It's Morphing Time: Unleashing the Potential of Multiple LLMs via Multi-objective Optimization

In this paper, we introduce a novel approach for 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, model merging faces two significant challenges: First, existing methods rely heavily on human intuition and customized strategies. Second, parameter conflicts often arise during merging, and while methods like DARE [1] can alleviate this issue, they tend to stochastically drop parameters, risking the loss of important delta parameters. To address these challenges, we propose the MM-MO method, which automates the search for optimal merging configurations using multi-objective optimization algorithms, eliminating the need for human intuition. During the configuration searching process, we use estimated performance across multiple diverse tasks as optimization objectives in order to alleviate the parameter conflicting between different source models without losing crucial delta parameters. We conducted comparative experiments with other mainstream model merging methods, demonstrating that our method consistently outperforms them. Moreover, our experiments reveal that even task types not explicitly targeted as optimization objectives show performance improvements, indicating that our method enhances the overall potential of the model rather than merely overfitting to specific task types. This approach provides a significant advancement in model merging techniques, offering a robust and plug-and-play solution for integrating diverse models into a unified, high-performing model.

Learning Mixture-of-Experts for General-Purpose Black-Box Discrete Optimization

Real-world applications involve various discrete optimization problems. Designing a specialized optimizer for each of these problems is challenging, typically requiring significant domain knowledge and human efforts. Hence, developing general-purpose optimizers as an off-the-shelf tool for a wide range of problems has been a long-standing research target. This article introduces MEGO, a novel general-purpose neural optimizer trained through a fully data-driven learning-to-optimize (L2O) approach. MEGO consists of a mixture-of-experts trained on experiences from solving training problems and can be viewed as a foundation model for optimization problems with binary decision variables. When presented with a problem to solve, MEGO actively selects relevant expert models to generate high-quality solutions. MEGO can be used as a standalone sample-efficient optimizer or in conjunction with existing search methods as an initial solution generator. The generality of MEGO is validated across six problem classes, including three classic problem classes and three problem classes arising from real-world applications in compilers, network analysis, and 3D reconstruction. Trained solely on classic problem classes, MEGO performs very well on all six problem classes, significantly surpassing widely used general-purpose optimizers in both solution quality and efficiency. In some cases, MEGO even surpasses specialized state-of-the-art optimizers. Additionally, MEGO provides a similarity measure between problems, yielding a new perspective for problem classification. In the pursuit of general-purpose optimizers through L2O, MEGO represents an initial yet significant step forward.

DPN: Decoupling Partition and Navigation for Neural Solvers of Min-max Vehicle Routing Problems

The min-max vehicle routing problem (min-max VRP) traverses all given customers by assigning several routes and aims to minimize the length of the longest route. Recently, reinforcement learning (RL)-based sequential planning methods have exhibited advantages in solving efficiency and optimality. However, these methods fail to exploit the problem-specific properties in learning representations, resulting in less effective features for decoding optimal routes. This paper considers the sequential planning process of min-max VRPs as two coupled optimization tasks: customer partition for different routes and customer navigation in each route (i.e., partition and navigation). To effectively process min-max VRP instances, we present a novel attention-based Partition-and-Navigation encoder (P&N Encoder) that learns distinct embeddings for partition and navigation. Furthermore, we utilize an inherent symmetry in decoding routes and develop an effective agent-permutation-symmetric (APS) loss function. Experimental results demonstrate that the proposed Decoupling-Partition-Navigation (DPN) method significantly surpasses existing learning-based methods in both single-depot and multi-depot min-max VRPs. Our code is available at

Towards Geometry-Aware Pareto Set Learning for Neural Multi-Objective Combinatorial Optimization

