-PSL attains superior performance compared with state-of-the-art MOBO algorithms.

In black-box optimization, when directly evaluating the function values of solutions is very costly or infeasible, access to the objective function is often limited to comparing pairs of solutions, which yields dueling black-box optimization. Dueling optimization is solely based on pairwise preferences, and thus notably reduces cost compared with function value based methods. However, the optimization performance of dueling optimization is often limited due to that most existing dueling optimization methods do not make full use of the pairwise preferences collected. To better utilize these preferences, this paper proposes relation-augmented dueling Bayesian optimization (RADBO) via preference propagation. By considering solution similarity, RADBO aims to uncover the potential dueling relations between solutions within different preferences through the proposed preference propagation technique. Specifically, RADBO first clusters solutions using a Gaussian mixture model. After obtaining the solution set with the highest intra-cluster similarity, RADBO utilizes a directed hypergraph to model the potential dueling relations between solutions, thereby realizing relation augmentation. Extensive experiments are conducted on both synthetic functions and real-world tasks such as motion control, car cab design and spacecraft trajectory optimization. The experimental results disclose the satisfactory accuracy of augmented preferences in RADBO, and show the superiority of RADBO compared with existing dueling optimization methods. Notably, it is verified that, under the same evaluation cost budget, RADBO can be competitive with or even surpass the function value based Bayesian optimization methods with respect to optimization performance.

A series of surrogate-assisted evolutionary algorithms (SAEAs) have been proposed for expensive multi-objective optimization problems (EMOPs), building cheap surrogate models to replace the expensive real function evaluations. However, the search efficiency of these SAEAs is not yet satisfactory. More efforts are needed to further exploit useful information from the real function evaluations in order to better guide the search process. Facing this challenge, this paper proposes a Hyperbolic Neural Network (HNN) based preselection operator to accelerate the optimization process based on limited evaluated solutions. First, the preselection task is modeled as a multi-label classification problem where solutions are classified into different layers (ordinal categories) through -relaxed objective aggregation. Second, in order to resemble the hierarchical structure of candidate solutions, a hyperbolic neural network is applied to tackle the multi-label classification problem. The reason for using HNN is that hyperbolic spaces more closely resemble hierarchical structures than Euclidean spaces. Moreover, to alleviate the data deficiency issue, a data augmentation strategy is employed for training the HNN. In order to evaluate its performance, the proposed HNN-based preselection operator is embedded into two surrogate-assisted evolutionary algorithms. Experimental results on two benchmark test suites and three real-world problems with up to 11 objectives and 150 decision variables involving seven state-of-the-art algorithms demonstrate the effectiveness of the proposed method.

Large-scale multiobjective optimization problems (LSMOPs), characterized by a substantial number of decision variables, pose significant challenges for many existing evolutionary algorithms. However, the search efficiency of these algorithms is not yet satisfactory. This is mainly because that the search efficiency of these algorithms may deteriorate dramatically since the search space increases exponentially with the number of decision variables. Having this in mind, we proposed a large-Scale multiobjective optimization framework named causal inference-based competitive swarm optimizer (CI-CSO). Specifically, a causal-information-(CI)-based operator is designed for competitive swarm optimizers. First, a causal inference technique named information geometric causal inference (IGCI) is introduced to adequately explore the CI between decision variables and fitness values. To further distinguish the positive or negative impacts of these critical variables on solution quality, a CI processing module is designed, facilitating targeted optimization. To enhance search efficiency, CI-based offspring generator are employed, leveraging the variance of causal effects to dynamically adjust the search step size and sampling range. To evaluate its performance, the proposed CI-based operator is embedded into two multiobjective evolutionary algorithms (MOEAs) (LSTPA and LMOCSO). To demonstrate the effectiveness of the proposed framework, experimental results are presented using the LSMOP test suite and five real-world problems, each involving up to 10 000 decision variables. In addition, six classic algorithms are included for comparison.

