Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userShareability Network Based Decomposition Approach for Solving Large-scale Multi-modal School Bus Routing Problems
67
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We consider the classic School Bus Routing Problem (SBRP) with a multi modal generalization, where students are either picked up by a fleet of school buses or transported by an alternate transportation mode, subject to a set of constraints. The constraints that are typically imposed for school buses are a maximum fleet size, a maximum walking distance to a pickup point and a maximum commute time for each student. This is a special case of the Vehicle Routing Problem (VRP) with a common destination. We propose a decomposition approach for solving this problem based on the existing notion of a shareability network, which has been used recently in the context of dynamic ridepooling problems. Moreover, we simplify the problem by introducing the connection between the SBRP and the weighted set covering problem (WSCP). To scale this method to large-scale problem instances, we propose i) a node compression method for the shareability network based decomposition approach, and ii) heuristic-based edge compression techniques that perform well in practice. We show that the compressed problem leads to an Integer Linear Programming (ILP) of reduced dimensionality that can be solved efficiently using off-the-shelf ILP solvers. Numerical experiments on small-scale, large-scale and benchmark networks are used to evaluate the performance of our approach and compare it to existing large-scale SBRP solving techniques.
rate research
Read More
Large-scale network systems describe a wide class of complex dynamical systems composed of many interacting subsystems. A large number of subsystems and their high-dimensional dynamics often result in highly complex topology and dynamics, which pose challenges to network management and operation. This chapter provides an overview of reduced-order modeling techniques that are developed recently for simplifying complex dynamical networks. In the first part, clustering-based approaches are reviewed, which aim to reduce the network scale, i.e., find a simplified network with a fewer number of nodes. The second part presents structure-preserving methods based on generalized balanced truncation, which can reduce the dynamics of each subsystem.
We consider the optimal coverage problem where a multi-agent network is deployed in an environment with obstacles to maximize a joint event detection probability. The objective function of this problem is non-convex and no global optimum is guaranteed by gradient-based algorithms developed to date. We first show that the objective function is monotone submodular, a class of functions for which a simple greedy algorithm is known to be within 0.63 of the optimal solution. We then derive two tighter lower bounds by exploiting the curvature information (total curvature and elemental curvature) of the objective function. We further show that the tightness of these lower bounds is complementary with respect to the sensing capabilities of the agents. The greedy algorithm solution can be subsequently used as an initial point for a gradient-based algorithm to obtain solutions even closer to the global optimum. Simulation results show that this approach leads to significantly better performance relative to previously used algorithms.
We report our progress on the project for solving larger scale quadratic assignment problems (QAPs). Our main approach to solve large scale NP-hard combinatorial optimization problems such as QAPs is a parallel branch-and-bound method efficiently implemented on a powerful computer system using the Ubiquity Generator (UG) framework that can utilize more than 100,000 cores. Lower bounding procedures incorporated in the branch-and-bound method play a crucial role in solving the problems. For a strong lower bounding procedure, we employ the Lagrangian doubly nonnegative (DNN) relaxation and the Newton-bracketing method developed by the authors group. In this report, we describe some basic tools used in the project including the lower bounding procedure and branching rules, and present some preliminary numerical results. Our next target problem is QAPs with dimension at least 50, as we have succeeded to solve tai30a and sko42 from QAPLIB for the first time.
Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article proposes a simple simulation-based approach for solving optimisation problems with steady state constraints relying on an ODE. This simulation-based optimisation method is tailored to the problem structure and exploits the local geometry of the steady state manifold and its stability properties. A parameterisation of the steady state manifold is not required. We prove local convergence of the method for locally strictly convex objective functions. Effciency and reliability of the proposed method are demonstrated in two examples. The proposed method demonstrated better convergence properties than existing general purpose methods and a significantly higher number of converged starts per time.
The capacitated arc routing problem is a very important problem with many practical applications. This paper focuses on the large scale capacitated arc routing problem. Traditional solution optimization approaches usually fail because of their poor scalability. The divide-and-conquer strategy has achieved great success in solving large scale optimization problems by decomposing the original large problem into smaller sub-problems and solving them separately. For arc routing, a commonly used divide-and-conquer strategy is to divide the tasks into subsets, and then solve the sub-problems induced by the task subsets separately. However, the success of a divide-and-conquer strategy relies on a proper task division, which is non-trivial due to the complex interactions between the tasks. This paper proposes a novel problem decomposition operator, named the route cutting off operator, which considers the interactions between the tasks in a sophisticated way. To examine the effectiveness of the route cutting off operator, we integrate it with two state-of-the-art divide-and-conquer algorithms, and compared with the original counterparts on a wide range of benchmark instances. The results show that the route cutting off operator can improve the effectiveness of the decomposition, and lead to significantly better results especially when the problem size is very large and the time budget is very tight.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
