Leveraging machine learning (ML) to predict an initial solution for mixed-integer linear programming (MILP) has gained considerable popularity in recent years. These methods predict a solution and fix a subset of variables to reduce the problem dimension. Then, they solve the reduced problem to obtain the final solutions. However, directly fixing variable values can lead to low-quality solutions or even infeasible reduced problems if the predicted solution is not accurate enough. To address this challenge, we propose an Alternating prediction-correction neural solving framework (Apollo-MILP) that can identify and select accurate and reliable predicted values to fix. In each iteration, Apollo-MILP conducts a prediction step for the unfixed variables, followed by a correction step to obtain an improved solution (called reference solution) through a trust-region search. By incorporating the predicted and reference solutions, we introduce a novel Uncertainty-based Error upper BOund (UEBO) to evaluate the uncertainty of the predicted values and fix those with high confidence. A notable feature of Apollo-MILP is the superior ability for problem reduction while preserving optimality, leading to high-quality final solutions. Experiments on commonly used benchmarks demonstrate that our proposed Apollo-MILP significantly outperforms other ML-based approaches in terms of solution quality, achieving over a 50% reduction in the solution gap.

Machine learning (ML) techniques have shown great potential in generating high-quality solutions for integer linear programs (ILPs). However, existing methods typically rely on a *supervised learning* paradigm, leading to (1) *expensive training cost* due to repeated invocations of traditional solvers to generate training labels, and (2) *plausible yet infeasible solutions* due to the misalignment between the training objective (minimizing prediction loss) and the inference objective (generating high-quality solutions). To tackle this challenge, we propose **DiffILO** (**Diff**erentiable **I**nteger **L**inear Programming **O**ptimization), an *unsupervised learning paradigm for learning to solve ILPs*. Specifically, through a novel probabilistic modeling, DiffILO reformulates ILPs---discrete and constrained optimization problems---into continuous, differentiable (almost everywhere), and unconstrained optimization problems. This reformulation enables DiffILO to simultaneously solve ILPs and train the model via straightforward gradient descent, providing two major advantages. First, it significantly reduces the training cost, as the training process does not need the aid of traditional solvers at all. Second, it facilitates the generation of feasible and high-quality solutions, as the model *learns to solve ILPs* in an end-to-end manner, thus aligning the training and inference objectives. Experiments on commonly used ILP datasets demonstrate that DiffILO not only achieves an average training speedup of $13.2$ times compared to supervised methods, but also outperforms them by generating heuristic solutions with significantly higher feasibility ratios and much better solution qualities.

Cutting planes (cuts) are essential for solving mixed-integer linear programming (MILP) problems, as they tighten the feasible solution space and accelerate the solving process. Modern MILP solvers offer diverse cutting plane separators to generate cuts, enabling users to leverage their potential complementary strengths to tackle problems with different structures. Recent machine learning approaches learn to configure separators based on problem-specific features, selecting effective separators and deactivating ineffective ones to save unnecessary computing time. However, they ignore the dynamics of separator efficacy at different stages of cut generation and struggle to adapt the configurations for the evolving problems after multiple rounds of cut generation. To address this challenge, we propose a novel **dyn**amic **sep**arator configuration (**DynSep**) method that models separator configuration in different rounds as a reinforcement learning task, making decisions based on an incremental triplet graph updated by iteratively added cuts. Specifically, we tokenize the incremental subgraphs and utilize a decoder-only Transformer as our policy to autoregressively predict when to halt separation and which separators to activate at each round. Evaluated on synthetic and large-scale real-world MILP problems, DynSep speeds up average solving time by 64% on easy and medium datasets, and reduces primal-dual gap integral within the given time limit by 16% on hard datasets. Moreover, experiments demonstrate that DynSep well generalizes to MILP instances of significantly larger sizes than those seen during training.

