Showing papers on "Assignment problem published in 2007"

Autonomous Vehicle-Target Assignment: A Game-Theoretical Formulation

Abstract: We consider an autonomous vehicle-target assignment problem where a group of vehicles are expected to optimally assign themselves to a set of targets. We introduce a game-theoretical formulation of the problem in which the vehicles are viewed as self-interested decision makers. Thus, we seek the optimization of a global utility function through autonomous vehicles that are capable of making individually rational decisions to optimize their own utility functions. The first important aspect of the problem is to choose the utility functions of the vehicles in such a way that the objectives of the vehicles are localized to each vehicle yet aligned with a global utility function. The second important aspect of the problem is to equip the vehicles with an appropriate negotiation mechanism by which each vehicle pursues the optimization of its own utility function. We present several design procedures and accompanying caveats for vehicle utility design. We present two new negotiation mechanisms, namely, "generalized regret monitoring with fading memory and inertia" and "selective spatial adaptive play," and provide accompanying proofs of their convergence. Finally, we present simulations that illustrate how vehicle negotiations can consistently lead to near-optimal assignments provided that the utilities of the vehicles are designed appropriately.

Experimental Analysis of Heuristics for the STSP

Abstract: In this and the following chapter, we consider what approaches one should take when one is confronted with a real-world application of the TSP. What algorithms should be used under which circumstances? We are in particular interested in the case where instances are too large for optimization to be feasible. Here theoretical results can be a useful initial guide, but the most valuable information will likely come from testing implementations of the heuristics on test beds of relevant instances. This chapter considers the symmetric TSP; the next considers the more general and less well-studied asymmetric case.

The Dynamic Hungarian Algorithm for the Assignment Problem with Changing Costs

Abstract: In this paper, we present the dynamic Hungarian algorithm, applicable to optimally solving the assignment problem in situations with changing edge costs or weights This problem is relevant, for example, in a transportation domain where the unexpected closing of a road translates to changed transportation costs When such cost changes occur after an initial assignment has been made, the new problem, like the original problem, may be solved from scratch using the well-known Hungarian algorithm However, the dynamic version of the algorithm which we present solves the new problem more efficiently by repairing the initial solution obtained before the cost changes We present proofs of the correctness and efficiency of our algorithm and present simulation results illustrating its efficiency

Direct Optimization of Ranking Measures

Abstract: Web page ranking and collaborative filtering require the optimization of sophisticated performance measures. Current Support Vector approaches are unable to optimize them directly and focus on pairwise comparisons instead. We present a new approach which allows direct optimization of the relevant loss functions. This is achieved via structured estimation in Hilbert spaces. It is most related to Max-Margin-Markov networks optimization of multivariate performance measures. Key to our approach is that during training the ranking problem can be viewed as a linear assignment problem, which can be solved by the Hungarian Marriage algorithm. At test time, a sort operation is sufficient, as our algorithm assigns a relevance score to every (document, query) pair. Experiments show that the our algorithm is fast and that it works very well.

Sub-population genetic algorithm with mining gene structures for multiobjective flowshop scheduling problems

Abstract: According to previous research of Chang et al [Chang, P C, Chen, S H, & Lin, K L (2005b) Two phase sub-population genetic algorithm for parallel machine scheduling problem Expert Systems with Applications, 29(3), 705-712], the sub-population genetic algorithm (SPGA) is effective in solving multiobjective scheduling problems Based on the pioneer efforts, this research proposes a mining gene structure technique integrated with the SPGA The mining problem of elite chromosomes is formulated as a linear assignment problem and a greedy heuristic using threshold to eliminate redundant information As a result, artificial chromosomes are created according to this gene mining procedure and these artificial chromosomes will be reintroduced into the evolution process to improve the efficiency and solution quality of the procedure In addition, to further increase the quality of the artificial chromosome, a dynamic threshold procedure is developed and the flowshop scheduling problems are applied as a benchmark problem for testing the developed algorithm Extensive tests in the flow-shop scheduling problem show that the proposed approach can improve the performance of SPGA significantly

Sorting out the document identifier assignment problem

Abstract: The compression of Inverted File indexes in Web Search Engines has received a lot of attention in these last years. Compressing the index not only reduces space occupancy but also improves the overall retrieval performance since it allows a better exploitation of the memory hierarchy. In this paper we are going to empirically show that in the case of collections of Web Documents we can enhance the performance of compression algorithms by simply assigning identifiers to documents according to the lexicographical ordering of the URLs. We will validate this assumption by comparing several assignment techniques and several compression algorithms on a quite large document collection composed by about six million documents. The results are very encouraging since we can improve the compression ratio up to 40% using an algorithm that takes about ninety seconds to finish using only 100 MB of main memory.

