Comparable Solution Quality Research Articles

A heuristic with a performance guarantee for the commodity constrained split delivery vehicle routing problem

AbstractThe commodity constrained split delivery vehicle routing problem (C‐SDVRP) is a routing problem where customer demands are composed of multiple commodities. A fleet of capacitated vehicles must serve customer demands in a way that minimizes the total routing costs. Vehicles can transport any set of commodities and customers are allowed to be visited multiple times. However, the demand for a single commodity must be delivered by one vehicle only. In this work, we developed a heuristic with a performance guarantee to solve the C‐SDVRP. The proposed heuristic is based on a set covering formulation, where the exponentially‐many variables correspond to routes. First, a subset of the variables is obtained by solving the linear relaxation of the formulation by means of a column generation approach which embeds a new pricing heuristic aimed to reduce the computational time. Solving the linear relaxation gives a valid lower bound used as a performance guarantee for the heuristic. Then, we devise a restricted master heuristic to provide good upper bounds: the formulation is restricted to the subset of variables found so far and solved as an integer program with a commercial solver. A local search based on a mathematical programming operator is applied to improve the solution. We test the heuristic algorithm on benchmark instances from the literature. The comparison with the state‐of‐the‐art heuristics for solving the C‐SDVRP shows that our approach significantly improves the solution time, while keeping a comparable solution quality and improving some best‐known solutions. In addition, our approach is able to solve large instances with 100 customers and six commodities, and also provides very good quality lower bounds. Furthermore, an instance of the C‐SDVRP can be transformed into a CVRP instance by simply duplicating each customer as many times as the requested commodities and by assigning as demand the demand of the single commodity. Hence, we compare heuristics for the C‐SDVRP against the state‐of‐the‐art heuristic for the Capacitated Vehicle Routing Problem (CVRP). The latter approach revealed to have the best performance. However, our approach provides solutions of comparable quality and has the interest of providing a performance guarantee.

Distributed genetic algorithm for application placement in the compute continuum leveraging infrastructure nodes for optimization

The increasing complexity of Compute Continuum environments calls for efficient resource optimization techniques. In this paper, we propose and evaluate three distributed designs of a genetic algorithm (GA) for resource optimization, within an increasing degree of distribution. The designs leverage the execution of the GA in the infrastructure devices themselves by dealing with the specific features of this domain: constrained resources and wide geographical distribution of the devices. For their evaluation, we implemented a benchmark case using the NSGA-II for the specific problem of optimizing the application placement, according to the guidelines of our three distributed designs. These three experimental scenarios were compared against a control case, representing a traditional centralized version of this GA algorithm, evaluating solution quality and network overhead. The results show that the design with the lowest distribution degree, which keeps centralized storage of the objective space, achieves comparable solution quality to the traditional approach but incurs a higher network load. The second design, which completely distributes the population between the workers, reduces network overhead but exhibits lower solution diversity while keeping enough good results in terms of optimization objective minimization. The second design demonstrates the highest overall efficiency in optimization performance and network cost. Finally, the proposal with a distributed population that only interchanges solutions between the workers’ neighbors achieves the lowest network load but with compromised solution quality.

On solving close enough orienteering problems with overlapped neighborhoods

The Close Enough Traveling Salesman Problem (CETSP) is a well-known variant of the classic Traveling Salesman Problem whereby the agent may complete its mission at any point within a target neighborhood. Heuristics based on overlapped neighborhoods, known as Steiner Zones (SZ), have gained attention in addressing CETSPs. While SZs offer effective approximations to the original graph, their inherent overlap imposes constraints on the search space, potentially conflicting with global optimization objectives. Here we show how such limitations can be converted into advantages in the Close Enough Orienteering Problem (CEOP) by aggregating prizes across overlapped neighborhoods. We further extend the classic CEOP with Non-uniform Neighborhoods (CEOP-N) by introducing non-uniform cost considerations for prize collection. To tackle CEOP (and CEOP-N), we develop a new approach featuring a Randomized Steiner Zone Discretization (RSZD) scheme coupled with a hybrid algorithm based on Particle Swarm Optimization (PSO) and Ant Colony System (ACS) — CRaSZe-AntS. The RSZD scheme identifies sub-regions for PSO exploration, and ACS determines the discrete visiting sequence. We evaluate the RSZD’s discretization performance on CEOP instances derived from established CETSP instances and compare CRaSZe-AntS against the most relevant state-of-the-art heuristic focused on single-neighborhood optimization for CEOP instances. We also compare the performance of the interior search within SZs and the boundary search on individual neighborhoods in the context of CEOP-N. Our experimental results show that CRaSZe-AntS can yield comparable solution quality with significantly reduced computation time compared to the single neighborhood strategy, where we observe an averaged 140.44% increase in prize collection and 55.18% reduction of algorithm execution time. CRaSZe-AntS is thus highly effective in solving emerging CEOP-N, examples of which include truck-and-drone delivery scenarios.