Diffusion in transformer is central to advances in high-quality multimodal generation but suffer from high inference latency due to their iterative nature. Inspired by speculative decoding's success in accelerating large language models, we propose Approximate Speculative Diffusion with Speculative Verification (ASDSV), a novel method to enhance the efficiency of diffusion models. Adapting speculative execution to diffusion processes presents unique challenges. First, the substantial computational cost of verifying numerous speculative steps for continuous, high-dimensional outputs makes traditional full verification prohibitively expensive. Second, determining the optimal number of speculative steps $K$ involves a trade-off between potential acceleration and verification success rates. To address these, ASDSV introduces two key innovations: 1) A speculative verification technique, which leverages the observed temporal correlation between draft and target model outputs, efficiently validates $K$ speculative steps by only checking the alignment of the initial and final states, significantly reducing verification overhead. 2) A multi-stage speculative strategy that adjusts $K$ according to the denoising phase—employing smaller $K$ during volatile early stages and larger $K$ during more stable later stages to optimize the balance between speed and quality. We apply ASDSV to state-of-the-art diffusion transformers, including Flux.1-dev for image generation and Wan2.1 for video generation. Extensive experiments demonstrate that ASDSV achieves up to 1.77$\times$-3.01$\times$ speedup in model inference with a minimal 0.3\%-0.4\% drop in VBench score, showcasing its effectiveness in accelerating multimodal diffusion models without significant quality degradation. The code will be publicly available once the acceptance of the paper.

As one of the most critical components in modern LP solvers, presolve in linear programming (LP) employs a rich set of presolvers to remove different types of redundancy in input problems by equivalent transformations. We found from extensive experiments that the presolve routine-that is, the method determining (P1) which presolvers to select, (P2) in what order to execute, and (P3) when to stop-significantly impacts the efficiency of solving LPs. However, designing high-quality presolve routines is highly challenging due to the enormous search space, and further optimizing the routines on different tasks for high performance demands extensive domain knowledge and manual tuning. To tackle this problem, we propose the first learning based framework-that is, reinforcement learning for presolve (RL4Presolve)-to learn high-quality presolve routines. An appealing feature is that we employ a novel adaptive action sequence that learns complex routines efficiently by generating combinations of presolvers automatically at each step. Extensive experiments demonstrate that RL4Presolve achieves significant improvement (up to roughly 90% ) in the efficiency of solving LPs. Furthermore, we extract routines from learned policies for simple and efficient deployment without GPU resources to Huawei's supply chain, where extensive manual tuning for each separate task was required previously due to the high economic value.

Multiple patterning lithography (MPL) has been introduced in the integrated circuits manufacturing industry to enhance feature density as the technology node advances. A crucial step of MPL is assigning layout features to different masks, namely layout decomposition. Exact algorithms like integer linear programming (ILP) can solve layout decomposition to optimality but lack scalability for dense patterns. Relaxation algorithms (e.g., linear programming and semi-definite programming) and heuristics (e.g., exact cover) are capable of handling large cases at the cost of inferior solution quality. These methods rely on different mathematical solvers and expert-designed heuristics to offer a balance between solution quality and computational efficiency. In this article, we propose a unified layout decomposition framework comprising three algorithms: 1) satisfiability (SAT)-exact; 2) SAT-bilevel; and 3) SAT-fast, all leveraging the capabilities of Boolean SAT solvers. The SAT-exact ensures optimality, but with faster convergence than ILP, SAT-bilevel addresses the decomposition as a bilevel optimization problem for rapid near-optimal solutions, and SAT-fast handles very large layouts in an incremental manner. Experimental results demonstrate our framework’s superiority over existing state-of-the-art methods in terms of solution quality and runtime.

