Computation and application of the paired combinatorial logit stochastic user equilibrium problem

The paired combinatorial logit (PCL) model is one of the recent extended logit models adapted to resolve the overlapping problem in the route choice problem, while keeping the analytical tractability of the logit choice probability function. However, the development of efficient algorithms for solving the PCL model under congested and realistic networks is quite challenging, since it has large-dimensional solution variables as well as a complex objective function. In this paper, we examine the computation and application of the PCL stochastic user equilibrium (SUE) problem under congested and realistic networks. Specifically, we develop an improved path-based partial linearization algorithm for solving the PCL SUE problem by incorporating recent advances in line search strategies to enhance the computational efficiency required to determine a suitable stepsize that guarantees convergence. A real network in the city of Winnipeg is applied to examine the computational efficiency of the proposed algorithm and the robustness of various line search strategies. In addition, in order to acquire the practical implications of the PCL SUE model, we investigate the effectiveness of how the PCL model handles the effects of congestion, stochasticity, and similarity in comparison with the multinomial logit stochastic traffic equilibrium problem and the deterministic traffic equilibrium problem.     

A bi-level programming for logistics network design with system-optimized flows

This paper proposes a bi-level programming for a logistics network design problem with system-optimized flows. We applied the Wardrop’s second principle to the logistics network design problem. A system-optimized logistics network design problem can be formulated as a bi-level program. For the system-optimized flows, a user equilibrium traffic assignment problem with marginal costs can be solved at the lower level problem. Due to the non-differentiability of the perturbed solutions in system-optimized flows, we present a novel solution algorithm to efficiently solve the logistics network design problem. By using the subgradients of the objective function, a new projection method is proposed with global convergence. Numerical calculations are implemented using a grid-size hypothetical network and comparisons are made with other alternatives in solving the logistics network design problem. Numerical results disclose that the proposed method has successful solved the logistics network design problem and achieved significant performance both in computational efficacy and cost reduction when compared to other alternatives.     

混合遗传算法求解配送车辆调度问题

车辆调度优化是物流配送的关键环节。针对有时间窗的车辆调度问题,综合考虑了路网中的交通状况,提出改进的车辆调度模型。并针对这个模型,设计了混合遗传算法,采用自适应策略调整交叉和变异概率,引进有效的交叉和变异算子,并结合模拟退火算法缓解遗传算法的选择压力,避免早熟收敛。仿真结果表明该算法与标准遗传算法相比有更好的性能。     

Study on continuous network design problem using simulated annealing and genetic algorithm

In general, a continuous network design problem (CNDP) is formulated as a bi-level program. The objective function at the upper level is defined as the total travel time on the network, plus total investment costs of link capacity expansions. The lower level problem is formulated as a certain traffic assignment model. It is well known that such bi-level program is non-convex and non-differentiable and algorithms for finding global optimal solutions are preferable to be used in solving it. Simulated annealing (SA) and genetic algorithm (GA) are two global methods and can then be used to determine the optimal solution of CNDP. Since application of SA and GA on continuous network design on real transportation network requires solving traffic assignment model many times at each iteration of the algorithm, computation time needed is tremendous. It is important to compare the efficacy of the two methods and choose the more efficient one as reference method in practice. In this paper, the continuous network design problem has been studied using SA and GA on a simulated network. The lower level program is formulated as user equilibrium traffic assignment model and Frank–Wolf method is used to solve it. It is found that when demand is large, SA is more efficient than GA in solving CNDP, and much more computational effort is needed for GA to achieve the same optimal solution as SA. However, when demand is light, GA can reach a more optimal solution at the expense of more computation time. It is also found that increasing the iteration number at each temperature in SA does not necessarily improve solution. The finding in this example is different from [Karoonsoontawong, A., & Waller, S. T. (2006). Dynamic continuous network design problem – Linear bilevel programming and metaheuristic approaches. Network Modeling 2006 Transportation Research Record (1964) (pp. 104–117)]. The reason might be the bi-level model in this example is nonlinear while the bi-level model in their study is linear.     