Graph clustering with Boltzmann machines

Graph clustering is the process of labeling nodes so that nodes sharing common labels form densely connected subgraphs with sparser connections to the remaining vertices. Because of its difficult formulation, we translate the intra-cluster density maximization problem to a distance minimization problem. To achieve this reformulation, we use a novel vertex–vertex distance that accurately reflects density. Specifically, we extend the recent binary quadratic K-medoids formulation to graph clustering. We also generalize a quadratic formulation originally designed for partitioning complete graphs. Because binary quadratic optimization is an NP-hard problem, we obtain numerical solutions for these formulations through the use of two novel Boltzmann machine (meta-)heuristics. For benchmarking purposes, we compare solution quality and computational performances to those obtained using a commercial solver, Gurobi. We also compare clustering quality to the clusters obtained using the popular Louvain modularity maximization method. Our initial results clearly demonstrate the superiority of our problem formulations combined with our Boltzmann machines. In the case of smaller less complex graphs, our formulations solved using Boltzmann machines provide the same solutions as Gurobi, but with solution times that are orders of magnitude lower. In the case of larger and more complex graphs, Gurobi either fails to return meaningful results within a reasonable time frame or returns inferior results. Finally, we also note that both our clustering formulations, the distance minimization and K-medoids, when solved using our Boltzmann machines, yield clusters of superior quality to those obtained with the Louvain algorithm.

A Constraint-Based Routing and Charging Methodology for Battery Electric Vehicles With Deep Reinforcement Learning

Electric vehicle route planning (EVRP) is generated from the collaborative operation of smart grids and intelligent transportation systems. It has become an essential issue for the widespread use of battery electric vehicles. However, the existed EVRP solutions are of either high computational complexity or low efficiency for large-scale problems. Towards such issues, we propose an efficient Deep Reinforcement Learning based methodology for constraint-based routing while simultaneously considering electric vehicles’ charging policies. We design a two-layer model to find near-optimal solutions and handle the broad range of problem instances according to the rewards and the preset feasibility rules. The first layer is to approximate a sequence of consecutive actions in reality and correspondingly produce a minimum time-consuming feasible route without re-training for each new problem instance. The second layer is to generate a charging scheme along the previously generated feasible path. The proposed methodology is independent of the road network topology and the electric vehicles’ types. Besides, the convergence of value function in the presented model for EVRP is studied. The experiment shows that our methodology outperforms the traditional ones in computation time with comparable solution quality. Moreover, the obtained model can be directly applied to treat other problem instances on various road networks without re-training procedures.

FlexBeamOpt: Hybrid solution methodologies for high‐throughput GEO satellite beam laydown and resource allocation

SummaryModern satellite communication systems are required to serve heterogeneous and geographically dispersed user demands with limited resources. In this paper, we investigate methodologies for dynamic resource allocation in Geosynchronous Earth Orbit (GEO) High‐throughput Satellite (HTS) systems. We designed three solution approaches FlexBeamOpt v1, FlexBeamOpt v2, and FlexBeamOpt v3, each as a hybridization of custom heuristics, integer linear programming, and/or constraint programming. We test the performance of the three approaches on 12 test instances that vary in user distribution (realistic, random, and clustered), user numbers (500 vs. 5000 users), and demand distribution (uniform vs. random). We observed that FlexBeamOpt v1 consistently outperformed FlexBeamOpt v2 and FlexBeamOpt v3 in terms of demand coverage and number of users covered for realistic and random user distribution test instances but at the cost of computation time. FlexBeamOpt v3 is the fastest in these instances. For clustered user distribution instances, FlexBeamOpt v3 performed better in terms of demand coverage and number of users covered, at the cost of using more beams. For these test instances, FlexBeamOpt v2 is the fastest in terms of computation time while providing a comparable solution quality.