Multi-objective optimization problems (MOPs) containing a large number of decision variables, which are also known as large-scale multi-objective optimization problems (LSMOPs), pose great challenges to most existing evolutionary algorithms. This is mainly because that a high dimensional decision space degrades the effectiveness of search operators notably, and balancing convergence and diversity becomes a challenging task. In this paper, we propose a two-population based algorithm for large-scale multi-objective optimization named LSTPA. In the proposed algorithm, solutions are classified in to two subpopulations: a Convergence subPopulation (CP) and a Diversity subPopulation (DP), aiming at convergence and diversity respectively. In order to improve convergence speed, a fitness-aware variation operator (FAVO) is applied to drive DP solutions towards CP. Besides, an adaptive penalty based boundary intersection (APBI) strategy is adopted for environmental selection in order to balance convergence and diversity temporally during different stages of evolution process. Experimental results on benchmark test problems with 100-2000 decision variables demonstrate that the proposed algorithm can achieve the best overall performance compared with several state-of-the-art large-scale multi-objective evolutionary algorithms.

Optimizing multiple conflicting black-box objectives simultaneously is a prevalent occurrence in many real-world applications, such as neural architecture search, and machine learning. These problems are known as expensive multi-objective optimization problems (EMOPs) when the function evaluations are computationally or financially costly. Multi-objective Bayesian optimization (MOBO) offers an efficient approach to discovering a set of Pareto optimal solutions. However, the data deficiency issue caused by limited function evaluations has posed a great challenge to current optimization methods. Moreover, most current methods tend to prioritize the quality of candidate solutions, while ignoring the quantity of promising samples. In order to tackle these issues, our paper proposes a novel multi-objective Bayesian optimization algorithm with a data augmentation strategy that provides ample high-quality samples for Pareto set learning (PSL). Specifically, it utilizes Generative Adversarial Networks (GANs) to enrich data and a dominance prediction model to screen out high-quality samples, mitigating the predicament of limited function evaluations in EMOPs. Additionally, we adopt the regularity model to expensive multi-objective Bayesian optimization for PSL. Experimental results on both synthetic and real-world problems demonstrate that our algorithm outperforms several state-of-the-art and classical algorithms.

Cognitive diagnosis models (CDMs) are designed to learn students' mastery levels using their response logs.CDMs play a fundamental role in online education systems since they significantly influence downstream applications such as teachers' guidance and computerized adaptive testing.Despite the success achieved by existing CDMs, we find that they suffer from a thorny issue that the learned students' mastery levels are too similar.This issue, which we refer to as oversmoothing, could diminish the CDMs' effectiveness in downstream tasks.CDMs comprise two core parts: learning students' mastery levels and assessing mastery levels by fitting the response logs.This paper contends that the oversmoothing issue arises from that existing CDMs seldom utilize response signals on exercises in the learning part but only use them as labels in the assessing part.To this end, this paper proposes an oversmoothing-resistant cognitive diagnosis framework (ORCDF) to enhance existing CDMs by utilizing response signals in the learning part.Specifically, OR-CDF introduces a novel response graph to inherently incorporate response signals as types of edges.Then, ORCDF designs a tailored response-aware graph convolution network (RGC) that effectively captures the crucial response signals within the response graph.Via ORCDF, existing CDMs are enhanced by replacing the input embeddings with the outcome of RGC, allowing for the consideration of response signals on exercises in the learning part.Extensive experiments on real-world datasets show that ORCDF not only *

Due to computationally and/or financially costly evaluation, tackling expensive multi-objective optimization problems is quite challenging for evolutionary algorithms. One popular approach to these problems is building cheap surrogate models to replace the expensive real function evaluations. To this end, various kinds of surrogate-assisted evolutionary algorithms (SAEAs) have been proposed, building surrogate models which predict the fitness values, classifications, or relation of the candidate solutions. However, off-spring generation, despite its important role in evolutionary optimization, has not received enough attention in these SAEAs. In this paper, a regularity model based framework, namely RM-SAEA, is proposed for better offspring generation in expensive multi-objective optimization. To be specific, RM-SAEA is featured with a heterogeneous offspring generation module, which is composed of a regularity model and a general genetic operator. Moreover, in order to alleviate the data deficiency issue in the expensive optimization scenario, a data augmentation strategy is employed while training the regularity model. Finally, two representative SAEAs are embedded into RM-SAEA in order to instantiate the proposed framework. Experimental results on benchmark multi-objective problems with up to 10 objectives demonstrate that RM-SAEA achieves the best overall performance compared with 6 state-of-the-art algorithms.

