Showing papers on "Assignment problem published in 2004"

Traffic signal timing optimisation based on genetic algorithm approach, including drivers’ routing

Abstract: The genetic algorithm approach to solve traffic signal control and traffic assignment problem is used to tackle the optimisation of signal timings with stochastic user equilibrium link flows. Signal timing is defined by the common network cycle time, the green time for each signal stage, and the offsets between the junctions. The system performance index is defined as the sum of a weighted linear combination of delay and number of stops per unit time for all traffic streams, which is evaluated by the traffic model of TRANSYT [User guide to TRANSYT, version 8, TRRL Report LR888, Transport and Road Research Laboratory, Crowthorne, 1980]. Stochastic user equilibrium assignment is formulated as an equivalent minimisation problem and solved by way of the Path Flow Estimator (PFE). The objective function adopted is the network performance index (PI) and its use for the Genetic Algorithm (GA) is the inversion of the network PI, called the fitness function. By integrating the genetic algorithms, traffic assignment and traffic control, the GATRANSPFE (Genetic Algorithm, TRANSYT and the PFE), solves the equilibrium network design problem. The performance of the GATRANSPFE is illustrated and compared with mutually consistent (MC) solution using numerical example. The computation results show that the GA approach is efficient and much simpler than previous heuristic algorithm. Furthermore, results from the test road network have shown that the values of the performance index were significantly improved relative to the MC.

Traffic grooming, routing, and wavelength assignment in optical WDM mesh networks

Abstract: In this paper, we consider the traffic grooming, routing, and wavelength assignment (GRWA) problem for optical mesh networks. In most previous studies on optical mesh networks, traffic demands are usually assumed to be wavelength demands, in which case no traffic grooming is needed. In practice, optical networks are typically required to carry a large number of lower rate (sub-wavelength) traffic demands. Hence, the issue of traffic grooming becomes very important since it can significantly impact the overall network cost. In our study, we consider traffic grooming in combination with traffic routing and wavelength assignment. Our objective is to minimize the total number of transponders required in the network. We first formulate the GRWA problem as an integer linear programming (ILP) problem. Unfortunately, for large networks it is computationally infeasible to solve the ILP problem. Therefore, we propose a decomposition method that divides the GRWA problem into two smaller problems: the traffic grooming and routing problem and the wavelength assignment problem, which can then be solved much more efficiently. In general, the decomposition method only produces an approximate solution for the GRWA problem. However, we also provide some sufficient condition under which the decomposition method gives an optimal solution. Finally, some numerical results are provided to demonstrate the efficiency of our method.

Simple Distributed Weighted Matchings

Abstract: Wattenhofer et al. [WW04] derive a complicated distributed algorithm to compute a weighted matching of an arbitrary weighted graph, that is at most a factor 5 away from the maximum weighted matching of that graph. We show that a variant of the obvious sequential greedy algorithm [Pre99], that computes a weighted matching at most a factor 2 away from the maximum, is easily distributed. This yields the best known distributed approximation algorithm for this problem so far.

On the power assignment problem in radio networks

Abstract: Given a finite set S of points (i.e. the stations of a radio network) on a d-dimensional Euclidean space and a positive integer 1 ≤ h ≤ |S| - 1, the MIN d D h-RANGE ASSIGNMENT problem consists of assigning transmission ranges to the stations so as to minimize the total power consumption, provided that the transmission ranges of the stations ensure the communication between any pair of stations in at most h hops.Two main issues related to this problem are considered in this paper: the trade-off between the power consumption and the number of hops; the computational complexity of the MIN dD h-RANGE ASSIGNMENT problem.As for the first question, we provide a lower bound on the minimum power consumption of stations on the plane for constant h. The lower bound is a function of |S|, h and the minimum distance over all the pairs of stations in S. Then, we derive a constructive upper bound as a function of |S|, h and the maximum distance over all pairs of stations in S (i.e. the diameter of S). It turns out that when the minimum distance between any two stations is "not too small" (i.e. well spread instances) the upper bound matches the lower bound. Previous results for this problem were known only for very special 1-dimensional configurations (i.e., when points are arranged on a line at unitary distance) [Kirousis, Kranakis, Krizanc and Pelc, 1997].As for the second question, we observe that the tightness of our upper bound implies that MIN 2D h-RANGE ASSIGNMENT restricted to well spread instances admits a polynomial time approximation algorithm. Then, we also show that the same approximation result can be obtained for random instances. On the other hand, we prove that for h=|S|-1 (i.e. the unbounded case) MIN 2D h-RANGE ASSIGNMENT is NP-hard and MIN 3D h-RANGE ASSIGNMENT is APX-complete.