Randomized Algorithms for 3-SAT

Schoning proposed a simple yet efficient randomized algorithm for solving the k-SAT problem. In the case of 3-SAT, the algorithm has an expected running time of poly(n)·(4/3)ⁿ = O(1.334ⁿ). In this paper we present randomized algorithms and show that one of them has O(1.3302ⁿ) expected running time, improving Schoning's algorithm. (Note. At this point, the fastest randomized algorithm for 3-SAT is the one given by Iwama and Tamaki that runs in O(1.324ⁿ).)     

An exact algorithm for the knapsack sharing problem

In this paper, we develop an exact algorithm for solving the knapsack sharing problem. The algorithm is a new version of the method proposed in Hifi and Sadfi (J. Combin. Optim. 6 (2002) 35). It seems quite efficient in the sense that it solves quickly some large problem instances. Its main principle consists of (i) finding a good set of capacities, representing a set of critical elements, using a heuristic approach, and (ii) varying the values of the obtained set in order to stabilize the optimal solution of the problem. Then, by exploiting dynamic programming properties, we obtain good equilibrium which lead to significant improvements. The performance of the proposed algorithm, based on a set of medium and large problem instances, is compared to the standard version of Hifi and Sadfi (2002). Encouraging results have been obtained.     

一种利用不完整数据检测交通异常的方法

城市化进程的加快带来了严重的交通问题,检测交通异常成为数据挖掘领域的热点之一。传统道路管理主要是应用视频监控,使得处理交通问题的效率受限。鉴于上述原因,提出了一种利用不完整数据检测交通异常的方法(Traffic Anomaly Detection,TAD)。首先,利用相关性聚类从手机数据中获取车辆密度信息,降低处理不完整数据的计算开销;然后,设计一个自适应无参数检测算法,根据手机呼叫量变化率捕捉车辆的分散式动态异常,以解决道路状况不确定性难题;最后,提出异常轨迹算法来追踪异常分布路线并预测影响范围,提高异常检测效率。实验结果表明,TAD方法在不同的实验环境下能够有效地检测交通异常,与现有算法相比,所提算法在有效性和伸缩性上效果更好。     

城市路网多路口路径动态实时选择方法

为了缓解城市交通拥堵问题,如何充分利用现有的道路资源进行有效的路线导航,一直是学者们关心的热点问题.现有的研究方法包括：优化交通灯信号周期以增大交通流量;对个别车辆的行驶路线进行优化;利用历史交通数据或者通过路网中心和车辆之间的主从式博弈进行路径导航等.然而,这些研究并没有考虑到微观行驶车辆的个性化交通需求以及多车辆彼此之间的路线选择冲突,对于城市路网中交通状况的动态不确定性也没有充分考虑.基于以上问题,提出了城市交通路网动态实时多路口路径选择模型DR²SM（dynamic and real-time route selection model in urban traffic networks）,结合车辆对前方可选路线的偏好以及可选路线的实时交通状况,并利用自适应学习算法SALA（self-adaptive learning algorithm）进行博弈,以使得各行驶车辆的动态路线选择策略达到Nash均衡.     

An in-place algorithm for Klee's measure problem in two dimensions

We present the first in-place algorithm for solving Klee's measure problem for a set of n axis-parallel rectangles in the plane. Our algorithm runs in O(n3/2logn) time and uses O(1) extra words in addition to the space needed for representing the input. The algorithm is surprisingly simple and thus very likely to yield an implementation that could be of practical interest. As a byproduct, we develop an optimal algorithm for solving Klee's measure problem for a set of n intervals; this algorithm runs in optimal time O(nlogn) and uses O(1) extra space.     

Self-adaptive ergodic algorithm for equilibrium problems over the fixed point set

ABSTRACT

We introduce a new ergodic algorithm for solving equilibrium problems over the fixed point set of a nonexpansive mapping. In contrast to the existing one in Kim [The Bruck's ergodic iteration method for the Ky Fan inequality over the fixed point set. Int. J. Comput. Math. 94 (2017), pp. 2466–2480], our algorithm uses self-adaptive step sizes. Thanks to that, the proposed algorithm converges under milder conditions. Moreover, at each step of our algorithm, instead of solving strongly convex problems, we only have to compute a subgradient of a convex function. Hence, our algorithm has lower computational cost.