Showing papers on "Assignment problem published in 2020"

Rethinking pooling in graph neural networks

Abstract: Graph pooling is a central component of a myriad of graph neural network (GNN) architectures. As an inheritance from traditional CNNs, most approaches formulate graph pooling as a cluster assignment problem, extending the idea of local patches in regular grids to graphs. Despite the wide adherence to this design choice, no work has rigorously evaluated its influence on the success of GNNs. In this paper, we build upon representative GNNs and introduce variants that challenge the need for locality-preserving representations, either using randomization or clustering on the complement graph. Strikingly, our experiments demonstrate that using these variants does not result in any decrease in performance. To understand this phenomenon, we study the interplay between convolutional layers and the subsequent pooling ones. We show that the convolutions play a leading role in the learned representations. In contrast to the common belief, local pooling is not responsible for the success of GNNs on relevant and widely-used benchmarks.

RBFNN-Based Minimum Entropy Filtering for a Class of Stochastic Nonlinear Systems

Abstract: This paper presents a novel minimum entropy filter design for a class of stochastic nonlinear systems, which are subjected to non-Gaussian noises. Motivated by stochastic distribution control, an output entropy model is developed using a radial basis function neural network, while the parameters of the model can be identified by the collected data. Based upon the presented model, the filtering problem has been investigated, while the system dynamics have been represented. As the model output is the entropy of the estimation error, the optimal nonlinear filter is obtained based on the Lyapunov design, which makes the model output minimum. Moreover, the entropy assignment problem has been discussed as an extension of the presented approach. To verify the presented design procedure, a numerical example is given, which illustrates the effectiveness of the presented algorithm. The contributions of this paper can be summarized as follows: 1) an output entropy model is presented using a neural network; 2) a nonlinear filter design algorithm is developed as the main result; and 3) a solution of the entropy assignment problem is obtained, which is an extension of the presented framework.

SRA: Secure Reverse Auction for Task Assignment in Spatial Crowdsourcing

Abstract: In this paper, we study a new type of spatial crowdsourcing, namely competitive detour tasking, where workers can make detours from their original travel paths to perform multiple tasks, and each worker is allowed to compete for preferred tasks by strategically claiming his/her detour costs. The objective is to make suitable task assignment by maximizing the social welfare of crowdsourcing systems and protecting workers’ private sensitive information. We first model the task assignment problem as a reverse auction process. We formalize the winning bid selection of reverse auction as an $n$ n -to-one weighted bipartite graph matching problem with multiple 0-1 knapsack constraints. Since this problem is NP-hard, we design an approximation algorithm to select winning bids and determine corresponding payments. Based on this, a Secure Reverse Auction (SRA) protocol is proposed for this novel spatial crowdsourcing. We analyze the approximation performance of the proposed protocol and prove that it has some desired properties, including truthfulness, individual rationality, computational efficiency, and security. To the best of our knowledge, this is the first theoretically provable secure auction protocol for spatial crowdsourcing systems. In addition, we also conduct extensive simulations on a real trace to verify the performance of the proposed protocol.

Combinatorial Learning of Robust Deep Graph Matching: an Embedding based Approach

Abstract: Graph matching aims to establish node correspondence between two graphs, which has been a fundamental problem for its NP-complete nature One practical consideration is the effective modeling of the affinity function in the presence of noise, such that the mathematically optimal matching result is also physically meaningful This paper resorts to deep neural networks to learn the node and edge feature, as well as the affinity model for graph matching in an end-to-end fashion The learning is supervised by combinatorial permutation loss over nodes Specifically, the parameters belong to convolutional neural networks for image feature extraction, graph neural networks for node embedding that convert the structural (beyond second-order) information into node-wise features that leads to a linear assignment problem, as well as the affinity kernel between two graphs Our approach enjoys flexibility in that the permutation loss is agnostic to the number of nodes, and the embedding model is shared among nodes such that the network can deal with varying numbers of nodes for both training and inference Moreover, our network is class-agnostic Experimental results on extensive benchmarks show its state-of-the-art performance It bears some generalization capability across categories and datasets, and is capable for robust matching against outliers