A nonhydrostatic atmospheric dynamical core on cubed sphere using multi-moment finite-volume method

A nonhydrostatic dynamical core has been developed by using the multi-moment finite volume method that ensures the rigorous numerical conservation of mass in this study. To represent the spherical geometry free of the polar problems, the cubed-sphere grid is adopted. A fourth-order multi-moment discretization formulation is applied to solve the governing equations cast in the local curvilinear coordinates on each patch of the cubed sphere through a gnomonic projection. In the vertical direction, the height-based terrain-following coordinate is used to deal with the topography and a finite difference scheme, also assuring the conservation of mass, is adopted for the spatial discretization. The proposed dynamical core adopts the nonhydrostatic governing equations. To get around the CFL stability restriction imposed by the sound wave and the relatively small grid spacing in the vertical direction, the dimensional splitting time integration algorithm using the HEVI (horizontally-explicit and vertically-implicit) strategy is implemented by applying the IMEX (implicit-explicit) Runge-Kutta method. The proposed model was checked by the widely-used benchmark tests in this study. The numerical results show that the multi-moment model has the comparable solution quality in comparison with the existing advanced ones and the great practical potential as a numerical platform for development of the atmospheric general circulation models.

Almost Linear Time Density Level Set Estimation via DBSCAN

In this work we focus on designing a fast algorithm for lambda-density level set estimation via DBSCAN clustering. Previous work (Jiang ICML’17, and Jang and Jiang ICML’19) shows that under some natural assumptions DBSCAN and its variant DBSCAN++ can be used to estimate the lambda-density level set with near-optimal Hausdorff distance, i.e., with rate O~(n^{-1/(2 * beta+D)}). However, to achieve this near-optimal rate, the current fastest DBSCAN algorithm needs near quadratic running time. This running time is not very practical for giant datasets. Usually when we are working with very large datasets we desire linear or almost linear time algorithms. With this motivation, in this work, we present a modified DBSCAN algorithm with near optimal Hausdorff distance for density level set estimation with O~(n) running time. In our empirical study, we show that our algorithm provides significant speedup over the previous algorithms, while achieving comparable solution quality.

On the propagation of quality requirements for mechanical assemblies in industrial manufacturing

A frequent challenge encountered by manufacturers of mechanical assemblies consists of the definition of quality criteria for the assembly lines of the subcomponents which are mounted into the final product. The rollout of Industry 4.0 standards paves the way for the usage of data-driven, intelligent approaches towards this goal. In this work, we investigate such a scenario originating in the daily operations of thyssenkrupp Presta AG, where new vibroacoustic quality specifications must be derived for the assembly line producing ball nut assemblies, based on the feedback offered by the vibroacoustic quality test of the steering gear, the final mechanical assembly they are mounted into. We first present a Mixed Integer Linear Programming (MILP) formulation for the problem and show that small instances of the corresponding available dataset can be solved to optimality. Upon ascertainment of the unsuitability of the MILP approach for industrial daily operations due to its long computation time, we propose a heuristic solving approach based on genetic algorithms and measure the performance gap between them in terms of achieved solution quality and computation time. Finally, we additionally propose a greedy heuristic designed to outperform the genetic algorithm in terms of computation time while still featuring a comparable solution quality. The practical relevance of the results is guaranteed, since the best solution reached by the genetic algorithm reduces the scrap costs with respect to the method currently employed by the company by 49.91%.

