Random Instances Research Articles

Evaluating graph neural networks under graph sampling scenarios.

BackgroundIt is often the case that only a portion of the underlying network structure is observed in real-world settings. However, as most network analysis methods are built on a complete network structure, the natural questions to ask are: (a) how well these methods perform with incomplete network structure, (b) which structural observation and network analysis method to choose for a specific task, and (c) is it beneficial to complete the missing structure.MethodsIn this paper, we consider the incomplete network structure as one random sampling instance from a complete graph, and we choose graph neural networks (GNNs), which have achieved promising results on various graph learning tasks, as the representative of network analysis methods. To identify the robustness of GNNs under graph sampling scenarios, we systemically evaluated six state-of-the-art GNNs under four commonly used graph sampling methods.ResultsWe show that GNNs can still be applied on single static networks under graph sampling scenarios, and simpler GNN models are able to outperform more sophisticated ones in a fairly experimental procedure. More importantly, we find that completing the sampled subgraph does improve the performance of downstream tasks in most cases; however, completion is not always effective and needs to be evaluated for a specific dataset. Our code is available at https://github.com/weiqianglg/evaluate-GNNs-under-graph-sampling.

The Cost-Balanced Path Problem: A Mathematical Formulation and Complexity Analysis

This paper introduces a new variant of the Shortest Path Problem (SPP) called the Cost-Balanced Path Problem (CBPP). Various real problems can either be modeled as BCPP or include BCPP as a sub-problem. We prove several properties related to the complexity of the CBPP problem. In particular, we demonstrate that the problem is NP-hard in its general version, but it becomes solvable in polynomial time in a specific family of instances. Moreover, a mathematical formulation of the CBPP, as a mixed-integer programming model, is proposed, and some additional constraints for modeling real requirements are given. This paper validates the proposed model and its extensions with experimental tests based on random instances. The analysis of the results of the computational experiments shows that the proposed model and its extension can be used to model many real applications. Obviously, due to the problem complexity, the main limitation of the proposed approach is related to the size of the instances. A heuristic solution approach should be required for larger-sized and more complex instances.

Optimization Approach for the Aggregation of Flexible Consumers

In an electric distribution system, the management of peak demands is becoming increasingly difficult. Every method we have to flatten the consumption curve greatly reduces the energy generation costs, CO2 emissions, and congestion in the generation, transmission, and distribution systems. Therefore, we can act on consumers’ consumption, especially when we know that some consumers can be interested in reducing their consumption levels for monetary compensations. This can be done by reporting a part of consumption or shifting it. For this, a new profession called aggregation is born to manage the flexible consumers and meet the network requirements. To maximize their revenues, aggregators need to own an intelligent system to manage their portfolio of flexible consumers. They should optimize the way they modify the load curve of their flexible assets by respecting the system requirements and a set of consumer constraints. In this article, we address this task by proposing a Mixed Integer Linear Programming (MILP) formulation for two different modes: The economic mode (Evaluation of the potential of the portfolio to generate benefits. The aggregator uses this mode to make bids on the energy market) and the dispatch mode (to be used in an operational situation to respect the bids already submitted). Experimentation studies on real and random in-stances (>1000 instances) demonstrate the effectiveness of the proposed MILP.

GO-MOCE: Greedy Order Method of Conditional Expectations for Max Sat

In this paper we present and study a new algorithm for the Maximum Satisfiability (Max Sat) problem. The algorithm is based on the Method of Conditional Expectations (MOCE, also known as Johnson’s Algorithm) and applies a greedy variable ordering to MOCE. Thus, we name it Greedy Order MOCE (GO-MOCE). We also suggest a combination of GO-MOCE with CCLS, a state-of-the-art solver. We refer to this combined solver as GO-MOCE-CCLS.We conduct a comprehensive comparative evaluation of GO-MOCE versus MOCE on random instances and on public competition benchmark instances. We show that GO-MOCE reduces the number of unsatisfied clauses by tens of percents, while keeping the runtime almost the same. The worst case time complexity of GO-MOCE is linear. We also show that GO-MOCE-CCLS improves on CCLS consistently by up to about 80%.We study the asymptotic performance of GO-MOCE. To this end, we introduce three measures for evaluating the asymptotic performance of algorithms for Max Sat. We point out to further possible improvements of GO-MOCE, based on an empirical study of the main quantities managed by GO-MOCE during its execution.