For enterprise storage systems, users' directory/file and IO access traces are critical for fine-tuning and new designs. However, once these systems are deployed, only trace features with small sizes are allowed to be sent back to vendors. Therefore, it is crucial to develop effective techniques for highly compressed feature extraction and feature-based high-fidelity trace regeneration. Existing works primarily focus on I/O trace modeling and regeneration without considering the directory/file access information. In this paper, we propose a new technique, called Sketcher, that can sketch massive traces into highly compressed “joint features” with both directory/file and I/O characteristics, and then based on these features regenerate high-fidelity traces with a learning-based approach. For trace feature extraction, one key idea is to divide traces into multiple distance-associated segments, where each segment contains all files and IO accesses operating under the same directory and the differences between segments are represented as displacement of segment inside the directory tree. A dynamic weight scaling technique is proposed to further compress features considering feature criticality and the size quota, thereby achieving high compression ratios with critical characteristics (e.g., abnormal IO access patterns). For trace regeneration, a new learning-based RNN model is proposed to regenerate high-fidelity traces from extracted features based on sampling directory trees. We have implemented a fully functional prototype based on typical enterprise storage systems and evaluated Sketcher with real applications and benchmarks on Huawei OceanStor Dorado storage server. Results show that Sketcher can effectively extract features with marginal runtime overheads while achieving compression ratios up to 15.2K and regenerating high-fidelity traces.

Machine learning (ML) has been shown to successfully accelerate solving NP-hard combinatorial optimization (CO) problems under the branch and bound framework. However, the high training and inference cost and limited interpretability of ML approaches severely limit their wide application to modern exact CO solvers. In contrast, human-designed policies---though widely integrated in modern CO solvers due to their compactness and reliability---can not capture data-driven patterns for higher performance. To combine the advantages of the two paradigms, we propose the first symbolic discovery framework---namely, deep symbolic discovery for exact combinatorial optimization solver (Symb4CO)---to learn high-performance symbolic policies on the branching task. Specifically, we show the potential existence of small symbolic policies empirically, employ a large neural network to search in the high-dimensional discrete space, and compile the learned symbolic policies directly for fast deployment. Experiments show that the Symb4CO learned purely CPU-based policies consistently achieve *comparable* performance to previous GPU-based state-of-the-art approaches. Furthermore, the appealing features of Symb4CO include its high training (*ten training instances*) and inference (*one CPU core*) efficiency and good interpretability (*one-line expressions*), making it simple and reliable for deployment. The results show encouraging potential for the *wide* deployment of ML to modern CO solvers.

Modern solvers for solving mixed integer programming (MIP) often rely on the branch-and-bound (B&B) algorithm which could be of high time complexity, and presolving techniques are well designed to simplify the instance as pre-processing before B&B. However, such presolvers in existing literature or open-source solvers are mostly set by default agnostic to specific input instances, and few studies have been reported on tailoring presolving settings. In this paper, we aim to dive into this open question and show that the MIP solver can be indeed largely improved when switching the default instance-agnostic presolving into instance-specific presolving. Specifically, we propose a combination of supervised learning and classic heuristics to achieve efficient presolving adjusting, avoiding tedious reinforcement learning. Notably, our approach is orthogonal from many recent efforts in incorporating learning modules into the B&B framework after the presolving stage, and to our best knowledge, this is the first work for introducing learning to presolve in MIP solvers. Experiments on multiple real-world datasets show that well-trained neural networks can infer proper presolving for arbitrary incoming MIP instances in less than 0.5s, which is neglectable compared with the solving time often hours or days.

Machine learning (ML) approaches have been successfully applied to accelerating exact combinatorial optimization (CO) solvers. However, many of them fail to explain what patterns they have learned that accelerate the CO algorithms due to the black-box nature of ML models like neural networks, and thus they prevent researchers from further understanding the tasks they are interested in. To tackle this problem, we propose the first graph-based algorithm discovery framework—namely, graph symbolic discovery for exact combinatorial optimization solver (GS4CO)—that learns interpretable branching policies directly from the general bipartite graph representation of CO problems. Specifically, we design a unified representation for symbolic policies with graph inputs, and then we employ a Transformer with multiple tree-structural encodings to generate symbolic trees end-to-end, which effectively reduces the cumulative error from iteratively distilling graph neural networks. Experiments show that GS4CO learned interpretable and lightweight policies outperform all the baselines on CPU machines, including both the human-designed and the learning-based. GS4CO shows an encouraging step towards general algorithm discovery on modern CO solvers.

