MATLAB Graph Theory Problem: Shortest Path Optimization with Multiple Agents

In this graph theory problem, we have four agents departing from a single starting point who need to visit all nodes while minimizing the total path length. To address this combinatorial optimization challenge, MATLAB provides several algorithmic approaches. One method involves implementing a greedy algorithm where at each step, agents select the nearest unvisited node, which can be coded using MATLAB's min() function to find the closest node from the current position. Another approach utilizes dynamic programming, breaking the problem into subproblems (like the Traveling Salesman Problem for each agent) and combining solutions using memoization techniques - this can be implemented with MATLAB's array indexing and recursive function capabilities. A third method employs genetic algorithms, simulating natural selection through MATLAB's Global Optimization Toolbox, where we can define chromosome structures representing agent routes, implement crossover and mutation operations, and use fitness functions to evaluate path lengths. Each algorithm can be compared using MATLAB's tic/toc timing functions and performance metrics to determine the most efficient solution for our specific problem constraints.