Destination-Aware Task Assignment in Spatial Crowdsourcing: A Worker Decomposition Approach

Abstract: With the proliferation of GPS-enabled smart devices and increased availability of wireless network, spatial crowdsourcing (SC) has been recently proposed as a framework to automatically request workers (i.e., smart device carriers) to perform location-sensitive tasks (e.g., taking scenic photos, reporting events). In this paper, we study a destination-aware task assignment problem that concerns the optimal strategy of assigning each task to proper worker such that the total number of completed tasks can be maximized whilst all workers can reach their destinations before deadlines after performing assigned tasks. Finding the global optimal assignment turns out to be an intractable problem since it does not imply optimal assignment for individual worker. Observing that the task assignment dependency only exists amongst subsets of workers, we utilize tree-decomposition technique to separate workers into independent clusters and develop an efficient depth-first search algorithm with progressive bounds to prune non-promising assignments. In order to make our proposed framework applicable to more scenarios, we further optimize the original framework by proposing strategies to reduce the overall travel cost and allow each task to be assigned to multiple workers. Extensive empirical studies verify that the proposed technique and optimization strategies perform effectively and settle the problem nicely.

Coverage Optimization with a Dynamic Network of Drone Relays

Abstract: The integration of aerial base stations carried by drones in cellular networks offers promising opportunities to enhance the connectivity enjoyed by ground users In this paper, we propose an optimization framework for the 3–D placement and repositioning of a fleet of drones with a realistic inter-drone interference model and drone connectivity constraints We show how to maximize network coverage by means of an extremal-optimization algorithm The design of our algorithm is based on a mixed-integer non-convex program formulation for a coverage problem that is NP-Complete, as we prove in the paper We not only optimize drone positions in a 3–D space in polynomial time, but also assign flight routes solving an assignment problem and using a strong geometrical tool, namely Bezier curves , which are extremely useful for non-uniform and realistic topologies Specifically, we propose to fly drones following Bezier curves to seek the chance of approaching to clusters of ground users This enhances coverage over time while users and drones move We assess the performance of our proposal for synthetic scenarios as well as realistic maps extracted from the topology of a capital city We demonstrate that our framework is near-optimal and using Bezier curves increases coverage up to 47 percent while drones move

Efficient Routing for Precedence-Constrained Package Delivery for Heterogeneous Vehicles

Abstract: This paper studies the precedence-constrained task assignment problem for a team of heterogeneous vehicles to deliver packages to a set of dispersed customers subject to precedence constraints that specify which customers need to be visited before which other customers. A truck and a micro drone with complementary capabilities are employed where the truck is restricted to travel in a street network and the micro drone, restricted by its loading capacity and operation range, can fly from the truck to perform the last-mile package deliveries. The objective is to minimize the time to serve all the customers respecting every precedence constraint. The problem is shown to be NP-hard, and a lower bound on the optimal time to serve all the customers is constructed by using tools from graph theory. Then, integrating with a topological sorting technique, several heuristic task assignment algorithms are proposed to solve the task assignment problem. Numerical simulations show the superior performances of the proposed algorithms compared with popular genetic algorithms. Note to Practitioners —This paper presents several task assignment algorithms for the precedence-constrained package delivery for the team of a truck and a micro drone. The truck can carry the drone moving in a street network, while the drone completes the last-mile package deliveries. The practical contributions of this paper are fourfold. First, the precedence constraints on the ordering of the customers to be served are considered, which enables complex logistic scheduling for customers prioritized according to their urgency or importance. Second, the package delivery optimization problem is shown to be NP-hard, which clearly shows the need for creative approximation algorithms to solve the problem. Third, the constructed lower bound on the optimal time to serve all the customers helps to clarify for practitioners the limiting performance of a feasible solution. Fourth, the proposed task assignment algorithms are efficient and can be adapted for real scenarios.

