In this project, we will discuss about **quickest flow problem**, Quick-TDQFP heuristic, Path-Finding Algorithms, Zero-Sum Cycles, and more. We will present a quick solution technique for the integral time-dependent quickest flow problem with no waiting. The offered method is in accordance with the successive shortest path technique and modifies a present algorithm to further improve its average performance. A reoptimization process is utilized to figure out the augmenting path given updates to the residual graph. The residual graph, by construction, usually has **zero-sum cycles** when used in this situation. These zero-sum cycles cause a distinctive problem for the reoptimization technique. We have proposed a heuristic which could be embedded in the reoptimization algorithm to give path solutions in the occurrence of zero-sum cycles. In the computational experiments, the heuristic provided an ideal solution nearly 100% of the times. Moreover, an altered implementation of a present path-finding algorithm is actually utilized to fix the time-dependent quickest flow problem with source waiting…..

*Contents*

Chapter 1: Introduction

Chapter 2: The **Quick-TDQFP Heuristic**

2.1 Introduction

2.2 The Quick-TDQFP heuristic

2.3 The Quick-TDQFP heuristic – Overview and Steps

Chapter 3: The Path-Finding Algorithms

3.1 Introduction

3.2 The TDLTP and the TDLTP Reoptimization Algorithms

3.3 *Shortest-Path Algorithms and Zero-Sum Cycles*

3.4 The Path Diving Procedure

3.5 The M-Chrono SPT algorithm

Chapter 4: Computational Results

4.1 Introduction

4.2 Experimental Design

4.3 Experimental Results

Chapter 5: Further Thoughts and Conclusions……

Source: UMD

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