Logic Synthesis (LS) plays a vital role in chip design. A key task in LS is to simplify circuits---modeled by directed acyclic graphs (DAGs)---with functionality-equivalent transformations. To tackle this task, many LS heuristics apply transformations to subgraphs---rooted at each node on an input DAG---sequentially. However, we found that a large number of transformations are ineffective, which makes applying these heuristics highly time-consuming. In particular, we notice that the runtime of the Resub and Mfs2 heuristics often dominates the overall runtime of LS optimization processes. To address this challenge, we propose a novel data-driven LS heuristic paradigm, namely PruneX, to reduce ineffective transformations. The major challenge of developing PruneX is to learn models that well generalize to unseen circuits, i.e., the out-of-distribution (OOD) generalization problem. Thus, the major technical contribution of PruneX is the novel circuit domain generalization framework, which learns domain-invariant representations based on the transformation-invariant domain-knowledge. To the best of our knowledge, PruneX is the first approach to tackle the OOD problem in LS heuristics. We integrate PruneX with the aforementioned Resub and Mfs2 heuristics. Experiments demonstrate that PruneX significantly improves their efficiency while keeping comparable optimization performance on industrial and very large-scale circuits, achieving up to $3.1\times$ faster runtime.

Mixed-integer linear programming (MILP) is one of the most popular mathematical formulations with numerous applications. In practice, improving the performance of MILP solvers often requires a large amount of high-quality data, which can be challenging to collect. Researchers thus turn to generation techniques to generate additional MILP instances. However, existing approaches do not take into account specific block structures—which are closely related to the problem formulations—in the constraint coefficient matrices (CCMs) of MILPs. Consequently, they are prone to generate computationally trivial or infeasible instances due to the disruptions of block structures and thus problem formulations. To address this challenge, we propose a novel MILP generation framework, called Block Structure Decomposition (MILP-StuDio), to generate high-quality instances by preserving the block structures. Specifically, MILP-StuDio begins by identifying the blocks in CCMs and decomposing the instances into block units, which serve as the building blocks of MILP instances. We then design three operators to construct new instances by removing, substituting, and appending block units in the original instances, enabling us to generate instances with flexible sizes. An appealing feature of MILP-StuDio is its strong ability to preserve the feasibility and computational hardness of the generated instances. Experiments on the commonly-used benchmarks demonstrate that using instances generated by MILP-StuDio is able to significantly reduce over 10% of the solving time for learning-based solvers.

Cutting planes (cuts) play an important role in solving mixed-integer linear programs (MILPs), which formulate many important real-world applications. Cut selection heavily depends on (P1) which cuts to prefer and (P2) how many cuts to select. Although modern MILP solvers tackle (P1)-(P2) by human-designed heuristics, machine learning carries the potential to learn more effective heuristics. However, many existing learning-based methods learn which cuts to prefer, neglecting the importance of learning how many cuts to select. Moreover, we observe that (P3) what order of selected cuts to prefer significantly impacts the efficiency of MILP solvers as well. To address these challenges, we propose a novel hierarchical sequence/set model (HEM) to learn cut selection policies. Specifically, HEM is a bi-level model: (1) a higher-level module that learns how many cuts to select, (2) and a lower-level module-that formulates the cut selection as a sequence/set to sequence learning problem-to learn policies selecting an ordered subset with the cardinality determined by the higher-level module. To the best of our knowledge, HEM is the first data-driven methodology that well tackles (P1)-(P3) simultaneously. Experiments demonstrate that HEM significantly improves the efficiency of solving MILPs on eleven challenging MILP benchmarks, including two Huawei's real problems.