Limits of Accuracy for Parameter Estimation and Localization in Single-Molecule Microscopy via Sequential Monte Carlo Methods

Assessing the quality of parameter estimates for models describing the motion of single molecules in cellular environments is an important problem in fluorescence microscopy. In this work, we consider the fundamental data model, where molecules emit photons at random time instances and these photons arrive at random locations on the detector according to complex point spread functions (PSFs). The randomness and non-Gaussian PSF of the detection process, and the random trajectory of the molecule, make inference challenging. Moreover, the presence of other closely spaced molecules causes further uncertainty in the origin of the measurements, which impacts the statistical precision of the estimates. We quantify the limits of accuracy of model parameter estimates and separation distance between closely spaced molecules (known as the resolution problem) by computing the Cramér--Rao lower bound (CRLB), or equivalently the inverse of the Fisher information matrix (FIM), for the variance of estimates. Results on the CRLB obtained from the fundamental model are crucial, in that they provide a lower bound for more practical scenarios. While analytic expressions for the FIM can be derived for static and deterministically moving molecules, the analytical tools to evaluate the FIM for molecules whose trajectories follow stochastic differential equations are still for the most part missing. We address this by presenting a general sequential Monte Carlo (SMC) based methodology for both parameter inference and computing the desired accuracy limits for nonstatic molecules and a non-Gaussian fundamental detection model. For the first time, we are able to estimate the FIM for stochastically moving molecules observed through the Airy and Born and Wolf detection models. This is achieved by estimating the score and observed information matrix via SMC. We summarize the outcome of our numerical work by delineating the qualitative behaviors for the accuracy limits as functions of various experimental settings like collected photon count, molecule diffusion, etc. We also verify that we can recover known results from the static molecule case.

Improved instance generation for kidney exchange programmes

Kidney exchange programmes increase the rate of living donor kidney transplants, and operations research techniques are vital to such programmes. These techniques, as well as changes to policy regarding kidney exchange programmes, are often tested using random instances created by a Saidman generator. We show that instances produced by such a generator differ from real-world instances across a number of important parameters, including the average number of recipients that are compatible with a certain donor. We exploit these differences to devise powerful upper and lower bounds and we demonstrate their effectiveness by optimally solving a benchmark set of Saidman instances in seconds; this set could not be solved in under thirty minutes with previous algorithms. We then present new techniques for generating random kidney exchange instances that are far more consistent with real-world instances from the UK kidney exchange programme. This new process for generating random instances provides a more accurate base for comparisons of algorithms and models, and gives policy-makers a better understanding of potential changes to policy leading to an improved decision-making process.

Mixed-integer linear programming, constraint programming and column generation approaches for operating room planning under block strategy

The planning of operating rooms under block strategy is addressed in this study. The decisions are about opening the operating rooms and assigning specialties and surgeons to blocks at the tactical level, and sequencing the surgeries at the operational level. This problem aims to minimize the costs of opening the operating rooms and their overtime, the waiting costs of patients, and the surgeons' idle costs. We propose two mixed-integer linear programming models, a constraint programming (CP) model and a constraint programming-based column generation (CPCG) method for handling the problem. The performance of the models is evaluated by random test instances. The results indicate that CP and CPCG models are more efficient than the linear programming models in terms of computational time, and the number of variables and constraints. The proposed method CPCG generates optimal solutions for problem instances of up to 30 surgeries in less than 4 min. The CP model finds the optimal solutions in about one minute but proving the optimality of the found solutions is time-consuming in some instances. The maximum optimality gap for the proposed two-step linear programming model is 2%, while its run time is less than 20 s. A sensitivity analysis is done on the main parameters of the problem like objectives' weights, opening cost of ORs, unit waiting cost of patients, and the maximum available time in surgery blocks. Among the three objectives, the unit waiting cost of patients has the most sensitivity to variations of the objective function weights.

An active-learning Pareto evolutionary algorithm for parcel locker network design considering accessibility of customers

The parcel delivery, which is one of the most important components in urban last-mile logistics, has been an increasing challenge with the rapid growth of e-commerce. To improve the efficiency of urban last-mile logistics, parcel locker has been widely advocated as an innovative alternative to the parcel delivery. In this paper, we concentrate on a multi-objective parcel locker network design problem (MOPLNDP), which is motivated by a real-life network design problem in urban last-mile logistics. The ultimate goal of MOPLNDP is to optimize the total cost of the network and the accessibility of customers to parcel locker stations, which is different from previous network design problems in logistics systems. Firstly, we establish the mathematical model of MOPLNDP based on which relevant problem-specific solution properties and heuristics are presented. Secondly, an active-learning Pareto evolutionary algorithm (ALPEA) is proposed to solve MOPLNDP. The proposed ALPEA relies on an elitist nondominated sorting method to discover promising search regions and a novel active-learning refinement mechanism to intensively find high-quality solutions in given search regions. Finally, experimental results on 70 random instances with different scales and a real-life case study are reported, from which the encouraging numerical results and management insights are obtained.