Social-Aware UAV-Assisted Mobile Crowd Sensing in Stochastic and Dynamic Environments for Disaster Relief Networks

Abstract: In this paper, we consider a social-aware unmanned aerial vehicle (UAV) assisted mobile crowd sensing (MCS) system for disaster relief networks, and investigate how to recruit suitable UAVs to perform sensing tasks in stochastic and dynamic environments (both UAVs and tasks arrive stochastically). We formulate the task assignment problem into a dynamic matching problem, and propose a multiple-waitlist based task assignment (MWTA) algorithm to find the stable matching in time-varying environment. We prove that MWTA can achieve the dynamic stability containing the strategy-proofness, efficiency, and envy-freeness. Simulation results demonstrate the performance improvement of our proposed scheme compared with the traditional matching algorithm applied to deterministic matching model in stochastic setting.

Parametric solutions to generalized periodic Sylvester bimatrix equations

Abstract: The problem considered in this paper is to solve generalized periodic Sylvester bimatrix equations. By utilizing bimatrix mapping tool and some algebraic technology, a parametric algorithm is presented to derive the complete and explicit solutions to this type of equations. The exact solutions derived by the proposed algorithm possess countless freely parameters, which can provide sufficient degree of freedom. The method is also applied to the pole assignment problem of complex-valued linear periodic system. Finally, two practical examples are employed to verify the correctness and validity of the proposed approach.

Applying the Quantum Approximate Optimization Algorithm to the Tail-Assignment Problem

Abstract: Airlines today are faced with a number of large-scale scheduling problems. One such problem is the tail-assignment problem, which is the task of assigning individual aircraft to a given set of flights, minimizing the overall cost. Each aircraft is identified by the registration number on its tail fin. In this paper, we simulate the quantum approximate optimization algorithm (QAOA) applied to instances of this problem derived from real-world data. The QAOA is a variational hybrid quantum-classical algorithm recently introduced and likely to run on near-term quantum devices. The instances are reduced to fit on quantum devices with 8, 15, and 25 qubits. The reduction procedure leaves only one feasible solution per instance, which allows us to map the tail-assignment problem onto the exact-cover problem. We find that repeated runs of the QAOA identify the feasible solution with close to unit probability for all instances. Furthermore, we observe patterns in the variational parameters such that an interpolation strategy can be employed, which significantly simplifies the classical optimization part of the QAOA. Finally, we empirically find a relation between the connectivity of the problem graph and the single-shot success probability of the algorithm.

A Socially-Aware Hybrid Computation Offloading Framework for Multi-Access Edge Computing

Abstract: Computation offloading manages resource-intensive and mobile collaborative applications (MCA) on mobile devices where much processing is replicated with multiple users in the same environment. In this article, we propose a novel hybrid multicast-based task execution framework for multi-access edge computing (MEC), where a crowd of mobile devices at the network edge leverage network-assisted device-to-device (D2D) collaboration for wireless distributed computing (MDC) and outcome sharing. The framework is socially aware in order to build effective D2D links. A key objective of this framework is to achieve an energy-efficient task assignment policy for mobile users. Specifically, we first introduce the socially aware hybrid computation offloading ( SAHCO ) system model, which combines of MEC offloading and D2D offloading in detail. Then, we formulate the energy-efficient task assignment problem by taking into account the necessary constraints. We next propose a Monte Carlo Tree Search based algorithm, named, TA-MCTS for the task assignment problem. Simulation results show that compared to four alternative benchmark solutions in literature, our proposal can reduce energy consumption up to 45.37 percent.

The integrated berth allocation, quay crane assignment and scheduling problem: mathematical formulations and a case study

Abstract: This paper considers the integration of three essential seaport terminal operations: the berth allocation problem, the quay crane assignment problem (QCAP), and the quay crane scheduling problem (QCSP). The paper presents a new mathematical formulation that captures all associated operations and constraints. Different quay crane operational policies are considered, namely permitting versus not permitting bay task preemption in QCSP and static versus dynamic crane allocations in QCAP. Thus, variants of the mathematical formulation are introduced to capture the different combinations of these scenarios. Due to the preemption consideration, the models include disaggregated quay crane (QC) tasks. Specifically, QC tasks are identified by single container movements as opposed to bay or stack task allocations that are commonly used in the literature. A case study based on Abu Dhabi’s container terminal is presented where the use of the proposed mathematical models are compared against the current existing operational approach. Results show that the service times can be significantly decreased by the use of the proposed models. Moreover, the policy choice effect on the total schedule is compared through simulated examples and Abu Dhabi’s container terminal case study. The results show that the policy improvements can depend on the problem’s attributes and thus a better policy cannot be generalized.

