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

Prompt Learning for Generalized Vehicle Routing

Neural combinatorial optimization (NCO) is a promising learning-based approach to solving various vehicle routing problems without much manual algorithm design. However, the current NCO methods mainly focus on the in-distribution performance, while the real-world problem instances usually come from different distributions. A costly fine-tuning approach or generalized model retraining from scratch could be needed to tackle the out-of-distribution instances. Unlike the existing methods, this work investigates an efficient prompt learning approach in NCO for cross-distribution adaptation. To be concrete, we propose a novel prompt learning method to facilitate fast zero-shot adaptation of a pre-trained model to solve routing problem instances from different distributions. The proposed model learns a set of prompts among various distributions and then selects the best-matched one to prompt a pre-trained attention model for each problem instance. Extensive experiments show that the proposed prompt learning approach facilitates the fast adaptation of pre-trained routing models. It also outperforms existing generalized models on both in-distribution prediction and zero-shot generalization to a diverse set of new tasks. Our code implementation is available online https://github.com/FeiLiu36/PromptVRP.

Instance-Conditioned Adaptation for Large-scale Generalization of Neural Combinatorial Optimization

The neural combinatorial optimization (NCO) approach has shown great potential for solving routing problems without the requirement of expert knowledge. However, existing constructive NCO methods cannot directly solve large-scale instances, which significantly limits their application prospects. To address these crucial shortcomings, this work proposes a novel Instance-Conditioned Adaptation Model (ICAM) for better large-scale generalization of neural combinatorial optimization. In particular, we design a powerful yet lightweight instance-conditioned adaptation module for the NCO model to generate better solutions for instances across different scales. In addition, we develop an efficient three-stage reinforcement learning-based training scheme that enables the model to learn cross-scale features without any labeled optimal solution. Experimental results show that our proposed method is capable of obtaining excellent results with a very fast inference time in solving Traveling Salesman Problems (TSPs) and Capacitated Vehicle Routing Problems (CVRPs) across different scales. To the best of our knowledge, our model achieves state-of-the-art performance among all RL-based constructive methods for TSP and CVRP with up to 1,000 nodes.

Self-Improved Learning for Scalable Neural Combinatorial Optimization

The end-to-end neural combinatorial optimization (NCO) method shows promising performance in solving complex combinatorial optimization problems without the need for expert design. However, existing methods struggle with large-scale problems, hindering their practical applicability. To overcome this limitation, this work proposes a novel Self-Improved Learning (SIL) method for better scalability of neural combinatorial optimization. Specifically, we develop an efficient self-improved mechanism that enables direct model training on large-scale problem instances without any labeled data. Powered by an innovative local reconstruction approach, this method can iteratively generate better solutions by itself as pseudo-labels to guide efficient model training. In addition, we design a linear complexity attention mechanism for the model to efficiently handle large-scale combinatorial problem instances with low computation overhead. Comprehensive experiments on the Travelling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP) with up to 100K nodes in both uniform and real-world distributions demonstrate the superior scalability of our method.

Multi-Task Learning for Routing Problem with Cross-Problem Zero-Shot Generalization

Vehicle routing problems (VRPs), which can be found in numerous real-world applications, have been an important research topic for several decades. Recently, the neural combinatorial optimization (NCO) approach that leverages a learning-based model to solve VRPs without manual algorithm design has gained substantial attention. However, current NCO methods typically require building one model for each routing problem, which significantly hinders their practical application for real-world industry problems with diverse attributes. In this work, we make the first attempt to tackle the crucial challenge of cross-problem generalization. In particular, we formulate VRPs as different combinations of a set of shared underlying attributes and solve them simultaneously via a single model through attribute composition. In this way, our proposed model can successfully solve VRPs with unseen attribute combinations in a zero-shot generalization manner. Extensive experiments are conducted on eleven VRP variants, benchmark datasets, and industry logistic scenarios. The results show that the unified model demonstrates superior performance in the eleven VRPs, reducing the average gap to around 5% from over 20% in the existing approach and achieving a significant performance boost on benchmark datasets as well as a real-world logistics application.

An Example of Evolutionary Computation + Large Language Model Beating Human: Design of Efficient Guided Local Search

It is often very tedious for human experts to design efficient algorithms. Recently, we have proposed a novel Algorithm Evolution using Large Language Model (AEL) framework for automatic algorithm design. AEL combines the power of a large language model and the paradigm of evolutionary computation to design, combine, and modify algorithms automatically. In this paper, we use AEL to design the guide algorithm for guided local search (GLS) to solve the well-known traveling salesman problem (TSP). AEL automatically evolves elite GLS algorithms in two days, with minimal human effort and no model training. Experimental results on 1,000 TSP20-TSP100 instances and TSPLib instances show that AEL-designed GLS outperforms state-of-the-art human-designed GLS with the same iteration budget. It achieves a 0% gap on TSP20 and TSP50 and a 0.032% gap on TSP100 in 1,000 iterations. Our findings mark the emergence of a new era in automatic algorithm design.