Multi-objective combinatorial optimization (MOCO) problems are prevalent in various real-world applications. Most existing neural methods for MOCO problems rely solely on decomposition and utilize precise hypervolume to enhance diversity. However, these methods often approximate only limited regions of the Pareto front and spend excessive time on diversity enhancement because of ambiguous decomposition and time-consuming hypervolume calculation. To address these limitations, we design a Geometry-Aware Pareto set Learning algorithm named GAPL, which provides a novel geometric perspective for neural MOCO via a Pareto attention model based on hypervolume expectation maximization. In addition, we propose a hypervolume residual update strategy to enable the Pareto attention model to capture both local and non-local information of the Pareto set/front. We also design a novel inference approach to further improve quality of the solution set and speed up hypervolume calculation and local subset selection. Experimental results on three classic MOCO problems demonstrate that our GAPL outperforms state-of-the-art neural baselines via superior decomposition and efficient diversity enhancement.

Expensive Multi-Objective Bayesian Optimization Based on Diffusion Models

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, namely CDM-PSL, for expensive MOBO. CDM-PSL includes both unconditional and conditional diffusion model for generating high-quality samples. Besides, we introduce an information entropy based weighting method to balance different objectives of EMOPs. This method is integrated with the guiding strategy, ensuring that all the objectives are appropriately balanced and given due consideration during the optimization process; Extensive experimental results on both synthetic benchmarks and real-world problems demonstrates that our proposed algorithm attains superior performance compared with various state-of-the-art MOBO algorithms.

S4TP: Social-Suitable and Safety-Sensitive Trajectory Planning for Autonomous Vehicles

In public roads, autonomous vehicles (AVs) face the challenge of frequent interactions with human-driven vehicles (HDVs), which render uncertain driving behavior due to varying social characteristics among humans. To effectively assess the risks prevailing in the vicinity of AVs in social interactive traffic scenarios and achieve safe autonomous driving, this article proposes a social-suitable and safety-sensitive trajectory planning (S4TP) framework. Specifically, S4TP integrates the Social-Aware Trajectory Prediction (SATP) and Social-Aware Driving Risk Field (SADRF) modules. SATP utilizes Transformers to effectively encode the driving scene and incorporates an AV's planned trajectory during the prediction decoding process. SADRF assesses the expected surrounding risk degrees during AVs-HDVs interactions, each with different social characteristics, visualized as two-dimensional heat maps centered on the AV. SADRF models the driving intentions of the surrounding HDVs and predicts trajectories based on the representation of vehicular interactions. S4TP employs an optimization-based approach for motion planning, utilizing the predicted HDVs'trajectories as input. With the integration of SADRF, S4TP executes real-time online optimization of the planned trajectory of AV within lowrisk regions, thus improving the safety and the interpretability of the planned trajectory. We have conducted comprehensive tests of the proposed method using the SMARTS simulator. Experimental results in complex social scenarios, such as unprotected left turn intersections, merging, cruising, and overtaking, validate the superiority of our proposed S4TP in terms of safety and rationality. S4TP achieves a pass rate of 100% across all scenarios, surpassing the current state-of-the-art methods Fanta of 98.25% and Predictive-Decision of 94.75%.

Agent-Pro: Learning to Evolve via Policy-Level Reflection and Optimization

Large Language Models exhibit robust problem-solving capabilities for diverse tasks. However, most LLM-based agents are designed as specific task solvers with sophisticated prompt engineering, rather than agents capable of learning and evolving through interactions. These task solvers necessitate manually crafted prompts to inform task rules and regulate LLM behaviors, inherently incapacitating to address complex dynamic scenarios e.g., large interactive games. In light of this, we propose Agent-Pro: an LLM-based Agent with Policy-level Reflection and Optimization that can learn a wealth of expertise from interactive experiences and progressively elevate its behavioral policy. Specifically, it involves a dynamic belief generation and reflection process for policy evolution. Rather than action-level reflection, Agent-Pro iteratively reflects on past trajectories and beliefs, fine-tuning its irrational beliefs for a better policy. Moreover, a depth-first search is employed for policy optimization, ensuring continual enhancement in policy payoffs. Agent-Pro is evaluated across two games: Blackjack and Texas Hold'em, outperforming vanilla LLM and specialized models. Our results show Agent-Pro can learn and evolve in complex and dynamic scenes, which also benefits numerous LLM-based applications.