Comparing heuristics for graph edit distance computation

Abstract: Because of its flexibility, intuitiveness, and expressivity, the graph edit distance (GED) is one of the most widely used distance measures for labeled graphs. Since exactly computing GED is NP-hard, over the past years, various heuristics have been proposed. They use techniques such as transformations to the linear sum assignment problem with error correction, local search, and linear programming to approximate GED via upper or lower bounds. In this paper, we provide a systematic overview of the most important heuristics. Moreover, we empirically evaluate all compared heuristics within an integrated implementation.

Optimal Task Assignment With Delay Constraint for Parked Vehicle Assisted Edge Computing: A Stackelberg Game Approach

Abstract: Parked vehicle assisted edge computing is a paradigm to employ parked vehicles for processing workloads in vehicular networks. They collaborate with edge servers for joint task execution within task deadline and parking durations. We study task assignment problem with Stackelberg game, where the overall cost of a task publisher in terms of monetary cost and subjective dissatisfaction caused by un-offloaded workloads is minimized. To reach Stackelberg equilibrium, a dedicated algorithm is performed among players in a distributed manner for privacy preservation. Numerical results indicate that the cost is decreased about 25% in our scheme compared to that in existing work.

Optimal transport: discretization and algorithms

Abstract: This chapter describes techniques for the numerical resolution of optimal transport problems. We will consider several discretizations of these problems, and we will put a strong focus on the mathematical analysis of the algorithms to solve the discretized problems. We will describe in detail the following discretizations and corresponding algorithms: the assignment problem and Bertsekas auction's algorithm; the entropic regularization and Sinkhorn-Knopp's algorithm; semi-discrete optimal transport and Oliker-Prussner or damped Newton's algorithm, and finally semi-discrete entropic regularization. Our presentation highlights the similarity between these algorithms and their connection with the theory of Kantorovich duality.

Cooperative Task Assignment of a Heterogeneous Multi-UAV System Using an Adaptive Genetic Algorithm

Abstract: The cooperative multiple task assignment problem (CMTAP) is an NP-hard combinatorial optimization problem. In this paper, CMTAP is to allocate multiple heterogeneous fixed-wing UAVs to perform a suppression of enemy air defense (SEAD) mission on multiple stationary ground targets. To solve this problem, we study the adaptive genetic algorithm (AGA) under the assumptions of the heterogeneity of UAVs and task coupling constraints. Firstly, the multi-type gene chromosome encoding scheme is designed to generate feasible chromosomes that satisfy the heterogeneity of UAVs and task coupling constraints. Then, AGA introduces the Dubins car model to simulate the UAV path formation and derives the fitness value of each chromosome. In order to comply with the chromosome coding strategy of multi-type genes, we designed the corresponding crossover and mutation operators to generate feasible offspring populations. Especially, the proposed mutation operators with the state-transition scheme enhance the stochastic searching ability of the proposed algorithm. Last but not least, the proposed AGA dynamically adjusts the number of crossover and mutation populations to avoid the subjective selection of simulation parameters. The numerical simulations verify that the proposed AGA has a better optimization ability and convergence effect compared with the random search method, genetic algorithm, ant colony optimization method, and particle search optimization method. Therefore, the effectiveness of the proposed algorithm is proven.

