Showing papers on "Assignment problem published in 2013"

The Quadratic Assignment Problem: Theory and Algorithms

Abstract: Preface. List of Figures. List of Tables. 1. Problem Statement and Complexity Aspects. 2. Exact Algorithms and Lower Bounds. 3. Heuristics and Asymptotic Behavior. 4. QAPs on Specially Structured Matrices. 5. Two More Restricted Versions of the QAP. 6. QAPs Arising as Optimization Problems in Graphs. 7. On the Biquadratic Assignment Problem (BIQAP). References. Notation Index. Subject Index.

Randomized primal-dual analysis of RANKING for online bipartite matching

Abstract: We give a simple proof that the ranking algorithm of Karp, Vazirani and Vazirani [KVV90] is 1-1/e competitive for the online bipartite matching problem. The proof is via a randomized primal-dual argument. Primal-dual algorithms have been successfully used for many online algorithm problems, but the dual constraints are always satisfied deterministically. This is the first instance of a non-trivial randomized primal-dual algorithm in which the dual constraints only hold in expectation. The approach also generalizes easily to the vertex-weighted version considered by Agarwal et al. [AGKM11]. Further we show that the proof is very similar to the deterministic primal-dual argument for the online budgeted allocation problem with small bids (also called the AdWords problem) of Mehta et al. [MSVV05].

An Optimal Online Algorithm for Weighted Bipartite Matching and Extensions to Combinatorial Auctions

Abstract: We study online variants of weighted bipartite matching on graphs and hypergraphs. In our model for online matching, the vertices on the right-hand side of a bipartite graph are given in advance and the vertices on the left-hand side arrive online in random order. Whenever a vertex arrives, its adjacent edges with the corresponding weights are revealed and the online algorithm has to decide which of these edges should be included in the matching. The studied matching problems have applications, e.g., in online ad auctions and combinatorial auctions where the right-hand side vertices correspond to items and the left-hand side vertices to bidders.

Relay Selection and Resource Allocation for Multi-User Cooperative OFDMA Networks

Abstract: The resource allocation problem is investigated for relay-based multi-user cooperative Orthogonal Frequency Division Multiple Access (OFDMA) uplink system, considering heterogeneous services. A quality of service (QoS) aware optimal relay selection, power allocation and subcarrier assignment scheme under a total power constraint is proposed. The relay selection, power allocation and subcarrier assignment problem is formulated as a joint optimization problem with the objective of maximizing the system throughput, which is solved by means of a two level dual decomposition and subgradient method. To further reduce the computational cost, two low-complexity suboptimal schemes are also proposed. The performance of the proposed schemes is demonstrated through computer simulations based on LTE-A network. Numerical results show that the proposed schemes support heterogeneous services while guaranteeing each user's QoS requirements with slight total system throughput degradation.

Reliability-based stochastic transit assignment with capacity constraints: Formulation and solution method

Abstract: This paper proposes a Linear Complementarity Problem (LCP) formulation for the reliability-based stochastic transit assignment problem with capacity constraints and non-additive link costs, where in-vehicle travel times and waiting times are uncertain. The capacity constraints are developed via the notions of effective capacity and chance constraints. An equivalent route-based linear program (LP) for the proposed problem is formulated to determine the patronage of each line section, critical links, critical service frequencies, unmet demand and the network capacity, which considers the risk-aversive behavior of travelers. A solution method is developed, utilizing the K-shortest path algorithm, the column generation technique, and the revised simplex method, to solve the proposed LP with guaranteed finite convergence. Numerical experiments are also set up to illustrate the properties of the problem and the application of the proposed model for reliability analysis.