Stockpile scheduling with geometry constraints in dry bulk terminals

In this article we consider how to construct schedules for the stacking and reclaiming activities of high-throughput dry-bulk export terminals (DBET) that operate large machines called stacker-reclaimers (SR) and handle iron ore, coking coal and thermal coal for export. In terminals with large and persistent stockpiles, the ever-changing geometry of stockpiles can impose challenging scheduling constraints. For those situations, we propose that each stockpile is modelled in detail, for instance as a collection of heterogeneous sized blocks. This is called a bench block model (BBM). We then demonstrate how stockpiles are manipulated via their BBM and how BBM can be integrated as a form of stockpile manager within a sophisticated DBET scheduling engine. Numerical testing of the DBET scheduling engine and three horizontal bench block model (HBBM) has been performed and indicates that the application of BBM is worthwhile, if not essential. The concept of BBM is generic, highly flexible, and integrable into existing optimisation routines. The results provided are superior to other approaches that model stockpiles as simple silos. We can provide schedules that are devoid of any stockpile geometry errors in contrast to others which cannot, and computational overheads to do this are no greater than previous approaches. In the three case studies considered, it was also pleasing to see that solutions of comparable quality with key performance criteria (KPI) equivalent to those constructed without any consideration of stockpile geometry are achievable. The new scheduling approach can significantly reduce the time to perform terminal planning and can increase the utilization of key resources within the terminal.

We Mind Your Well-Being: Preventing Depression in Uncertain Social Networks by Sequential Interventions

Mental health has become a major concern according to WHO who estimates that more than 350 million people worldwide are affected by depression. Studies have shown that interventions and social support can reduce stress and depression. However, counselling centers do not have enough resources to provide counselling and social support to all the participants in their interest. This paper helps social support organizations (e.g., university counselling centers) sequentially select the participants for interventions. Unfortunately, previous works do not consider emotion propagation from other neighbours of the influencees and initial uncertainties of mental states and influence. Moreover, they fail to scale up to solve problems with a large number of participants due to the huge state space. Our contributions in this paper are fourfold. Firstly, we propose a new model that addresses the sequential intervention of participants while considering the propagation of emotions and formulate it as a Partially Observable Markov Decision Process (POMDP) to handle uncertainties about their mental states and the influence between them. Secondly, we apply reasoning to refine belief to improve solution quality for the lack of initial information on mental state values. Thirdly, we improve the scalability by the abstraction of states to reduce the number of states by representing the mental states with an abstracted discrete set. We further improve the scalability by multi-level partitioning to get smaller POMDPs. Finally, we conduct extensive experiments on both synthetic and real networks to show that our algorithm significantly improves scalability with comparable solution quality compared to the state-of-the-art algorithms.

The convex hull heuristic for nonlinear integer programming problems with linear constraints and application to quadratic 0–1 problems

The convex hull heuristic is a heuristic for mixed-integer programming problems with a nonlinear objective function and linear constraints. It is a matheuristic in two ways: it is based on the mathematical programming algorithm called simplicial decomposition, or SD (von Hohenbalken in Math Program 13:49–68, 1977), and at each iteration, one solves a mixed-integer programming problem with a linear objective function and the original constraints, and a continuous problem with a nonlinear objective function and a single linear constraint. Its purpose is to produce quickly feasible and often near optimal or optimal solutions for convex and nonconvex problems. It is usually multi-start. We have tested it on a number of hard quadratic 0–1 optimization problems and present numerical results for generalized quadratic assignment problems, cross-dock door assignment problems, quadratic assignment problems and quadratic knapsack problems. We compare solution quality and solution times with results from the literature, when possible.