Multi-skill aware task assignment in real-time spatial crowdsourcing

Abstract: With the development of mobile Internet and the prevalence of sharing economy, spatial crowdsourcing (SC) is becoming more and more popular and attracts attention from both academia and industry. A fundamental issue in SC is assigning tasks to suitable workers to obtain different global objectives. Existing works often assume that the tasks in SC are micro and can be completed by any single worker. However, there also exist macro tasks which need a group of workers with different kinds of skills to complete collaboratively. Although there have been a few works on macro task assignment, they neglect the dynamics of SC and assume that the information of the tasks and workers can be known in advance. This is not practical as in reality tasks and workers appear dynamically and task assignment should be performed in real time according to partial information. In this paper, we study the multi-skill aware task assignment problem in real-time SC, whose offline version is proven to be NP-hard. To solve the problem effectively, we first propose the Online-Exact algorithm, which always computes the optimal assignment for the newly appearing tasks or workers. Because of Online-Exact’s high time complexity which may limit its feasibility in real time, we propose the Online-Greedy algorithm, which iteratively tries to assign workers who can cover more skills with less cost to a task until the task can be completed. We finally demonstrate the effectiveness and efficiency of our solutions via experiments conducted on both synthetic and real datasets.

Parking Assignment: Minimizing Parking Expenses and Balancing Parking Demand Among Multiple Parking Lots

Abstract: Recently, a rapid growth in the number of vehicles on the road has led to an unexpected surge of parking demand. Consequently, finding a parking space has become increasingly difficult and expensive. One of the viable approaches is to utilize both public and private parking lots (PLs) to effectively share the parking spaces. However, when the parking demands are not balanced among PLs, a local congestion problem occurs where some PLs are overloaded, and others are underutilized. Therefore, in this article, we formulate the parking assignment problem with two objectives: 1) minimizing parking expenses and 2) balancing parking demand among multiple PLs. First, we derive a matching solution for minimizing parking expenses. Then, we extend our study by considering both parking expenses and balancing parking demand, formulating this as a mixed-integer linear programming problem. We solve that problem by using an alternating direction method of multipliers (ADMM)-based algorithm that can enable a distributed implementation. Finally, the simulation results show that the matching game approach outperforms the greedy approach by 8.5% in terms of parking utilization, whereas the ADMM-based algorithm produces performance gains up to 27.5% compared with the centralized matching game approach. Furthermore, the ADMM-based proposed algorithm can obtain a near-optimal solution with a fast convergence that does not exceed eight iterations for the network size with 1000 vehicles. Note to Practitioners —The efficiency of the parking assignment is critical to the parking management systems in order to provide the best parking guides. This article investigates the cost minimization problem for parking assignment while balancing parking demand among multiple parking lots (PLs). Previous parking assignment approaches do not jointly investigate the cost of parking and the cost of PL utilization. Therefore, they can fail to the local congestion problem caused by a large number of vehicles driving toward the same PL. In this article, a new method that considers both of minimizing parking expenses and balancing parking demand is proposed. It is obtained by using the alternating direction method of multipliers (ADMM)-based proposal that distributively solves a constrained optimization problem. Based on the experimental results, the ADMM-based algorithm outperforms the matching-based algorithm and the greedy algorithm in terms of the balancing parking demand and reducing parking expenses. The proposed method can be readily implemented in real-world industrial PLs. In the future work where parking assignments for electric vehicles are needed, our proposed mechanism can then be extended to solve the balanced electricity overload multiple charging stations.

Neural approximate dynamic programming for on-demand ride-pooling

Abstract: On-demand ride-pooling (e.g., UberPool, LyftLine, GrabShare) has recently become popular because of its ability to lower costs for passengers while simultaneously increasing revenue for drivers and aggregation companies (e.g., Uber). Unlike in Taxi on Demand (ToD) services – where a vehicle is assigned one passenger at a time – in on-demand ride-pooling, each vehicle must simultaneously serve multiple passengers with heterogeneous origin and destination pairs without violating any quality constraints. To ensure near real-time response, existing solutions to the real-time ride-pooling problem are myopic in that they optimise the objective (e.g., maximise the number of passengers served) for the current time step without considering the effect such an assignment could have on assignments in future time steps. However, considering the future effects of an assignment that also has to consider what combinations of passenger requests can be assigned to vehicles adds a layer of combinatorial complexity to the already challenging problem of considering future effects in the ToD case.A popular approach that addresses the limitations of myopic assignments in ToD problems is Approximate Dynamic Programming (ADP). Existing ADP methods for ToD can only handle Linear Program (LP) based assignments, however, as the value update relies on dual values from the LP. The assignment problem in ride pooling requires an Integer Linear Program (ILP) that has bad LP relaxations. Therefore, our key technical contribution is in providing a general ADP method that can learn from the ILP based assignment found in ride-pooling. Additionally, we handle the extra combinatorial complexity from combinations of passenger requests by using a Neural Network based approximate value function and show a connection to Deep Reinforcement Learning that allows us to learn this value-function with increased stability and sample-efficiency. We show that our approach easily outperforms leading approaches for on-demand ride-pooling on a real-world dataset by up to 16%, a significant improvement in city-scale transportation problems.