Unsupervised Person Re-Identification With Stochastic Training Strategy.

Unsupervised person re-identification (re-ID) has attracted increasing research interests because of its scalability and possibility for real-world applications. State-of-the-art unsupervised re-ID methods usually follow a clustering-based strategy, which generates pseudo labels by clustering and maintains a memory to store instance features and represent the centroid of the clusters for contrastive learning. This approach suffers two problems. First, the centroid generated by unsupervised learning may not be a perfect prototype. Forcing images to get closer to the centroid emphasizes the result of clustering, which could accumulate clustering errors during iterations. Second, previous instance memory based methods utilize features updated at different training iterations to represent one centroid, these features are inconsistent due to the change of encoder. To this end, we propose an unsupervised re-ID approach with a stochastic learning strategy. Specifically, we adopt a stochastic updated memory, where a random instance from a cluster is used to update the cluster-level memory for contrastive learning. In this way, the relationship between randomly selected pair of images are learned to avoid the training bias caused by unreliable pseudo labels. By picking a sole last seen sample to directly update each cluster center, the stochastic memory is also always up-to-date for classifying to keep the consistency. Besides, to relieve the issue of camera variance, a unified distance matrix is proposed during clustering, where the distance bias from different camera domains is reduced and the variances of identities are emphasized. Our proposed method outperforms the state-of-the-arts in all the common unsupervised and UDA re-ID tasks. The code will be available at https://github.com/lithium770/Unsupervised-Person-re-ID-with-Stochastic-Training-Strategy.

Robust Job Shop Scheduling with Condition-Based Maintenance and Random Breakdowns

This paper presents a simulation-optimization approach for solving the Job Shop Scheduling Problem (JSSP) under both planned and unplanned machine unavailability. Two maintenance policies are considered: Condition-Based Maintenance (CBM) and Corrective Maintenance (CM). The real makespan objective function is first approximated using several surrogate functions that are independently optimized using Genetic Algorithm (GA), before their best solutions are evaluated through simulation with stochastic degradation of machines, random breakdowns, and uncertain CBM and CM duration. To ensure schedule robustness, a weighted average of the expected makespan and its 90th percentile is used as the evaluation criterion, and the best schedule is added to an elite list to initiate the next iteration. A stopping rule inspired by Simulated Annealing (SA) is employed to prevent premature conversion. Numerical experimentation on random instances showed that the proposed approach can reach high-quality solutions effectively.

Which rectangle sets have perfect packings?

In the perfect rectangle packing problem, a set of rectangular items have to be placed inside a rectangular container without overlap or empty space. In this paper, we generate a large number of random instances and decide them all with an exact solving algorithm. Both an instance’s solution probability and its hardness measured in recursions or system time, seems to critically depend on tmax, a parameter in the generation procedure that assigns the maximally choosable random side lengths of items in the instance. We numerically characterize the solvability across instance sizes, and derive a rule for generating (un)solvable problem instances of arbitrary size.

Learning variable ordering heuristics for solving Constraint Satisfaction Problems

Backtracking search algorithms are often used to solve the Constraint Satisfaction Problem (CSP), which is widely applied in various domains such as automated planning and scheduling. The efficiency of backtracking search depends greatly on the variable ordering heuristics. Currently, the most commonly used heuristics are hand-crafted based on expert knowledge. In this paper, we propose a deep reinforcement learning based approach to automatically discover new variable ordering heuristics that are better adapted for a given class of CSP instances, without the need of relying on hand-crafted features and heuristics. We show that directly optimizing the search tree size is not convenient for learning, and propose to optimize the expected cost of reaching a leaf node in the search tree. To capture the complex relations among the variables and constraints, we design a representation scheme based on Graph Neural Network that can process CSP instances with different sizes and constraint arities. Experimental results on random CSP instances show that on small and medium sized instances, the learned policies outperform classical hand-crafted heuristics with smaller search tree (up to 10.36% reduction). Moreover, without further training, our policies directly generalize to instances of larger sizes and much harder to solve than those in training, with even larger reduction in the search tree size (up to 18.74%).