Label Informed Contrastive Pretraining for Node Importance Estimation on Knowledge Graphs

Node Importance Estimation (NIE) is a task of inferring importance scores of the nodes in a graph. Due to the availability of richer data and knowledge, recent research interests of NIE have been dedicating to knowledge graphs for predicting future or missing node importance scores. Existing state-of-the-art NIE methods train the model by available labels, and they consider every interested node equally before training. However, the nodes with higher importance often require or receive more attention in real-world scenarios, e.g., people may care more about the movies or webpages with higher importance. To this end, we introduce Label Informed ContrAstive Pretraining (LICAP) to the NIE problem for being better aware of the nodes with high importance scores. Specifically, LICAP is a novel type of contrastive learning framework that aims to fully utilize the continuous labels to generate contrastive samples for pretraining embeddings. Considering the NIE problem, LICAP adopts a novel sampling strategy called top nodes preferred hierarchical sampling to first group all interested nodes into a top bin and a non-top bin based on node importance scores, and then divide the nodes within top bin into several finer bins also based on the scores. The contrastive samples are generated from those bins, and are then used to pretrain node embeddings of knowledge graphs via a newly proposed Predicate-aware Graph Attention Networks (PreGAT), so as to better separate the top nodes from non-top nodes, and distinguish the top nodes within top bin by keeping the relative order among finer bins. Extensive experiments demonstrate that the LICAP pretrained embeddings can further boost the performance of existing NIE methods and achieve the new state-of-the-art performance regarding both regression and ranking metrics. The source code for reproducibility is available at https://github.com/zhangtia16/LICAP

Bridging Evolutionary Algorithms and Reinforcement Learning: A Comprehensive Survey

Evolutionary Reinforcement Learning (ERL), which integrates Evolutionary Algorithms (EAs) and Reinforcement Learning (RL) for optimization, has demonstrated remarkable performance advancements. By fusing the strengths of both approaches, ERL has emerged as a promising research direction. This survey offers a comprehensive overview of the diverse research branches in ERL. Specifically, we systematically summarize recent advancements in relevant algorithms and identify three primary research directions: EA-assisted optimization of RL, RL-assisted optimization of EA, and synergistic optimization of EA and RL. Following that, we conduct an in-depth analysis of each research direction, organizing multiple research branches. We elucidate the problems that each branch aims to tackle and how the integration of EA and RL addresses these challenges. In conclusion, we discuss potential challenges and prospective future research directions across various research directions.

Pointer Networks Trained Better via Evolutionary Algorithms

Pointer Network (PtrNet) is a specific neural network for solving Combinatorial Optimization Problems (COPs). While PtrNets offer real-time feed-forward inference for complex COPs instances, its quality of the results tends to be less satisfactory. One possible reason is that such issue suffers from the lack of global search ability of the gradient descent, which is frequently employed in traditional PtrNet training methods including both supervised learning and reinforcement learning. To improve the performance of PtrNet, this paper delves deeply into the advantages of training PtrNet with Evolutionary Algorithms (EAs), which have been widely acknowledged for not easily getting trapped by local optima. Extensive empirical studies based on the Travelling Salesman Problem (TSP) have been conducted. Results demonstrate that PtrNet trained with EA can consistently perform much better inference results than eight state-of-the-art methods on various problem scales. Compared with gradient descent based PtrNet training methods, EA achieves up to 30.21\% improvement in quality of the solution with the same computational time. With this advantage, this paper is able to at the first time report the results of solving 1000-dimensional TSPs by training a PtrNet on the same dimensionality, which strongly suggests that scaling up the training instances is in need to improve the performance of PtrNet on solving higher-dimensional COPs.