Decision support for hospital bed management using adaptable individual length of stay estimations and shared resources

Abstract: Elective patient admission and assignment planning is an important task of the strategic and operational management of a hospital and early on became a central topic of clinical operations research. The management of hospital beds is an important subtask. Various approaches have been proposed, involving the computation of efficient assignments with regard to the patients’ condition, the necessity of the treatment, and the patients’ preferences. However, these approaches are mostly based on static, unadaptable estimates of the length of stay and, thus, do not take into account the uncertainty of the patient’s recovery. Furthermore, the effect of aggregated bed capacities have not been investigated in this context. Computer supported bed management, combining an adaptable length of stay estimation with the treatment of shared resources (aggregated bed capacities) has not yet been sufficiently investigated. The aim of our work is: 1) to define a cost function for patient admission taking into account adaptable length of stay estimations and aggregated resources, 2) to define a mathematical program formally modeling the assignment problem and an architecture for decision support, 3) to investigate four algorithmic methodologies addressing the assignment problem and one base-line approach, and 4) to evaluate these methodologies w.r.t. cost outcome, performance, and dismissal ratio. The expected free ward capacity is calculated based on individual length of stay estimates, introducing Bernoulli distributed random variables for the ward occupation states and approximating the probability densities. The assignment problem is represented as a binary integer program. Four strategies for solving the problem are applied and compared: an exact approach, using the mixed integer programming solver SCIP; and three heuristic strategies, namely the longest expected processing time, the shortest expected processing time, and random choice. A baseline approach serves to compare these optimization strategies with a simple model of the status quo. All the approaches are evaluated by a realistic discrete event simulation: the outcomes are the ratio of successful assignments and dismissals, the computation time, and the model’s cost factors. A discrete event simulation of 226,000 cases shows a reduction of the dismissal rate compared to the baseline by more than 30 percentage points (from a mean dismissal ratio of 74.7% to 40.06% comparing the status quo with the optimization strategies). Each of the optimization strategies leads to an improved assignment. The exact approach has only a marginal advantage over the heuristic strategies in the model’s cost factors (≤3%). Moreover,this marginal advantage was only achieved at the price of a computational time fifty times that of the heuristic models (an average computing time of 141 s using the exact method, vs. 2.6 s for the heuristic strategy). In terms of its performance and the quality of its solution, the heuristic strategy RAND is the preferred method for bed assignment in the case of shared resources. Future research is needed to investigate whether an equally marked improvement can be achieved in a large scale clinical application study, ideally one comprising all the departments involved in admission and assignment planning.

On Good and Fair Paper-Reviewer Assignment

Abstract: Peer review has become the most common practice for judging papers submitted to a conference for decades. An extremely important task involved in peer review is to assign submitted papers to reviewers with appropriate expertise which is referred to as paper-reviewer assignment. In this paper, we study the paper-reviewer assignment problem from both the goodness aspect and the fairness aspect. For the goodness aspect, we propose to maximize the topic coverage of the paper-reviewer assignment. This objective is new and the problem based on this objective is shown to be NP-hard. To solve this problem efficiently, we design an approximate algorithm which gives a 1/3-approximation. For the fairness aspect, we perform a detailed study on conflict-of-interest (COI) types and discuss several issues related to using COI, which, we hope, can raise some open discussions among researchers on the COI study. Finally, we conducted experiments on real datasets which verified the effectiveness of our algorithm and also revealed some interesting results of COI.

A Mean-Risk Model for the Traffic Assignment Problem with Stochastic Travel Times