Bounds for the quadratic assignment problem using the bundle method

Abstract: Semidefinite programming (SDP) has recently turned out to be a very powerful tool for approximating some NP-hard problems. The nature of the quadratic assignment problem (QAP) suggests SDP as a way to derive tractable relaxations. We recall some SDP relaxations of QAP and solve them approximately using a dynamic version of the bundle method. The computational results demonstrate the efficiency of the approach. Our bounds are currently among the strongest ones available for QAP. We investigate their potential for branch and bound settings by looking also at the bounds in the first levels of the branching tree.

A parallel approximation algorithm for the weighted maximum matching problem

Abstract: We consider the problem of computing a weighted edge matching in a large graph using a parallel algorithm. This problem has application in several areas of combinatorial scientific computing. Since an exact algorithm for the weighted matching problem is both fairly expensive to compute and hard to parallelise we instead consider fast approximation algorithms. We analyse a distributed algorithm due to Hoepman [8] and show how this can be turned into a parallel algorithm. Through experiments using both complete as well as sparse graphs we show that our new parallel algorithm scales well using up to 32 processors.

Lexicographic Maxmin Fairness for Data Collection in Wireless Sensor Networks

Abstract: The ad hoc deployment of a sensor network causes unpredictable patterns of connectivity and varied node density, resulting in uneven bandwidth provisioning on the forwarding paths. When congestion happens, some sensors may have to reduce their data rates. It is an interesting but difficult problem to determine which sensors must reduce rates and how much they should reduce. This paper attempts to answer a fundamental question about congestion resolution: What are the maximum rates at which the individual sensors can produce data without causing congestion in the network and unfairness among the peers? We define the maxmin optimal rate assignment problem in a sensor network, where all possible forwarding paths are considered. We provide an iterative linear programming solution, which finds the maxmin optimal rate assignment and a forwarding schedule that implements the assignment in a low-rate sensor network. We prove that there is one and only one such assignment for a given configuration of the sensor network. We also study the variants of the maxmin fairness problem in sensor networks.

An effective and fast heuristic for the Dial-a-Ride problem

Abstract: Dial-a-Ride is an emerging transport system, in which a fleet of vehicles, without fixed routes and schedules, carries people from the desired pickup point to the desired delivery point, during a pre-specified time interval. It can be modeled as an $$\mathcal{NP}$$ -hard routing and scheduling problem, with a suitable mixed integer programming formulation. Exact approaches to this problem are too limited to tackle real-life instances (hundred of trips), therefore heuristics are needed. The heuristic method proposed in this paper builds an auxiliary graph and then solves an assignment problem on this graph. The auxiliary graph is obtained by replacing pairs of nodes with a single one and associating an ad hoc cost function to the new set of arcs. Two different simple methods are employed to transform the infeasible solution given by the assignment problem into a feasible one. The proposed algorithms have been tested on instances created using the Milan network and shown to be fast and effective.

Learning Graph Matching

Abstract: As a fundamental problem in pattern recognition, graph matching has found a variety of applications in the field of computer vision. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. There are many ways in which the problem has been formulated, but most can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility functions and a quadratic term encodes edge compatibility functions. The main research focus in this theme is about designing efficient algorithms for solving approximately the quadratic assignment problem, since it is NP-hard. In this paper, we turn our attention to the complementary problem: how to estimate compatibility functions such that the solution of the resulting graph matching problem best matches the expected solution that a human would manually provide. We present a method for learning graph matching: the training examples are pairs of graphs and the "labels" are matchings between pairs of graphs. We present experimental results with real image data which give evidence that learning can improve the performance of standard graph matching algorithms. In particular, it turns out that linear assignment with such a learning scheme may improve over state-of-the-art quadratic assignment relaxations. This finding suggests that for a range of problems where quadratic assignment was thought to be essential for securing good results, linear assignment, which is far more efficient, could be just sufficient if learning is performed.

A Dynamical System Model of the Traffic Assignment Problem

Abstract: User equilibrium is a central concept for studying transportation networks, and one can view it as the result of a dynamical process of drivers’ route choice behavior In this paper, based on a definition of O–D first-in-first-out violation, we propose a new dynamical system model of the route choice behavior at the aggregate, route level for both static and dynamic transportation networks An equilibrium of such a dynamical system can be a user equilibrium or a partial user equilibrium We prove that, for static, symmetric traffic assignment problem with fixed or variable demand, only user equilibria are stable for the dynamical system, and the objective function in the mathematical programming formulation [Beckmann, M, McGuire, CB, Winsten, CB, 1956 Studies in the Economics of Transportation Yale University Press, New Haven, Connecticut, also published as Rand-RM-1488-PR, Rand Corporation, Santa Monica, CA, May 12, 1955] can be considered as the potential energy of the dynamical system We then present an Euler-based perturbation method for finding user equilibrium and solve two examples for both static and dynamic traffic assignment problems This new model is simple in form and could be applied to analyze other properties of transportation networks

An Additive Branch-and-Bound Algorithm for the Pickup and Delivery Traveling Salesman Problem with LIFO or FIFO Loading

Abstract: This paper introduces an additive branch-and-bound algorithm for two variants of the pickup and delivery traveling salesman problem in which loading and unloading operations have to be performed either in a Last-In-First-Out (LIFO) or in a First-In-First-Out (FIFO) order. Two relaxations are used within the additive approach: the assignment problem and the shortest spanning r-arborescence problem. The quality of the lower bounds is further improved by a set of elimination rules applied at each node of the search tree to remove from the problem arcs that cannot belong to feasible solutions because of precedence relationships. The performance of the algorithm and the effectiveness of the elimination rules are assessed on instances from the literature.

