最短路问题是一个重要的网络优化问题，其应用广泛，包括计算机网络、交通运输、电信通讯等领域。最短路问题的解决方法可以帮助我们在网络中找到最优路径，从而节省时间和成本，提高效率。本文将介绍最短路问题的应用和求解方法，包括经典算法和Floyd改进算法，以及它们的优缺点。

本文首先对最短路问题研究进行了综述，包括研究历史、现实意义和研究现状等，然后详细讲解了图论中和最短路问题有关的概念和定理、介绍了了四种解决最短路问题的算法——Dijkstra算法、Bellman-Ford 算法、Floyd 算法和拓扑排序法，以及他们的算法思想、算法步骤，部分算法给出了伪代码，并从它们的适用性、复杂度等进行比较比较，找出各自的优缺点。在创新方面，通过对其中Floyd算法的进一步探究，提出了最短路问题的 Floyd 改进算法。利用MATLAB程序，将改进算法与原算法在随机生成的网络中进行仿真实验，结果说明了改进算法的准确性和高效性。最后讲解了一个最短路问题应用的例子：通过画决策图将背包问题转化为最短路问题。

The shortest-circuit problem is an important network optimization problem in modern society with a wide range of applications, including computer networks, transportation, and telecommunication communications. The solution of the shortest-circuit problem can help us find the optimal path in a network, thus saving time and cost and improving efficiency. In this paper, we will introduce the applications and solution methods of the shortest-circuit problem, including classical and improved Floyd algorithms, and their advantages and disadvantages.

This paper first gives an overview of the shortest-circuit problem research, including research history, practical significance and current status of research, and then explains in detail the concepts and theorems related to the shortest-circuit problem in graph theory, introduces four algorithms for solving the shortest-circuit problem - Dijkstra's algorithm, Bellman-Ford's algorithm, Floyd's algorithm, and topological ranking, Floyd algorithm and topological sorting method, their algorithmic ideas, algorithmic steps, some of them are given in pseudo-code, and their applicability, complexity, etc. are compared to find out the advantages and disadvantages of each. In terms of innovation, the Floyd improvement algorithm for the shortest-circuit problem is proposed by further exploration of one of the Floyd algorithms. Using MATLAB program, networks of different sizes are randomly generated, and the improved algorithm is simulated with the original algorithm in a large network for experiments, and the simulation results illustrate the accuracy and efficiency of the improved algorithm. Finally, an example of shortest-circuit problem application is explained: the backpack problem is transformed into a shortest-circuit problem by drawing a decision diagram.