Abstract: Heavy and uncertain traffic conditions exacerbate the commuting experience of millions of people across the globe. When planning important trips, commuters typically add an extra buffer to the expected trip duration to ensure on-time arrival. Motivated by this, we propose a new traffic assignment model that takes into account the stochastic nature of travel times. Our model extends the traditional model of Wardrop competition when uncertainty is present in the network. The focus is on strategic risk-averse users who capture the tradeoff between travel times and their variability in a mean-standard deviation (mean-stdev) objective, defined as the mean travel time plus a risk-aversion factor times the standard deviation of travel time along a path. We consider both infinitesimal users, leading to a non-atomic game, and atomic users, leading to a discrete finite game.We establish conditions that characterize an equilibrium traffic assignment and find when it exists. The main challenge is posed by the users’ risk aversion, since the mean-stdev objective is non-convex and non-separable, meaning that a path cannot be split as a sum of edge costs. As a result, even an individual user’s sub-problem — a stochastic shortest path problem — is a non-convex optimization problem for which no polynomial time algorithms are known. In turn, the mathematical structure of the traffic assignment model with stochastic travel times is fundamentally different from the deterministic counterpart. In particular, an equilibrium characterization requires exponentially many variables, one for each path in the network, since an edge-flow has multiple possible path-flow decompositions that are not equivalent. Because of this, characterizing the equilibrium and the socially-optimal assignment, which minimizes the total user cost, is more challenging than in the traditional deterministic setting. Nevertheless, we prove that both can be encoded by a representation with just polynomially-many paths. Finally, for the case of uncertainty parameters that are independent from edge loads, we show that although an equilibrium assignment results in a total user cost that is higher than that of the socially-optimal one, it is not higher than the analogous ratio in the deterministic setting. In other words, uncertainty does not further degrade the system performance in addition to strategic user behavior alone.

Binary particle swarm optimization (BPSO) based state assignment for area minimization of sequential circuits

Abstract: State assignment (SA) for finite state machines (FSMs) is one of the main optimization problems in the synthesis of sequential circuits It determines the complexity of its combinational circuit and thus area, delay, testability and power dissipation of its implementation Particle swarm optimization (PSO) is a non-deterministic heuristic that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality PSO optimizes a problem by having a population of candidate solutions called particles, and moving them around in the search-space according to a simple mathematical formulae In this paper, we propose an improved binary particle swarm optimization (BPSO) algorithm and demonstrate its effectiveness in solving the state assignment problem in sequential circuit synthesis targeting area optimization It will be an evident that the proposed BPSO algorithm overcomes the drawbacks of the original BPSO algorithm Experimental results demonstrate the effectiveness of the proposed BPSO algorithm in comparison to other BPSO variants reported in the literature and in comparison to Genetic Algorithm (GA), Simulated Evolution (SimE) and deterministic algorithms like Jedi and Nova

Gate Assignment to Minimize Passenger Transit Time and Aircraft Taxi Time

Abstract: This research focuses on airport gates, which are limited resources in the air transportation system. In spite of its importance, ramp congestion has not been considered in traditional research on gate assignment. This research, therefore, proposes a new perspective on the gate assignment problem that accounts for ramp congestion, as well as passenger flow. The proposed gate assignment problem minimizes weighted nominal taxi time and weighted taxi delay, as well as passenger transit time in the terminal. Nominal taxi time and taxi delay are weighted by the number of passengers on board. As a result, the flow in the passenger terminal and on ramps becomes efficient. To get near-optimal solutions within a reasonable amount of time, two metaheuristic algorithms, tabu search and genetic algorithm, are implemented for two ramp configurations. Also, the tradeoff between passenger flow and ramp congestion is analyzed.

A model induced max-min ant colony optimization for asymmetric traveling salesman problem

Abstract: A large number of hybrid metaheuristics for asymmetric traveling salesman problem (ATSP) have been proposed in the past decades which produced better solutions by exploiting the complementary characteristics of different optimization strategies. However, most of the hybridizations are criticized due to lacking of sufficient analytical basis. In this paper, a model induced max-min ant colony optimization (MIMM-ACO) is proposed to bridge the gap between hybridizations and theoretical analysis. The proposed method exploits analytical knowledge from both the ATSP model and the dynamics of ACO guiding the behavior of ants which forms the theoretical basis for the hybridization. The contribution of this paper mainly includes three supporting propositions that lead to two improvements in comparison with classical max-min ACO optimization (MM-ACO): (1) Adjusted transition probabilities are developed by replacing the static biased weighting factors with the dynamic ones which are determined by the partial solution that ant has constructed. As a byproduct, nonoptimal arcs will be indentified and excluded from further consideration based on the dual information derived from solving the associated assignment problem (AP). (2) A terminal condition is determined analytically based on the state of pheromone matrix structure rather than intuitively as in most traditional hybrid metaheuristics. Apart from the theoretical analysis, we experimentally show that the proposed algorithm exhibits more powerful searching ability than classical MM-ACO and outperforms state of art hybrid metaheuristics.