Multiple patterning lithography (MPL) has been introduced in the integrated circuits manufacturing industry to enhance feature density as the technology node advances. A crucial step of MPL is assigning layout features to different masks, namely layout decomposition. Exact algorithms like integer linear programming (ILP) can solve layout decomposition to optimality but lacks scalability for very dense patterns. Approximation algorithms (e.g., linear programming, semi-definite programming) and heuristics (e.g., Exact-Cover) are capable of handling large cases but can only get inferior solutions. In this paper, we propose a new exact algorithm that tackles layout decomposition by solving a series of boolean satisfiability instances. Our algorithm can preserve optimality and achieve more than 4× speedup compared to ILP. In addition, we provide an approximation algorithm by reformulating the layout decomposition to a bilevel optimization problem. Experiments show that our approximation algorithm can attain higher solution quality compared to SDP and heuristics within faster convergence.

Data prefetching is important for storage system optimization and access performance improvement. Traditional prefetchers work well for mining access patterns of sequential logical block address (LBA) but cannot handle complex non-sequential patterns that commonly exist in real-world applications. The state-of-the-art (SOTA) learning-based prefetchers cover more LBA accesses. However, they do not adequately consider the spatial interdependencies between LBA deltas, which leads to limited performance and robustness. This paper proposes a novel Stream-Graph neural network-based Data Prefetcher (SGDP). Specifically, SGDP models LBA delta streams using a weighted directed graph structure to represent interactive relations among LBA deltas and further extracts hybrid features by graph neural networks for data prefetching. We conduct extensive experiments on eight real-world datasets. Empirical results verify that SGDP outperforms the SOTA methods in terms of the hit ratio by 6.21%, the effective prefetching ratio by 7.00%, and speeds up inference time by 3.13× on average. Besides, we generalize SGDP to different variants by different stream constructions, further expanding its application scenarios and demonstrating its robustness. SGDP offers a novel data prefetching solution and has been verified in commercial hybrid storage systems in the experimental phase. Our codes and appendix are available at https://github.com/yyysjz1997/SGDP/.

Industrial SAT formula generation is a critical yet challenging task. Existing SAT generation approaches can hardly simultaneously capture the global structural properties and maintain plausible computational hardness. We first present an in-depth analysis for the limitation of previous learning methods in reproducing the computational hardness of original instances, which may stem from the inherent homogeneity in their adopted split-merge procedure. On top of the observations that industrial formulae exhibit clear community structure and oversplit substructures lead to the difficulty in semantic formation of logical structures, we propose HardSATGEN, which introduces a fine-grained control mechanism to the neural split-merge paradigm for SAT formula generation to better recover the structural and computational properties of the industrial benchmarks. Experiments including evaluations on private and practical corporate testbed show the superiority of HardSATGEN being the only method to successfully augments formulae maintaining similar computational hardness and capturing the global structural properties simultaneously. Compared to the best previous methods, the average performance gains achieve 38.5% in structural statistics, 88.4% in computational metrics, and over 140.7% in the effectiveness of guiding solver tuning by our generated instances. Source code is available at https://github.com/Thinklab-SJTU/HardSATGEN.

In the past few years, there has been an explosive surge in the use of machine learning (ML) techniques to address combinatorial optimization (CO) problems, especially mixed-integer linear programs (MILPs). Despite the achievements, the limited availability of real-world instances often leads to sub-optimal decisions and biased solver assessments, which motivates a suite of synthetic MILP instance generation techniques. However, existing methods either rely heavily on expert-designed formulations or struggle to capture the rich features of real-world instances. To tackle this problem, we propose G2MILP, *the first* deep generative framework for MILP instances. Specifically, G2MILP represents MILP instances as bipartite graphs, and applies a masked variational autoencoder to iteratively corrupt and replace parts of the original graphs to generate new ones. The appealing feature of G2MILP is that it can learn to generate novel and realistic MILP instances without prior expert-designed formulations, while preserving the structures and computational hardness of real-world datasets, simultaneously. Thus the generated instances can facilitate downstream tasks for enhancing MILP solvers under limited data availability. We design a suite of benchmarks to evaluate the quality of the generated MILP instances. Experiments demonstrate that our method can produce instances that closely resemble real-world datasets in terms of both structures and computational hardness. The deliverables are released at [https://miralab-ustc.github.io/L2O-G2MILP](https://miralab-ustc.github.io/L2O-G2MILP).