A dynamic schedule-based model for congested transit networks

Abstract: In this paper we propose a model and algorithm for solving the equilibrium assignment problem in a congested, dynamic and schedule-based transit network. We assume that the time varying origin–destination trip demand is given. All travelers have full predictive information (that have been gained through past experience) about present and future network conditions and select paths that minimize a generalized cost function that encompasses four components: (a) in-vehicle time; (b) waiting time; (c) walking time; and (d) a line change penalty. All transit vehicles have a fixed capacity and operate precisely as specified in pre-set timetables. Passengers queue at platforms according to the single channel first-in-first-out discipline. By using time-increment simulation, the passenger demand is loaded onto the network and the available capacity of each vehicle is updated dynamically. After each simulation run, the passenger arrival and departure profiles at all stations are recorded and these are used to predict dynamic queuing delays. From such delays, minimum paths are updated and used for the next simulation run. The user equilibrium assignment problem is solved iteratively by the method of successive averages.

The Dynamic Assignment Problem

Abstract: There has been considerable recent interest in the dynamic vehicle routing problem, but the complexities of this problem class have generally restricted research to myopic models. In this paper, we address the simpler dynamic assignment problem, where a resource (container, vehicle, or driver) can serve only one task at a time. We propose a very general class of dynamic assignment models, and propose an adaptive, nonmyopic algorithm that involves iteratively solving sequences of assignment problems no larger than what would be required of a myopic model. We consider problems where the attribute space of future resources and tasks is small enough to be enumerated, and propose a hierarchical aggregation strategy for problems where the attribute spaces are too large to be enumerated. Finally, we use the formulation to also test the value of advance information, which offers a more realistic estimate over studies that use purely myopic models.

Convergence of Traffic Assignments: How Much Is Enough? 1

Abstract: Daily traffic assignments to a large-scale road network are described for Build and No-Build scenarios to evaluate the addition of two proposed ramps between I-295 and SR-42 in the New Jersey part of the Delaware Valley Region. The road network consists of 39,800 links connecting 1,510 zones. The user-equilibrium traffic assignment problem was solved with a new algorithm called origin-based assignment (OBA), which can achieve highly converged solutions with reasonable computing effort. Following a description of the user-equilibrium traffic assignment problem and the OBA algorithm, the stability of link flow differences between the two scenarios in the vicinity of the proposed ramps are examined over a broad range of assignment convergence levels. Then, link flow differences over this range of convergence levels are compared to link flow differences between two very highly converged solutions. Examination of the findings reveals in the authors' view that a relative gap of 0.01% (0.0001) is required to assure that the traffic assignments are sufficiently converged to achieve link flow stability. These convergence levels are then interpreted in terms of the number of Frank-Wolfe iterations needed to achieve comparable relative gaps, as well as the computational effort required.

Minimal Assignments for Bounded Model Checking

Abstract: A traditional counterexample to a linear-time safety property shows the values of all signals at all times prior to the error. However, some signals may not be critical to causing the failure. A succinct explanation may help human understanding as well as speed up algorithms that have to analyze many such traces. In Bounded Model Checking (BMC), a counterexample is constructed from a satisfying assignment to a Boolean formula, typically in CNF. Modern SAT solvers usually assign values to all variables when the input formula is satisfiable. Deriving minimal satisfying assignments from such complete assignments does not lead to concise explanations of counterexamples because of how CNF formulae are derived from the models. Hence, we formulate the extraction of a succinct counterexample as the problem of finding a minimal assignment that, together with the Boolean formula describing the model, implies an objective. We present a two-stage algorithm for this problem, such that the result of each stage contributes to identify the “interesting” events that cause the failure. We demonstrate the effectiveness of our approach with an example and with experimental results.