A Network-Based Model for the Integrated Weekly Aircraft Maintenance Routing and Fleet Assignment Problem

Abstract: Most studies in airline operations planning research are focused on the optimization problems that deal with a daily flight schedule, which is considered to be the same for every day in the week. While the weekly schedule is more realistic and practical, it increases the complexity of the optimization problems drastically. In this paper, we present a novel weekly rotation-tour network representation for the weekly aircraft maintenance routing problem (WAMRP). Based on this representation, we propose a new network-based mixed-integer linear programming (LP) formulation for the WAMRP; namely, weekly rotation-tour network model (WRTNM). The main advantage of this formulation is that the size of WRTNM only increases linearly with the size of the weekly schedule, and it provides a very tight LP relaxation. In addition, because of the tight LP relaxation, we develop a diving heuristic to solve WRTNM efficiently and effectively. To assess the performance of WRTNM, we tested the WRTNM using eight real-life test c...

Distributed algorithm design for multi-robot task assignment with deadlines for tasks

Abstract: In this paper, we present provably-good algorithms for multi-robot task assignment, where each task has to be completed within its deadline. Each robot has a upper limit on the maximum number of tasks that it can perform due to its limited battery life, and each task takes the same amount of time to complete. Each robot has a different payoff (or cost) for the tasks and the objective is to assign the tasks to the robots such that the total payoff (cost) is maximized (minimized) while respecting the task deadline constraints. This problem is an extension of a special generalized assignment problem (where each task consumes the same time resource and must be finished), with additional deadline constraints for the time resource assignment. We show that the problem can be reduced to a problem of assigning tasks to robots, where the tasks are organized in overlapping sets, and each robot has a limit on the number of tasks it can perform from each set, which is a variant of multi-robot assignment problem with set precedence constraint (SPC-MAP) discussed in [1].We present a distributed auction-based algorithm for this problem and prove that the solution is almost-optimal. We also present simulation results to depict the performance of our algorithm.

Trajectory Planning and Assignment in Multirobot Systems

Abstract: In this paper, we consider the problem of tasking large numbers of homogenous robots to move to a set of specified goal locations, addressing both the assignment and trajectory planning subproblems concurrently. This is related to the standard linear Euclidean assignment problem except that the solution to the trajectory generation subproblem must result in time-parameterized trajectories and guarantee collision avoidance.We begin with a centralized approach and derive an optimal centralized solution and study the computational complexity. The main contribution of this paper, however, is a decentralized algorithm with limited communication between neighbors that guarantees collision-avoidance and overcomes the computational challenges of the centralized method at the cost of suboptimal solutions. We demonstrate the performance of the algorithm as the number of robots is increased to tens of robots and the resulting increase in communication across neighbors required for safe execution.