Algorithm Evolution Using Large Language Model

Optimization can be found in many real-life applications. Designing an effective algorithm for a specific optimization problem typically requires a tedious amount of effort from human experts with domain knowledge and algorithm design skills. In this paper, we propose a novel approach called Algorithm Evolution using Large Language Model (AEL). It utilizes a large language model (LLM) to automatically generate optimization algorithms via an evolutionary framework. AEL does algorithm-level evolution without model training. Human effort and requirements for domain knowledge can be significantly reduced. We take constructive methods for the salesman traveling problem as a test example, we show that the constructive algorithm obtained by AEL outperforms simple hand-crafted and LLM-generated heuristics. Compared with other domain deep learning model-based algorithms, these methods exhibit excellent scalability across different problem sizes. AEL is also very different from previous attempts that utilize LLMs as search operators in algorithms.

Large Language Model for Multi-objective Evolutionary Optimization

Multiobjective evolutionary algorithms (MOEAs) are major methods for solving multiobjective optimization problems (MOPs). Many MOEAs have been proposed in the past decades, of which the search operators need a carefully handcrafted design with domain knowledge. Recently, some attempts have been made to replace the manually designed operators in MOEAs with learning-based operators (e.g., neural network models). However, much effort is still required for designing and training such models, and the learned operators might not generalize well on new problems. To tackle the above challenges, this work investigates a novel approach that leverages the powerful large language model (LLM) to design MOEA operators. With proper prompt engineering, we successfully let a general LLM serve as a black-box search operator for decomposition-based MOEA (MOEA/D) in a zero-shot manner. In addition, by learning from the LLM behavior, we further design an explicit white-box operator with randomness and propose a new version of decomposition-based MOEA, termed MOEA/D-LO. Experimental studies on different test benchmarks show that our proposed method can achieve competitive performance with widely used MOEAs. It is also promising to see the operator only learned from a few instances can have robust generalization performance on unseen problems with quite different patterns and settings. The results reveal the potential benefits of using pre-trained LLMs in the design of MOEAs.

Heuristics for Vehicle Routing Problem: A Survey and Recent Advances

Vehicle routing is a well-known optimization research topic with significant practical importance. Among different approaches to solving vehicle routing, heuristics can produce a satisfactory solution at a reasonable computational cost. Consequently, much effort has been made in the past decades to develop vehicle routing heuristics. In this article, we systematically survey the existing vehicle routing heuristics, particularly on works carried out in recent years. A classification of vehicle routing heuristics is presented, followed by a review of their methodologies, recent developments, and applications. Moreover, we present a general framework of state-of-the-art methods and provide insights into their success. Finally, three emerging research topics with notable works and future directions are discussed.

A Data-Driven Column Generation Algorithm For Bin Packing Problem in Manufacturing Industry

The bin packing problem exists widely in real logistic scenarios (e.g., packing pipeline, express delivery), with its goal to improve the packing efficiency and reduce the transportation cost. In this NP-hard combinatorial optimization problem, the position and quantity of each item in the box are strictly restricted by complex constraints and special customer requirements. Existing approaches are hard to obtain the optimal solution since rigorous constraints cannot be handled within a reasonable computation load. In this paper, for handling this difficulty, the packing knowledge is extracted from historical data collected from the packing pipeline of Huawei. First, by fully exploiting the relationship between historical packing records and input orders(orders to be packed) , the problem is reformulated as a set cover problem. Then, two novel strategies, the constraint handling and process acceleration strategies are applied to the classic column generation approach to solve this set cover problem. The cost of solving pricing problem for generating new columns is high due to the complex constraints and customer requirements. The proposed constraints handling strategy exploits the historical packing records with the most negative value of the reduced cost. Those constraints have been implicitly satisfied in these historical packing records so that there is no need to conduct further evaluation on constraints, thus the computational load is saved. To further eliminate the iteration process of column generation algorithm and accelerate the optimization process, a Learning to Price approach called Modified Pointer Network is proposed, by which we can determine which historical packing records should be selected directly. Through experiments on realworld datasets, we show our proposed method can improve the packing success rate and decrease the computation time simultaneously.