Topic
Assignment problem
About: Assignment problem is a research topic. Over the lifetime, 7588 publications have been published within this topic receiving 172820 citations. The topic is also known as: marriage problem.
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TL;DR: The results show that the bi-level model performs well with regard to the objective of reducing travel time costs for all travelers and balancing transit service level among all bus lines.
Abstract: This paper proposes a bi-level programming model to solve the design problem for bus lane distribution in multi-modal transport networks. The upper level model aims at minimizing the average travel time of travelers, as well as minimizing the difference of passengers’ comfort among all the bus lines by optimizing bus frequencies. The lower level model is a multi-modal transport network equilibrium model for the joint modal split/traffic assignment problem. The column generation algorithm, the branch-and-bound algorithm and the method of successive averages are comprehensively applied in this paper for the solution of the bi-level model. A simple numerical test and an empirical test based on Dalian economic zone are employed to validate the proposed model. The results show that the bi-level model performs well with regard to the objective of reducing travel time costs for all travelers and balancing transit service level among all bus lines.
121 citations
TL;DR: 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 and demonstrates that CTAP is computationally tractable even for large-scale problems.
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.
120 citations
TL;DR: In this paper, instead of modeling the pilot design as a combinatorial assignment problem, as in prior works, instead of expressing the pilot signals using a pilot basis and treating the associated power coefficients as continuous optimization variables, a lower bound on the uplink capacity for Rayleigh fading channels with maximum ratio detection was derived.
Abstract: This paper considers pilot design to mitigate pilot contamination and provide good service for everyone in multi-cell massive multiple-input-multiple-output systems. Instead of modeling the pilot design as a combinatorial assignment problem, as in prior works, we express the pilot signals using a pilot basis and treat the associated power coefficients as continuous optimization variables. We compute a lower bound on the uplink capacity for Rayleigh fading channels with maximum ratio detection that applies with arbitrary pilot signals. We further formulate the max-min fairness problem under power budget constraints, with the pilot signals and data powers as optimization variables. Because this optimization problem is non-deterministic polynomial-time hard due to signomial constraints, we then propose an algorithm to obtain a local optimum with polynomial complexity. Our framework serves as a benchmark for pilot design in scenarios with either ideal or non-ideal hardware. Numerical results manifest that the proposed optimization algorithms are close to the optimal solution obtained by exhaustive search for different pilot assignments and the new pilot structure and optimization bring large gains over the state-of-the-art suboptimal pilot design.
120 citations
TL;DR: A new randomized algorithm for the maximum matching problem is presented that is algebraic and works on the Tutte matrix of the given graph and the current best running time is O(m).
120 citations
01 Jul 1996
TL;DR: In this paper, the authors present a formulation of the continuous dynamic network loading problem where travel delays may be nonlinear functions of arc traffic volumes and propose a unique solution to the problem and propose for its solution a finite-step algorithm.
Abstract: The continuous dynamic network loading problem (CDNLP) consists in determining, on a congested network, time-dependent arc volumes, together with arc and path travel times, given the time varying path flow departure rates over a finite time horizon This problem constitutes an intrinsic part of the dynamic traffic assignment problem In this paper, the authors present a formulation of the CDNLP where travel delays may be nonlinear functions of arc traffic volumes They show, under a boundedness condition, that there exists a unique solution to the problem and propose for its solution a finite-step algorithm Some computational results are reported for a discretized version of the algorithm(A)
120 citations