A Model for Integrated Inventory and Assortment Planning

Integrating inventory and assortment planning decisions is a challenging task that requires comparing the value of demand expansion through broader choice for consumers with the value of higher in-stock availability. We develop a stockout-based substitution model for trading off these values in a setting with inventory replenishment, a feature missing in the literature. Using the closed form solution for the single-product case, we develop an accurate approximation for the multiproduct case. This approximated formulation allows us to optimize inventory decisions by solving a fractional integer program with a fixed point equation constraint. When products have equal margins, we solve the integer program exactly by bisection over a one-dimensional parameter. In contrast, when products have different margins, we propose a fractional relaxation that we can also solve by bisection and that results in near-optimal solutions. Overall, our approach provides solutions within 0.1% of the optimal policy and finds the optimal solution in 80% of the random instances we generate. This paper was accepted by David Simchi-Levi, optimization.

Algorithms for Smooth, Safe and Quick Routing on Sensor-Equipped Grid Networks.

Automation plays an important role in modern transportation and handling systems, e.g., to control the routes of aircraft and ground service equipment in airport aprons, automated guided vehicles in port terminals or in public transportation, handling robots in automated factories, drones in warehouse picking operations, etc. Information technology provides hardware and software (e.g., collision detection sensors, routing and collision avoidance logic) that contribute to safe and efficient operations, with relevant social benefits in terms of improved system performance and reduced accident rates. In this context, we address the design of efficient collision-free routes in a minimum-size routing network. We consider a grid and a set of vehicles, each moving from the bottom of the origin column to the top of the destination column. Smooth nonstop paths are required, without collisions nor deviations from shortest paths, and we investigate the minimum number of horizontal lanes allowing for such routing. The problem is known as fleet quickest routing problem on grids. We propose a mathematical formulation solved, for small instances, through standard solvers. For larger instances, we devise heuristics that, based on known combinatorial properties, define priorities, and design collision-free routes. Experiments on random instances show that our algorithms are able to quickly provide good quality solutions.

Exact and metaheuristic approaches for unrelated parallel machine scheduling

In this paper, we study an important real-life scheduling problem that can be formulated as an unrelated parallel machine scheduling problem with sequence-dependent setup times, due dates, and machine eligibility constraints. The objective is to minimise total tardiness and makespan. We adapt and extend a mathematical model to find optimal solutions for small instances. Additionally, we propose several variants of simulated annealing to solve very large-scale instances as they appear in practice. We utilise several different search neighbourhoods and additionally investigate the use of innovative heuristic move selection strategies. Further, we provide a set of real-life problem instances as well as a random instance generator that we use to generate a large number of test instances. We perform a thorough evaluation of the proposed techniques and analyse their performance. We also apply our metaheuristics to approach a similar problem from the literature. Experimental results show that our methods are able to improve the results produced with state-of-the-art approaches for a large number of instances.

Two-Echelon Routing Problem for Parcel Delivery by Cooperated Truck and Drone

A new variant of the two-echelon routing problem is investigated, where the truck and the drone are used to cooperatively complete the deliveries of all parcels. The truck not only acts as a tool for parcel delivery but also serves as a moving depot for the drone. The drone can carry several parcels and take off from the truck, while returning to the truck after completing the delivery. The energy consumption model for the routing process of the drone is analyzed, when it is utilized to deliver multiple parcels. A two-stage route-based modeling approach is proposed to optimize both the truck’s main route and the drone’s adjoint flying routes. A hybrid heuristic integrating nearest neighbor and cost saving strategies is developed to quickly construct a feasible solution. The simulated annealing algorithm is integrated with Tabu search, to improve the quality of the solution as well as the search efficiency. Random instances at different scales are used to test the performance of the proposed algorithm. A case study based on the practical road network in Changsha, China, is presented, through which the sensitivity analysis is conducted with respect to some critical factors.

A bi-atrial statistical shape model for large-scale in silico studies of human atria: Model development and application to ECG simulations.