Models and algorithms for the traffic assignment problem with link capacity constraints

Abstract: This paper explores the models as well as solution techniques for the link capacitated traffic assignment problem (CTAP) that is capable of offering more realistic traffic assignment results. CTAP can be approximated by the uncapacitated TAP using different dual/penalty strategies. Two important and distinctive approaches in this category are studied and implemented efficiently. The inner penalty function (IPF) approach establishes a barrier on the boundary of the feasible set so that constraints are not violated in the solution process, and the augmented Lagrangian multiplier (ALM) approach combines the exterior penalty with primal–dual and Lagrangian multipliers concepts. In both implementations, a gradient projection (GP) algorithm was adopted as the uniform subproblem solver for its excellent convergence property and reoptimization capability. Numerous numerical results demonstrated through efficient implementations of either the IPF or the ALM approach that CTAP is computationally tractable even for large-scale problems. Moreover, the relative efficiency of IPF and ALM was explored and their sensitivity to different algorithmic issues was investigated.

An Improved Hybrid Genetic Algorithm: New Results for the Quadratic Assignment Problem

Abstract: Genetic algorithms (GAs) have been proven to be among the most powerful intelligent techniques in various areas of the computer science, including difficult optimization problems. In this paper, we propose an improved hybrid genetic algorithm (IHGA). It uses a robust local improvement procedure (a limited iterated tabu search (LITS)) as well as an effective restart (diversification) mechanism that is based on so-called “shift mutations”. IHGA has been applied to the well-known combinatorial optimization problem, the quadratic assignment problem (QAP). The results obtained from the numerous experiments on different QAP instances from the instances library QAPLIB show that the proposed algorithm appears to be superior to other modem heuristic approaches that are among the best algorithms for the QAP. The high efficiency of our algorithm is also corroborated by the fact that the new, recordbreaking solutions were obtained for a number of large real-life instances.

A proof of Parisi’s conjecture on the random assignment problem

Abstract: An assignment problem is the optimization problem of finding, in an m by n matrix of nonnegative real numbers, k entries, no two in the same row or column, such that their sum is minimal. Such an optimization problem is called a random assignment problem if the matrix entries are random variables. We give a formula for the expected value of the optimal k-assignment in a matrix where some of the entries are zero, and all other entries are independent exponentially distributed random variables with mean 1. Thereby we prove the formula 1+1/4+1/9+\...+1/k2 conjectured by G. Parisi for the case k=m=n, and the generalized conjecture of D. Coppersmith and G. B. Sorkin for arbitrary k, m and n.

Parametric eigenstructure assignment in second-order descriptor linear systems

Abstract: This note considers eigenstructure assignment in second-order descriptor linear systems via proportional plus derivative feedback. It is shown that the problem is closely related with a type of so-called second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable. The second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effect of the proposed approaches.

A hybrid Hopfield network-genetic algorithm approach for the terminal assignment problem

Abstract: This paper presents a hybrid Hopfield network-genetic algorithm (GA) approach to tackle the terminal assignment (TA) problem. TA involves determining minimum cost links to form a communications network, by connecting a given set of terminals to a given collection of concentrators. Some previous approaches provide very good results if the cost associated with assigning a single terminal to a given concentrator is known. However, there are situations in which the cost of a single assignment is not known in advance, and only the cost associated with feasible solutions can be calculated. In these situations, previous algorithms for TA based on greedy heuristics are no longer valid, or fail to get feasible solutions. Our approach involves a Hopfield neural network (HNN) which manages the problem's constraints, whereas a GA searches for high quality solutions with the minimum possible cost. We show that our algorithm is able to achieve feasible solutions to the TA in instances where the cost of a single assignment in not known in advance, improving the results obtained by previous approaches. We also show the applicability of our approach to other problems related to the TA.