Cache plays an important role to maintain high and stable performance (i.e. high throughput, low tail latency and throughput jitter) in storage systems. Existing rule-based cache management methods, coupled with engineers' manual configurations, cannot meet ever-growing requirements of both time-varying workloads and complex storage systems, leading to frequent cache overloading.

Scheduling job flows efficiently and rapidly on distributed computing clusters is one of huge challenges for daily operation of data centers. In a practical scenario, a single job consists of numerous stages with complex dependency relation represented as a Directed Acyclic Graph (DAG) structure. Nowa-days a data center usually equips with a cluster of heterogeneous computing servers which are different in the hardware/software configuration. From both the cost saving and environmental friendliness, the data centers could benefit a lot from optimizing the job scheduling problems in the heterogeneous environment. Thus the problem has attracted more and more attention from both the industry and academy. In this paper, we propose a task-duplication based learning algorithm, namely LACHESIS22The second of the Three Fates in ancient Greek mythology, who deter-mines destiny., aiming to optimize the problem. In the proposed approach, it first perceives the topological dependencies between jobs using a reinforcement learning framework and a specially designed graph neural network (GNN) to select the most promising task to be executed. Then the task is assigned to a specific executor with the consideration of duplicating all its precedent tasks according to an expert-designed rules. We have conducted extensive experiments over standard workloads to evaluate the proposed solution. The experimental results suggest that LACHESIS can achieve at most 26.7% reduction of makespan and 35.2% improvement of speedup ratio over seven strong baseline algorithms, including the state-of-the-art heuristics methods and a variety of deep reinforcement learning based algorithms.

This work is geared toward a real-world manufacturing planning (MP) task, whose two objectives are to maximize the order fulfillment rate and minimize the total cost. More important, the requirements and constraints in real manufacturing make the MP task very challenging in several aspects. For example, the MP needs to cover many production components of multiple plants over a 30-day horizon, which means that it involves a large number of decision variables. Furthermore, the MP task's two objectives have extremely different magnitudes, and some constraints are difficult to handle. Facing these uncompromising practical requirements, we introduce an interactive multiobjective optimization-based MP system in this article. It can help the decision maker reach a satisfactory tradeoff between the two objectives without consuming massive calculations. In the MP system, the submitted MP task is modeled as a multiobjective integer programming (MOIP) problem. Then, the MOIP problem is addressed via a two-stage multiobjective optimization algorithm (TSMOA). To alleviate the heavy calculation burden, TSMOA transforms the optimization of the MOIP problem into the optimization of a series of single-objective problems (SOPs). Meanwhile, a new SOP solving strategy is used in the MP system to further reduce the computational cost. It utilizes two sequential easier SOPs as the approximator of the original complex SOP for optimization. As part of the MP system, TSMOA and the SOP solving strategy are demonstrated to be efficient in real-world MP applications. In addition, the effectiveness of TSMOA is also validated on benchmark problems. The results indicate that TSMOA as well as the MP system are promising.

The Dynamic Pickup and Delivery Problem (DPDP) is aimed at dynamically scheduling vehicles among multiple sites in order to minimize the cost when delivery orders are not known a priori. Although DPDP plays an important role in modern logistics and supply chain management, state-of-the-art DPDP algorithms are still limited on their solution quality and efficiency. In practice, they fail to provide a scalable solution as the numbers of vehicles and sites become large. In this paper, we propose a data-driven approach, Spatial-Temporal Aided Double Deep Graph Network (ST-DDGN), to solve industry-scale DPDP. In our method, the delivery demands are first forecast using spatial-temporal prediction method, which guides the neural network to perceive spatial-temporal distribution of delivery demand when dispatching vehicles. Besides, the relationships of individuals such as vehicles are modelled by establishing a graph-based value function. ST-DDGN incorporates attention-based graph embedding with Double DQN (DDQN). As such, it can make the inference across vehicles more efficiently compared with traditional methods. Our method is entirely data driven and thus adaptive, i.e., the relational representation of adjacent vehicles can be learned and corrected by ST-DDGN from data periodically. We have conducted extensive experiments over real-world data to evaluate our solution. The results show that ST-DDGN reduces 11.27% number of the used vehicles and decreases 13.12% total transportation cost on average over the strong baselines, including the heuristic algorithm deployed in our UAT (User Acceptance Test) environment and a variety of vanilla DRL methods. We are due to fully deploy our solution into our online logistics system and it is estimated that millions of USD logistics cost can be saved per year.