Space\u2013time computational analysis of tire aerodynamics with actual geometry, road contact, tire deformation, road roughness and fluid film

The space–time (ST) computational method “ST-SI-TC-IGA” has recently enabled computational analysis of tire aerodynamics with actual tire geometry, road contact and tire deformation. The core component of the ST-SI-TC-IGA is the ST Variational Multiscale (ST-VMS) method, and the other key components are the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods and the ST Isogeometric Analysis (ST-IGA). These ST methods played their parts in overcoming the computational challenges, including (i) the complexity of an actual tire geometry with longitudinal and transverse grooves, (ii) the spin of the tire, (iii) maintaining accurate representation of the boundary layers near the tire while being able to deal with the flow-domain topology change created by the road contact, and (iv) the turbulent nature of the flow. The combination of the ST-VMS, ST-SI and the ST-IGA has also recently enabled solution of fluid film problems with a computational cost comparable to that of the Reynolds-equation model for the comparable solution quality. This was accomplished with the computational flexibility to go beyond the limitations of the Reynolds-equation model. Here we include and address the computational challenges associated with the road roughness and the fluid film between the tire and the road. The new methods we add to accomplish that include a remedy for the trapped fluid, a method for reducing the number of control points as a space occupied by the fluid shrinks down to a narrow gap, and a method for representing the road roughness. We present computations for a 2D test problem with a straight channel, a simple 2D model of the tire, and a 3D model with actual tire geometry and road roughness. The computations show the effectiveness of our integrated set of ST methods targeting tire aerodynamics.

Space–time Isogeometric flow analysis with built-in Reynolds-equation limit

We present a space–time (ST) computational flow analysis method with built-in Reynolds-equation limit. The method enables solution of lubrication fluid dynamics problems with a computational cost comparable to that of the Reynolds-equation model for the comparable solution quality, but with the computational flexibility to go beyond the limitations of the Reynolds-equation model. The key components of the method are the ST Variational Multiscale (ST-VMS) method, ST Isogeometric Analysis (ST-IGA), and the ST Slip Interface (ST-SI) method. The VMS feature of the ST-VMS serves as a numerical stabilization method with a good track record, the moving-mesh feature of the ST framework enables high-resolution flow computation near the moving fluid–solid interfaces, and the higher-order accuracy of the ST framework strengthens both features. The ST-IGA enables more accurate representation of the solid-surface geometries and increased accuracy in the flow solution in general. With the ST-IGA, even with just one quadratic NURBS element across the gap of the lubrication fluid dynamics problem, we reach a solution quality comparable to that of the Reynolds-equation model. The ST-SI enables moving-mesh computation when the spinning solid surface is noncircular. The mesh covering the solid surface spins with it, retaining the high-resolution representation of the flow near the surface, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. We present detailed 2D test computations to show how the method performs compared to the Reynolds-equation model, compared to finite element discretization, at different circumferential and normal mesh refinement levels, when there is an SI in the mesh, and when the no-slip boundary conditions are weakly-enforced.

A Branch-and-Bound Approach to the Traveling Salesman Problem with a Drone

The Traveling Salesman Problem with a Drone (TSP-D) is a hybrid truck and drone model of delivery, in which the drone rides on the truck and launches from the truck to deliver packages. Our approach to the TSP-D uses branch and bound, whereby each node of the branch-and-bound tree corresponds with a potential order to deliver a subset of packages. An approximate lower bound at each node is given by solving a dynamic program. We provide additional variants of our heuristic approach and compare solution quality and computation times. Consideration is given to various input parameters and distance metrics. The online supplement is available at https://doi.org/10.1287/ijoc.2018.0826 .

A Dynamic Regrouping Based Dynamic Programming Approach for Unit Commitment of the Transmission-Constrained Multi-Site Combined Heat and Power System

Combined heat and power (CHP) systems offer additional advantage and flexibility for addressing power grid balance resulting from large-scale introduction of intermittent renewable energy sources (RES) in contrast to power-only systems. The dependence between heat and power production in the CHP plant can be utilized to adjust power production level to accommodate more RES. Furthermore, electricity can be transformed into heat by electric heater and heat pump to avoid starting up heat led CHP plants when RES production is abundant. This paper focuses on solving efficiently unit commitment of the interconnected multi-site CHP system without considering RES. A relaxed on/off state based dynamic programming applying sequential commitment scheme in conjunction with dynamic regrouping is used to coordinate heat and power production in each site (region) as well as power transmission across sites. Computational experiments for real-life daily scheduling demonstrate that our method generates solutions much more quickly than a standard high-performance optimizer (CPLEX) with comparable solution quality, and lays foundation for the future handling of uncertainties of intermittent RES.