Large-scale electrophysiological simulations to obtain electrocardiograms (ECG) carry the potential to produce extensive datasets for training of machine learning classifiers to, e.g., discriminate between different cardiac pathologies. The adoption of simulations for these purposes is limited due to a lack of ready-to-use models covering atrial anatomical variability. We built a bi-atrial statistical shape model (SSM) of the endocardial wall based on 47 segmented human CT and MRI datasets using Gaussian process morphable models. Generalization, specificity, and compactness metrics were evaluated. The SSM was applied to simulate atrial ECGs in 100 random volumetric instances. The first eigenmode of our SSM reflects a change of the total volume of both atria, the second the asymmetry between left vs. right atrial volume, the third a change in the prominence of the atrial appendages. The SSM is capable of generalizing well to unseen geometries and 95% of the total shape variance is covered by its first 24 eigenvectors. The Pwaves in the 12-lead ECG of 100 random instances showed a duration of 109.7±12.2ms in accordance with large cohort studies. The novel bi-atrial SSM itself as well as 100 exemplary instances with rule-based augmentation of atrial wall thickness, fiber orientation, inter-atrial bridges and tags for anatomical structures have been made publicly available. This novel, openly available bi-atrial SSM can in future be employed to generate large sets of realistic atrial geometries as a basis for in silico big data approaches.

Multi-Queue Request Scheduling for Profit Maximization in IaaS Clouds

In cloud computing, service providers rent heterogeneous servers from cloud providers, i.e., Infrastructure as a Service (IaaS), to meet requests of consumers. The heterogeneity of servers and impatience of consumers pose great challenges to service providers for profit maximization. In this article, we transform this problem into a multi-queue model where the optimal expected response time of each queue is theoretically analyzed. A multi-queue request scheduling algorithm framework is proposed to maximize the total profit of service providers, which consists of three components: request stream splitting, requests allocation, and server assignment. A request stream splitting algorithm is designed to split the arriving requests to minimize the response time in the multi-queue system. An allocation algorithm, which adopts a one-step improvement strategy, is developed to further optimize the response time of the requests. Furthermore, an algorithm is developed to determine the appropriate number of required servers of each queue. After statistically calibrating parameters and algorithm components over a comprehensive set of random instances, the proposed algorithms are compared with the state-of-the-art over both simulated and real-world instances. The results indicate that the proposed multi-queue request scheduling algorithm outperforms the other algorithms with acceptable computational time.

Maximum weighted induced forests and trees: new formulations and a computational comparative review

AbstractGiven a graph with a weight associated with each vertex , the maximum weighted induced forest problem (MWIF) consists of encountering a maximum weighted subset of the vertices such that induces a forest. This NP‐hard problem is known to be equivalent to the minimum weighted feedback vertex set problem, which has applicability in a variety of domains. The closely related maximum weighted induced tree problem (MWIT), on the other hand, requires that the subset induces a tree. We propose two new integer programming formulations with an exponential number of constraints and branch‐and‐cut procedures for MWIF. Computational experiments using benchmark instances are performed comparing several formulations, including the newly proposed approaches and those available in the literature, when solved by a standard commercial mixed integer programming solver. More specifically, five formulations are compared, two compact ones (i.e., with a polynomial number of variables and constraints) and the three others with an exponential number of constraints. The experiments show that a new formulation for the problem based on directed cutset inequalities for eliminating cycles (DCUT) offers stronger linear relaxation bounds earlier in the search process. The results also indicate that the other new formulation, denoted tree with cycle elimination (TCYC), outperforms those available in the literature when it comes to the average times for proving optimality for the benchmark instances with up to 81 vertices. Additionally, this formulation can achieve much lower average times for solving the larger random instances that can be optimally solved. Furthermore, we show how the formulations for MWIF can be easily extended for MWIT. Such extension allowed us to analyze the difference between the optimal solution values of the two problems when considering different classes of graphs.

Evolution of group-theoretic cryptology attacks using hyper-heuristics

Abstract In previous work, we developed a single evolutionary algorithm (EA) to solve random instances of the Anshel–Anshel–Goldfeld (AAG) key exchange protocol over polycyclic groups. The EA consisted of six simple heuristics which manipulated strings. The present work extends this by exploring the use of hyper-heuristics in group-theoretic cryptology for the first time. Hyper-heuristics are a way to generate new algorithms from existing algorithm components (in this case, simple heuristics), with EAs being one example of the type of algorithm which can be generated by our hyper-heuristic framework. We take as a starting point the above EA and allow hyper-heuristics to build on it by making small tweaks to it. This adaptation is through a process of taking the EA and injecting chains of heuristics built from the simple heuristics. We demonstrate we can create novel heuristic chains, which when placed in the EA create algorithms that out perform the existing EA. The new algorithms solve a greater number of random AAG instances than the EA. This suggests the approach may be applied to many of the same kinds of problems, providing a framework for the solution of cryptology problems over groups. The contribution of this article is thus a framework to automatically build algorithms to attack cryptology problems given an applicable group.