Assigning Micro UAVs to Task Tours in an Urban Terrain

Abstract: An optimization algorithm for assigning in realtime multiple unmanned aerial vehicles (UAVs) to task tours is presented and tested as part of a flight demonstration program. The scenario of interest is one where multiple microaerial vehicles are launched from a small UAV in order to investigate selected targets in an urban terrain. For path planning, we use the Dubin's car model so that the vehicles' dynamic constraint of minimum turning radius is taken into account. Due to the prohibitive computational complexity of the coupled path optimization and assignment problem, we solve the problem by ordering a set of tasks based on the Euclidean distance, utilizing a traveling salesman problem solver. We apply upper and lower bounding procedures iteratively on active subsets within the set of feasible group assignments, enabling efficient search of the solution space. The online implementation of the algorithm is discussed and simulation results confirm the efficiency of the proposed algorithm. Results from recent flight tests are also provided.

The AI conference paper assignment problem

Abstract: The Conference Paper Assignment Problem (CPAP) is the problem of assigning reviewers to conference paper submissions in a manner intended to minimize whingeing It is assumed that papers are reviewed by members of a preset program committee (PC), each of whom has the opportunity to bid on papers prior to the assignment algorithm being run In this survey, we show that CPAP is in P if the only information given is individual program committee members’ preferences for individual papers However, if both preferences and expertise (based on, say, keywords) are given, the problem is potentially more complex

An efficient Genetic Algorithm with uniform crossover for the multi-objective Airport Gate Assignment Problem

Abstract: Genetic Algorithms (GAs) have a good potential of solving the Gate Assignment Problem (GAP) at airport terminals, and the design of feasible and efficient evolutionary operators, particularly, the crossover operator, is crucial to successful implementations. This paper reports an application of GAs to the multi-objective GAP. The relative positions between aircraft rather than their absolute positions in the queues to gates is used to construct chromosomes in a novel encoding scheme, and a new uniform crossover operator, free of feasibility problems, is then proposed, which is effective and efficient to identify, inherit and protect useful common sub-queues to gates during evolution. Extensive simulation studies illustrate the advantages of the proposed GA scheme with uniform crossover operator.

Exact Methods for the Asymmetric Traveling Salesman Problem

Abstract: In the present chapter we concentrate on the exact solution methods for the Asymmetric TSP proposed in the literature after the writing of the survey of [81] In Section 2 two specific branch-and-bound methods, based on the solution of the assignment problem as a relaxation, are presented and compared In Section 3 a branch- and-bound method based on the computation of an additive bound is described, while in Section 4 a branch-and-cut approach is discussed Finally, in Section 5 all these methods are computationally tested on a large set of instances, and compared with an effective branch-and-cut code for the symmetric TSP

Assignment and Scheduling in Flexible Job-Shops by Hierarchical Optimization

Abstract: In this paper, we propose a new hierarchical method for the flexible job-shop scheduling problem (FJSP). This approach is mainly adapted to a job-shop problem (JSP) with high flexibility and is based on the decomposition of the problem in an assignment subproblem and a sequencing subproblem. For the first subproblem, we propose two methods: the first one is based successively on a heuristic approach and a local search; the second one, however, is based on a branch-and-bound algorithm. The quality of the assignment is evaluated by a lower bound. For the second subproblem we apply a hybrid genetic algorithm to deal with the sequencing problem. Computational tests are finally presented.

Optimization of air vehicles operations using mixed-integer linear programming

Abstract: A scenario where multiple air vehicles are required to prosecute geographically dispersed targets is considered. Furthermore, multiple tasks are to be successively performed on each target, that is, the targets must be classified, attacked, and verified as destroyed. The optimal, for example, minimum time, performance of these tasks requires cooperation among the vehicles such that critical timing constraints are satisfied, that is, a target must be classified before it can be attacked, and an air vehicle is sent to a target area to verify its destruction only after the target has been attacked. In this paper, the optimal task assignment/scheduling problem is posed as a mixed-integer linear program (MILP). The solution of the MILP assigns all tasks to the vehicles and performs the scheduling in an optimal manner, including staged departure times. Coupled tasks involving timing and task order constraints are automatically addressed. When the air vehicles have sufficient endurance, the existence of a solution is guaranteed.