Computer systems such as storage systems normally require transparent white-box algorithms that are interpretable for human experts. In this work, we propose a learning-aided heuristic design method, which automatically generates human-readable strategies from Deep Reinforcement Learning (DRL) agents. This method benefits from the power of deep learning but avoids the shortcoming of its black-box property. Besides the white-box advantage, experiments in our storage production's resource allocation scenario also show that this solution outperforms the system's default settings and the elaborately handcrafted strategy by human experts.

Industrial telecommunication applications prefer to run at the optimal capacity configuration to achieve the required Quality of Service (QoS) at the minimum cost. The optimal capacity configuration is usually achieved through the selection of cell towers capacities and locations. Given a set of service providers (e.g., cell towers) and a set of customers (e.g., major residential areas), where each customer has an amount of demand and each provider has multiple candidate capacities and corresponding costs, the optimal capacity selection is configured through spatial matching to satisfy the demand of each customer at the minimum cost. However, existing solutions developed for spatial matching, in which each provider's capacity is fixed, cannot be directly applied to the capacity configuration problem with multiple capacities and location selections. In this paper, we are the first to study Service Provider Configuration and Planning with Optimal Spatial Matching (SPC-POSM) problem, in which the objectives are 1) to select the proper capacity for each provider at the minimum total cost and 2) to assign providers' service to satisfy the demand of each customer on a condition that the matching distance is no more than service quality requirement. We prove that SPC-POSM problem is NP-hard and design an efficient two-layer meta-heuristic framework to solve the problem. Unsupervised learning technique is designed to accelerate the calculation and a novel local search mechanism is embedded to further improve solution quality. Extensive experimental results on both real and synthetic datasets verify the effectiveness and efficiency of the proposed framework.

Split Delivery Vehicle Routing Problem with 3D Loading Constraints (3L-SDVRP) can be seen as the most important problem in large-scale manufacturing logistics. The goal is to devise a strategy consisting of three NP-hard planning components: vehicle routing, cargo splitting and container loading, which shall be jointly optimized for cost savings. The problem is an enhanced variant of the classical logistics problem 3L-CVRP, and its complexity leaps beyond current studies of solvability. Our solution employs a novel data-driven three-layer search algorithm (DTSA), which we designed to improve both the efficiency and effectiveness of traditional meta-heuristic approaches, through learning from data and from simulation.

Distribution of intangible information goods is experiencing tremendous growth in recent years, which has facilitated a blossoming of information goods economics. As big data develops, there are more and more information goods markets for data trading. In the current of data pricing policies in data trading, there are many metrics to measure the value of data goods, such as the data generation date, data volume, and data integrity, etc. However, it is very challenging to identify the amount of data information and its distribution, and the corresponding data pricing has rarely been discussed. In this paper, we propose a new data pricing metric, i.e., the data information entropy, which helps to make a reasonable price in the data trading. We first demonstrate a data information measurement method based on information entropy, and then propose a pricing function based on the result of data information measurement. To comprehensively understand the new data pricing metric and facilitate its application in data trading, we verify the rationality of the data information measurement method and give three concrete pricing functions. It is the first time to look at the information entropy-based data pricing, which can inspire the research concerning the pricing mechanism of data goods, further promoting the development of data products business.