The estimation of distribution algorithm (EDA) is an efficient heuristic method for handling black-box optimization problems since the ability for global population distribution modeling and gradient-free searching. However, the trial and error search mechanism relies on a large number of function evaluations, which is a considerable challenge under expensive black-box problems. Therefore, this article presents a surrogate assisted EDA with multi-acquisition functions. Firstly, a variable-width histogram is used as the global distribution model that focuses on promising areas. Next, the evaluated-free local search method improves the quality of new generation solutions. Fi-nally, model management with multiple acquisitions maintains global and local exploration preferences. Several commonly used benchmark functions with 20 and 50 dimensions are adopted to evaluate the proposed algorithm compared with several state-of-the-art surrogate assisted evaluation algorithms (SAEAs) and Bayesian optimization method. In addition, a rover trajectories optimizing problem is used to verify the ability to solve complex problems. The experimental results demonstrate the superiority of the proposed algorithm over these comparison algorithms.

With the explosively increase of information and products, recommender systems have played a more and more important role in the recent years. Various recommendation algorithms, such as content-based methods and collaborative filtering methods, have been proposed. There are a number of performance metrics for evaluating recommender systems, and considering only the precision or diversity might be inappropriate. However, to the best of our knowledge, no existing work has considered recommendation with many objectives. In this paper, we model a many-objective search-based recommender system and adopt a recently proposed many-objective evolutionary algorithm to optimize it. Experimental results on the Movielens data set demonstrate that our algorithm performs better in terms of Generational Distance (GD), Inverted Generational Distance (IGD) and Hypervolume (HV) on most test cases.

Traditional multiobjective evolutionary algorithms face a great challenge when dealing with many objectives. This is due to a high proportion of nondominated solutions in the population and low selection pressure toward the Pareto front. In order to tackle this issue, a series of indicator-based algorithms have been proposed to guide the search process toward the Pareto front. However, a single indicator might be biased and lead the population to converge to a subregion of the Pareto front. In this paper, a multi-indicator-based algorithm is proposed for many-objective optimization problems. The proposed algorithm, namely stochastic ranking-based multi-indicator Algorithm (SRA), adopts the stochastic ranking technique to balance the search biases of different indicators. Empirical studies on a large number (39 in total) of problem instances from two well-defined benchmark sets with 5, 10, and 15 objectives demonstrate that SRA performs well in terms of inverted generational distance and hypervolume metrics when compared with state-of-the-art algorithms. Empirical studies also reveal that, in the case a problem requires the algorithm to have strong convergence ability, the performance of SRA can be further improved by incorporating a direction-based archive to store well-converged solutions and maintain diversity.

Multi-Objective Evolutionary Algorithms have been deeply studied in the research community and widely used in the real-world applications. However, the performance of traditional Pareto-based MOEAs, such as NSGA-II and SPEA2, may deteriorate when tackling Many-Objective Problems, which refer to the problems with at least four objectives. The main cause for the degradation lies in that the high-proportional non-dominated solutions severely weaken the differentiation ability of Pareto-dominance. This may lead to stagnation. The Two Archive Algorithm (TAA) uses two archives, namely Convergence Archive (CA) and Diversity Archive (DA) as non-dominated solution repositories, focusing on convergence and diversity respectively. However, as the objective dimension increases, the size of CA increases enormously, leaving little space for DA. Besides, the update rate of CA is quite low, which causes severe problems for TAA to drive forth. Moreover, since TAA prefers DA members that are far away from CA, DA might drag the population backwards. In order to deal with these weaknesses, this paper proposes an improved version of TAA, namely ITAA. Compared to TAA, ITAA incorporates a ranking mechanism for updating CA which enables truncating CA while CA overflows. Besides, a shifted density estimation technique is embedded to replace the old ranking method in DA. The efficiency of ITAA is demonstrated by the experimental studies on benchmark problems with up to 20 objectives.