An improved hybrid genetic algorithm for the generalized assignment problem

Abstract: We consider the generalized assignment problem in which the objective is to find a minimum cost assignment of a set of jobs to a set of agents subject to resource constraints. The presented new approach is based on a previously published, successful hybrid genetic algorithm and includes as new features two alternative initialization heuristics, a modified selection and replacement scheme for handling infeasible solutions more appropriately, and a heuristic mutation operator. Tests are performed on standard test instances from the literature and on newly created, larger and more difficult instances. The presented genetic algorithm with its two initialization variants is compared to the previous genetic algorithm and to the commercial general purpose branch-and-cut system CPLEX. Results indicate that CPLEX is able to solve relatively large instances of the general assignment problem to provable optimality. For the largest and most difficult instances, however, the proposed genetic algorithm yields on average the best results in shortest time.

Modeling queues at signalized intersections

Abstract: Traffic control is one of the most effective techniques for a road manager to adapt network capacity to flow. It also provides possibilities to modify users' choices of modes and routes. An important area of research is formed by the dynamic assignment problem, in which the effect of delays at controlled intersections is taken into account. This problem requires realistic queuing models. If the degree of saturation of an intersection is close to or larger than 1.0, the queue size has a dynamic character. The case in which the initial queue is nonzero is similar. Existing queue models have important limitations. A Markov model was developed to calculate the dynamics of the queue. It appears that the variance of the queue length is an important determinant of queue dynamics. The case of decreasing queues is analyzed and shows that available models in this case underestimate the mean values and are barely applicable in modeling time-of-day dynamics. An approximate expression for the case of decreasing queues is provided and analyzed with its parameters. Finally the same approach also suggests an approximate formulation for the evolution of the standard deviation with time and provides better knowledge of the uncertainties at signalized intersections. The analytical model introduced is suited for application in dynamic assignment problems.

Robust planning for coupled cooperative UAV missions

Abstract: This paper presents a new formulation for the UAV task assignment problem with uncertainty in the environment. The problem is posed as a task assignment with uncertainty in the cost information, and we apply a modified robust technique that allows the operator to tune the level of robustness in the optimization. This formulation is then used to solve the assignment problem for a heterogeneous fleet of vehicles operating in an uncertain environment. The key aspect of this formulation is that it directly addresses the inherent coupling in deciding how to assign vehicles to perform reconnaissance tasks that provide the most benefit to the strike part of the missions. We demonstrate that the robust solution to this coupled problem can be solved as single mixed-integer linear problem. The paper presents and discusses simulations for the proposed formulation, demonstrating significant improvements over previous ones.

GRASP with Path-Relinking for the Quadratic Assignment Problem

Abstract: This paper describes a GRASP with path-relinking heuristic for the quadratic assignment problem. GRASP is a multi-start procedure, where different points in the search space are probed with local search for high-quality solutions. Each iteration of GRASP consists of the construction of a randomized greedy solution, followed by local search, starting from the constructed solution. Path-relinking is an approach to integrate intensification and diversification in search. It consists in exploring trajectories that connect high-quality solutions. The trajectory is generated by introducing in the initial solution, attributes of the guiding solution. Experimental results illustrate the effectiveness of GRASP with path-relinking over pure GRASP on the quadratic assignment problem.

An empirical analysis of integer programming formulations for the permutation flowshop

Abstract: An empirical analysis was conducted to assess the relative effectiveness of four integer programming models for the regular permutation flowshop problem. Each of these models was used to solve a set of 60 flowshop problems. Analysis of the resultant computer solution times for each model indicated that the two assignment problem based models solved these problem instances in significantly less computer time than either of the two dichotomous constraints based models. Further, these computer solution time differences increased dramatically with increased numbers of jobs and machines in the flowshop problem. These results contradict Pan's conclusion that a variant of Manne's dichotomous constraints approach was superior to the assignment problem approaches of Wagner and Wilson because the Manne model required less than half of the binary integer variables required by the assignment problem based models.

Optimal pairing of signal components separated by blind techniques

Abstract: In this letter, the problem of optimal pairing of signal components separated by blind techniques in different time-windows or in different frequency bins is addressed. The optimum pairing is defined as the one which minimizes the sum of some distances (criteria of dissimilarity) of the to-be-assigned signal components. It is shown that the optimal pairing can be achieved by the Kuhn-Munkres algorithm known in graph theory as a solution to the optimal assignment problem. An advantage of the proposed pairing method is shown on data from electroencephalogram, which are blindly separated using the FastICA algorithm in a sliding time-window with the aim to study the time evolution of elements of the estimated mixing matrix.