How to sell hyperedges: the hypermatching assignment problem

Abstract: We are given a set of clients with budget constraints and a set of indivisible items. Each client is willing to buy one or more bundles of (at most) k items each (bundles can be seen as hyperedges in a k-hypergraph). If client i gets a bundle e, she pays bi,e and yields a net profit wi,e. The Hypermatching Assignment Problem (HAP) is to assign a set of pairwise disjoint bundles to clients so as to maximize the total profit while respecting the budgets. This problem has various applications in production planning and budget-constrained auctions and generalizes well-studied problems in combinatorial optimization: for example the weighted (unweighted) k-hypergraph matching problem is the special case of HAP with one client having unbounded budget and general (unit) profits; the Generalized Assignment Problem (GAP) is the special case of HAP with k = 1.Let e > 0 denote an arbitrarily small constant. In this paper we obtain the following main results:• We give a randomized (k + 1 + e) approximation algorithm for HAP, which is based on rounding the 1-round Lasserre strengthening of a novel LP. This is one of a few approximation results based on Lasserre hierarchies and our approach might be of independent interest. We remark that for weighted k-hypergraph matching no LP nor SDP relaxation is known to have integrality gap better than k − 1 + 1/k for general k [Chan and Lau, SODA'10].• For the relevant special case that one wants to maximize the total revenue (i.e., bi,e = wi,e), we present a local search based (k + O (√k))/2 approximation algorithm for k = O(1). This almost matches the best known (k + 1 + e)/2 approximation ratio by Berman [SWAT'00] for the (less general) weighted k-hypergraph matching problem.• For the unweighted k-hypergraph matching problem, we present a (k + 1 + e)/3 approximation in quasipolynomial time. This improves over the (k + 2)/3 approximation by Halldorsson [SODA'95] (also in quasipolynomial time). In particular this suggests that a 4/3 + e approximation for 3-dimensional matching might exist, whereas the currently best known polynomial-time approximation ratio is 3/2.

A heuristic algorithm based on multi-assignment procedures for nurse scheduling

Abstract: This paper tackles a Nurse Scheduling Problem which consists of generating work schedules for a set of nurses while considering their shift preferences and other requirements. The objective is to maximize the satisfaction of nurses? preferences and minimize the violation of soft constraints. This paper presents a new deterministic heuristic algorithm, called MAPA (multi-assignment problem-based algorithm), which is based on successive resolutions of the assignment problem. The algorithm has two phases: a constructive phase and an improvement phase. The constructive phase builds a full schedule by solving successive assignment problems, one for each day in the planning period. The improvement phase uses a couple of procedures that re-solve assignment problems to produce a better schedule. Given the deterministic nature of this algorithm, the same schedule is obtained each time that the algorithm is applied to the same problem instance. The performance of MAPA is benchmarked against published results for almost 250,000 instances from the NSPLib dataset. In most cases, particularly on large instances of the problem, the results produced by MAPA are better when compared to best-known solutions from the literature. The experiments reported here also show that the MAPA algorithm finds more feasible solutions compared with other algorithms in the literature, which suggest that this proposed approach is effective and robust.

Minimizing Warehouse Space with a Dedicated Storage Policy

Abstract: Given the increasingly significant impact of an efficient product-location strategy on warehouses' performance from a service level and operational costs perspective, this paper presents a possible operations research-oriented solution to provide a tangible reduction of the overall required warehousing space, thereby translating the storage location assignment problem (SLAP) into a vertex colouring problem (VCP). Developing the topic of their previous work on the development of an effective multi-product slot- code optimization heuristic, the authors focused on finding a cost-effective way to solve the SLAP through a mathematical-optimization approach. The formulation validation on a real industrial case showed its high optimization potential, and benchmarking simulations displayed performances significantly close to the best theoretical case. Indeed, the optimized value results were definitively close to the SLAP lower bound calculated assuming a randomized storage policy which, distinct from the developed solution, must inevitably be supported by warehouse management system software. On the contrary, the proposed methodology relies upon a dedicated storage policy, which is easily implementable by companies of all sizes without the need for investing in expensive IT tools.

A Memetic Algorithm for staff scheduling problem in airport security service

Abstract: The staff scheduling problem is widely studied in Operational Research. Various surveys are available in the literature dealing with this problem which concerns various objectives and various constraints. In this article, we present a staff scheduling problem in airport security service. First, a modeling of the problem, and a representation of solutions are shown. The problem is solved in three steps, days-off scheduling, shift scheduling, and staff assignment. We focus on the last step, by providing a Memetic Algorithm (MA) which merged an Evolutionary Algorithm and Local Search techniques. We propose a chromosome encoding, a crossover operator and a combined neighborhood function, specially dedicated to this staff assignment problem. Besides providing better solutions than software currently used, this algorithm provides up to 50% of improvement from initial feasible solutions.