A Design Space Exploration Methodology for Parameter Optimization in Multicore Processors

The need for application-specific design of multicore/manycore processing platforms is evident with computing systems finding use in diverse application domains. In order to tailor multicore/manycore processors for application specific requirements, a multitude of processor design parameters have to be tuned accordingly which involves rigorous and extensive design space exploration over large search spaces. In this paper, we propose an efficient methodology for design space exploration. We evaluate our methodology over two search spaces - small and large, using a cycle-accurate simulator (ESESC) and a standard set of PARSEC and SPLASH-2 benchmarks. For the smaller design space, we compare results obtained from our design space exploration methodology with results obtained from fully exhaustive search. The results show that solution quality obtained from our methodology are within 1.35% - 3.69% of the results obtained from fully exhaustive search while only exploring 2.74% - 3% of the design space. For larger design space, we compare solution quality of different results obtained by varying the number of tunable processor design parameters included in the exhaustive search phase of our methodology. The results show that including more number of tunable parameters in the exhaustive search phase of our methodology greatly improves solution quality.

Social hash partitioner

We design and implement a distributed algorithm for balanced k -way hypergraph partitioning that minimizes fanout, a fundamental hypergraph quantity also known as the communication volume and ( k - 1)-cut metric, by optimizing a novel objective called probabilistic fanout. This choice allows a simple local search heuristic to achieve comparable solution quality to the best existing hypergraph partitioners. Our algorithm is arbitrarily scalable due to a careful design that controls computational complexity, space complexity, and communication. In practice, we commonly process hypergraphs with billions of vertices and hyperedges in a few hours. We explain how the algorithm's scalability, both in terms of hypergraph size and bucket count, is limited only by the number of machines available. We perform an extensive comparison to existing distributed hypergraph partitioners and find that our approach is able to optimize hypergraphs roughly 100 times bigger on the same set of machines. We call the resulting tool Social Hash Partitioner , and accompanying this paper, we open-source the most scalable version based on recursive bisection.

Drawing Large Graphs by Multilevel Maxent-Stress Optimization.

Drawing large graphs appropriately is an important step for the visual analysis of data from real-world networks. Here we present a novel multilevel algorithm to compute a graph layout with respect to the maxent-stress metric proposed by Gansner etal.(2013) that combines layout stress and entropy. As opposed to previous work, we do not solve the resulting linear systems of the maxent-stress metric with a typical numerical solver. Instead we use a simple local iterative scheme within a multilevel approach. To accelerate local optimization, we approximate long-range forces and use shared-memory parallelism. Our experiments validate the high potential of our approach, which is particularly appealing for dynamic graphs. In comparison to the previously best maxent-stress optimizer, which is sequential, our parallel implementation is on average 30 times faster already for static graphs (and still faster if executed on a single thread) while producing a comparable solution quality.

Roster evaluation based on classifiers for the nurse rostering problem

The personnel scheduling problem is a well-known NP-hard combinatorial problem. Due to the complexity of this problem and the size of the real-world instances, it is not possible to use exact methods, and thus heuristics, meta-heuristics, or hyper-heuristics must be employed. The majority of heuristic approaches are based on iterative search, where the quality of intermediate solutions must be calculated. Unfortunately, this is computationally highly expensive because these problems have many constraints and some are very complex. In this study, we propose a machine learning technique as a tool to accelerate the evaluation phase in heuristic approaches. The solution is based on a simple classifier, which is able to determine whether the changed solution (more precisely, the changed part of the solution) is better than the original or not. This decision is made much faster than a standard cost-oriented evaluation process. However, the classification process cannot guarantee 100% correctness. Therefore, our approach, which is illustrated using a tabu search algorithm in this study, includes a filtering mechanism, where the classifier rejects the majority of the potentially bad solutions and the remaining solutions are then evaluated in a standard manner. We also show how the boosting algorithms can improve the quality of the final solution compared with a simple classifier. We verified our proposed approach and premises, based on standard and real-world benchmark instances, to demonstrate the significant speedup obtained with comparable solution quality.