On Virtual Id Assignment in Networks for High Resilience Routing: A Theoretical Framework

Abstract: In recent years, the effort of promoting versatile, easy to manage routing schemes, as a replacement to OSPF has gathered momentum particularly in the context of large-scale enterprise networks, data center networks and software-defined wide area networks (SD-WANs). Such routing schemes rely on embedding the network into a geometric/topological space (e.g. a binary tree) to facilitate multi-path routing with reduced state maintenance and quick recovery in localized failure scenarios. In this work, we propose a systematic framework to embed the network topology into a hierarchical binary virtual-identityspace that is particularly amenable to multi-path routing. Our methodology firstly involves a relaxed form of the connected graph bi-partitioning problem that exploits a geometric embedding of the network in an n-dimensional Euclidean space (n being the number of hosts in the network) based on the Moore-Penrose pseudo inverse of the Laplacian for the graph associated with the network. The edges of the network are mapped to a weight distribution that helps construct a spanning tree from the core of the network towards the periphery, thereby providing a point of symmetry in the network to facilitate balanced bipartitions. This, in turn, yields a (nearly) full balanced binary tree embedding of the network and consequently a good virtual-id space. We also explore the binary identity assignment problem in another point of view by using bi-connected graph as the input graph to introduce a recursive bipartition algorithm. Through rigorous theoretical analysis and experimentation, we demonstrate that our methods perform well within reasonable bounds of computational complexity.

Visual-Semantic Graph Matching for Visual Grounding

Abstract: Visual Grounding is the task of associating entities in a natural language sentence with objects in an image. In this paper, we formulate visual grounding as a graph matching problem to find node correspondences between a visual scene graph and a language scene graph. These two graphs are heterogeneous, representing structure layouts of the sentence and image, respectively. We learn unified contextual node representations of the two graphs by using a cross-modal graph convolutional network to reduce their discrepancy. The graph matching is thus relaxed as a linear assignment problem because the learned node representations characterize both node information and structure information. A permutation loss and a semantic cycle-consistency loss are further introduced to solve the linear assignment problem with or without ground-truth correspondences. Experimental results on two visual grounding tasks, i.e., referring expression comprehension and phrase localization, demonstrate the effectiveness of our method.

Algorithmic approaches to the multiple knapsack assignment problem

Abstract: We consider a variant of the multiple knapsack problem in which some assignment-type side constraints have to be satisfied. The problem finds applications in logistics sectors related, e.g., to transportation and maritime shipping. We derive upper bounds from Lagrangian and surrogate relaxations of a mathematical model of the problem. We introduce a constructive heuristic and a metaheuristic refinement. We study the computational complexity of the proposed methods and evaluate their practical performance through extensive computational experiments on benchmarks from the literature and on new sets of randomly generated instances.

Cooperative Multiple Task Assignment of Heterogeneous UAVs Using a Modified Genetic Algorithm with Multi-type-gene Chromosome Encoding Strategy