A Task Assignment Algorithm for Multiple Aerial Vehicles to Attack Targets With Dynamic Values

Abstract: A good task assignment is an important guarantee to achieve great combat effectiveness. This paper investigates the task assignment problem, where the value of the targets is time changing in the battlefield, and presents a solution approach that is a combination of two algorithms: the multidestination route planning algorithm based on dynamic programming and the multisubgroup ant colony algorithm (MSACO). The two algorithms coordinately solve the task assignment problem. The route planning algorithm can obtain available routes between any two targets and provide reasonable routing information for MSACO. Then, the ant colony algorithm is applied to solve the task assignment problem. To solve the task assignment problem in the battlefield environment, several key technologies are introduced to improve the traditional ant colony algorithm, which include the subgroup selection strategy, the dynamic candidate aggregate policy, the state transferring policy, and the information-element updating mechanism. Simulation results show that the proposed approach can produce a reasonable and available plan for all the test cases in short computational time.

Achieving User-Level Fairness in Open-Access Femtocell-Based Architecture

Abstract: Femtocell-based architectures have the potential to position the cellular service providers to compete head-on with the WiFi market. However, significant interference can happen due to unplanned deployments. Current use of hard partitioning approaches for resource allocation, and lack of guidelines for configuring the femtocells, makes it difficult to obtain significant performance gains over traditional cellular networks. In this paper, we study the dynamic OFDMA subchannel assignment problem while jointly considering power assignment and association control to provide maxmin fairness. Toward this objective, we first consider a noninterfering model (NINT model), which disallows interfering femtocells in the solution. A more general interfering model (INT model) is then considered under which the problem is transformed into the partition coloring problem. We then show the NP-hardness of the problems and design centralized approximation algorithms with provable bounds and distributed solutions. Through extensive simulations in realistic settings we show that, compared to previous work, our solutions under the NINT model can achieve two times the minimum throughput, and under the INT model the minimum throughput can be up to three times the baseline algorithms.

Barrier Coverage in Hybrid Directional Sensor Networks

Abstract: Barrier coverage is a critical issue in wireless sensor networks for security applications (e.g., border protection) where directional sensors (e.g., cameras) are becoming more popular and advantageous than omni-directional scalar sensors for the extra dimensional information they provide. However, barrier coverage can not be guaranteed after initial random deployment of sensors, especially for directional sensors with limited sensing angles. In this paper, we study how to efficiently achieve barrier coverage in hybrid directional sensor networks by moving mobile sensors to fill in gaps and form a barrier with stationary sensors. In specific, we introduce the notion of directional barrier graph to model the barrier coverage formation problem. We prove that the minimum number of mobile sensors required to form a barrier with stationary sensors is the length of the shortest path from the source node to the destination node on the directional barrier graph. We then formulate the problem of minimizing the cost of moving mobile sensors to fill in the gaps on the shortest path as a minimum cost bipartite assignment problem, and solve it in polynomial time using the Hungarian algorithm. Both analytical and experimental studies demonstrate the effectiveness of the proposed algorithm.

A Logarithmic Method for Reducing Binary Variables and Inequality Constraints in Solving Task Assignment Problems

Abstract: This paper studies the classical task assignment problem TAP in which M unbreakable tasks are assigned to N agents with the objective to minimize the communication and process costs subject to each agent's capacity constraint. Because a large-size TAP involves many binary variables, most, if not all, traditional methods experience the difficulty in solving the problem within a reasonable time period. Recent works present a logarithmic approach to reduce the number of binary variables in problems with mixed-integer variables. This study proposes a new logarithmic method that significantly reduces the numbers of binary variables and inequality constraints in solving task assignment problems. Our numerical experiments demonstrate that the proposed method is superior to other known methods of this kind for solving large-size TAPs.