On the Design of ACO for the Biobjective Quadratic Assignment Problem

Abstract: Few applications of ACO algorithms to multiobjective problems have been presented so far and it is not clear how to design an effective ACO algorithms for such problems. In this article, we study the performance of several ACO variants for the biobjective Quadratic Assignment Problem that are based on two fundamentally different search strategies. The first strategy is based on dominance criteria, while the second one exploits different scalarizations of the objective function vector. Further variants differ in the use of multiple colonies, the use of local search, and the pheromone update strategy. The experimental results indicate that the use of local search procedures and the correlation between objectives play an essential role in the performance of the variants studied in this paper.

New heuristics for over-constrained flight to gate assignments

Abstract: We consider the over-constrained Airport Gate Assignment Problem where the number of flights exceed the number of gates available, and where the objectives are to minimize the number of ungated flights and the total walking distances. The problem is formulated as a binary quadratic programming problem. We design a greedy algorithm and use a Tabu Search meta-heuristic to solve the problem. The greedy algorithm minimizes ungated flights while we devise a new neighbourhood search technique, the Interval Exchange Move, which allows us flexibility in seeking good solutions, especially when flight schedules are dense in time. Experiments conducted give good results.

Filter-Embedded UAV Task Assignment Algorithms for Dynamic Environments

Abstract: This paper presents a modified formulation of the classical task assignment problem that has recently been used to coordinate teams of UAVs. The main contribution is a version of the task assignment problem that can be used to tailor the control system to mitigate the eect of noise in the situational awareness on the solution. The net eect will be to limit the rate of change in the reassignment in a well-defined manner. The approach here is to perform reassignment at the rate that information is updated, which enables immediate reaction to any significant changes in the environment. We demonstrate that the modified formulation can be interpreted as a noise rejection algorithm that can be tuned to reduce the eect of variation in the uncertain parameters in the problem. Simulations are presented to demonstrate the eectiveness of this algorithm.

Aircraft and gate scheduling optimization at airports

Abstract: In this paper, we consider the over-constrained airport gate assignment problem where the number of flights exceeds the number of gates available, and where the objectives are to minimize the number of ungated flights and the total walking distances or connection. We design a greedy algorithm and use a tabu search meta-heuristic to solve the problem. The greedy algorithm minimizes ungated flights while providing initial feasible solutions while we devise a new neighborhood search technique, the interval exchange move, which allows us flexibility in seeking good solutions, especially in case when flight schedules are dense in time. Experiment conducted give good results.

Fleet Assignment Using Collective Intelligence

Abstract: Product distribution theory is a new collective intelligence-based framework for analyzing and controlling distributed systems. Its usefulness in distributed stochastic optimization is illustrated here through an airline fleet assignment problem. This problem involves the allocation of aircraft to a set of flights legs in order to meet passenger demand, while satisfying a variety of linear and non-linear constraints. Over the course of the day, the routing of each aircraft is determined in order to minimize the number of required flights for a given fleet. The associated flow continuity and aircraft count constraints have led researchers to focus on obtaining quasi-optimal solutions, especially at larger scales. In this paper, the authors propose the application of this new stochastic optimization algorithm to a non-linear objective cold start fleet assignment problem. Results show that the optimizer can successfully solve such highly-constrained problems (130 variables, 184 constraints).

From linear to semidefinite programming :An algorithm to obtain semidefinite relaxations for bivalent quadratic problems

Abstract: In this paper, we present a simple algorithm to obtain mechanically SDP relaxations for any quadratic or linear program with bivalent variables, starting from an existing linear relaxation of the considered combinatorial problem. A significant advantage of our approach is that we obtain an improvement on the linear relaxation we start from. Moreover, we can take into account all the existing theoretical and practical experience accumulated in the linear approach. After presenting the rules to treat each type of constraint, we describe our algorithm, and then apply it to obtain semidefinite relaxations for three classical combinatorial problems: the K-CLUSTER problem, the Quadratic Assignment Problem, and the Constrained-Memory Allocation Problem. We show that we obtain better SDP relaxations than the previous ones, and we report computational experiments for the three problems.