Abstract: The cooperative multiple task assignment problem (CMTAP) of heterogeneous fixed-wing unmanned aerial vehicles (UAVs) performing the Suppression of Enemy Air Defense (SEAD) mission against multiple ground stationary targets is studied in this paper. The CMTAP is a NP-hard combinatorial optimization problem, which faces many challenges like problem scale, heterogeneity of UAVs (different capability and maneuverability), task coupling and task precedence constraints. To address this issue, we proposed a modified genetic algorithm (GA) with multi-type-gene chromosome encoding strategy. Firstly, the multi-type-gene encoding scheme is raised to generate feasible chromosomes that satisfy the UAV capability, task coupling and task precedence constraints. Then, Dubins car model is adopted to calculate the mission execution time (objective function of CMTAP model) of each chromosome, and make each chromosome conform to the UAV maneuverability constraint. To balance the searching ability of algorithm and the diversity of population, we raise the modified crossover operator and multiple mutation operators according to the multi-type-gene chromosome encoding. The simulation results demonstrate that the modified GA has better optimization performance compared with random search method, ant colony optimization method and particle search optimization method.

Solving the Tree-Structured Task Allocation Problem via Group Multirole Assignment

Abstract: Task allocation is a critical phase of project management. Tree-type structures are frequently used constraints to obtain a pertinent task allocation. They can illustrate where one task may require numerous agents and when an agent can be assigned to different tasks (roles). The process of task allocation is made more complex when administrators need to satisfy sequential and fixed branch relationships between/among tasks (roles). This paper formalizes the tree-structured task allocation problem (TSTAP) with group multirole assignment (GMRA) and proves necessary conditions, the necessary and sufficient condition, as well as sufficient conditions, of TSTAP. The formalization makes it easy to find a solution with the IBM ILOG CPLEX optimization package (CPLEX). The necessary conditions improve the CPLEX solution by eliminating infeasible cases. The necessary and sufficient condition describes the solution space of TSTAP completely. Another exciting result is that the sufficient conditions can not only improve the CPLEX solution by describing a practical approximate solution space but also help decision-makers and human resource officers organize a team in order to successfully assign tasks. The proposed approach is verified by simulation experiments with respect to a real-world problem. The experimental results present the practicability of the proposed solutions in this paper. This paper was motivated by general cooperative projects whose tasks have tree-structured relationships. This can make the problem of successful multitask assignment extremely challenging. The traditional method of assignment such as the KM algorithm can no longer solve this problem. To solve the assignment problem with tree-structured relationships, an efficient many-to-many assignment with constraints is required. The proposed approach provides theoretical and technical foundations for efficient assignment of TSTA, which can not only provide a viable and effective assignment scheme for TSTA problems but also help human resource officers to formulate reasonable plans according to the relationships between/among tasks.

Maximizing Group Performance While Minimizing Budget

Abstract: Role assignment is an important and complex task in collaboration and management. Group role assignment (GRA) pursues the optimal team performance by assigning pertinent roles to agents in a team from the team’s viewpoint. There are many factors that should be considered when conducting role assignment. Budgets are such a factor. This paper presents a challenging role assignment problem in collaboration, called GRA with budget constraints (GRABC). This paper contributes a thorough investigation of the GRABC problem including: 1) the first formalization of the proposed problem; 2) a set of practical solutions to different forms of this problem by using the IBM ILOG CPLEX optimization package (CPLEX); 3) a set of necessary conditions for these problems to possess feasible solutions to improve the CPLEX solutions; and 4) a synthesized process to deal with GRABC problems. Contribution 2) actually clarifies a list of requirements in solving the GRABC problem. Simulations, experiments and a case study are used to verify the practicability and efficiency of the proposed solutions.

A parallel computing approach to solve traffic assignment using path-based gradient projection algorithm

Abstract: This paper presents a Parallel Block-Coordinate Descent (PBCD) algorithm for solving the user equilibrium traffic assignment problem. Most of the existing algorithms for the user equilibrium-based traffic assignment problem are developed and implemented sequentially. This paper aims to study and investigate the parallel computing approach to utilize the widely available parallel computing resources. The PBCD algorithm is developed based on the state-of-the-art path-based algorithm, i.e., the improved path-based gradient projection algorithm (iGP). The computationally expensive components in the iGP are identified and parallelized. A parallel block-coordinate method is proposed to replace the widely used Gauss-Seidel method for the procedure of path flow adjustment. A new rule is proposed to group OD pairs into different blocks. The numerical examples show that the implemented PBCD algorithm can significantly reduce the computing time.