A Reply to Hofman On: "Why LP cannot solve large instances of NP-complete problems in polynomial time"

Using an approach that seems to be patterned after that of Yannakakis, Hofman argues that an NP-complete problem cannot be formulated as a polynomial bounded-sized linear programming problem. He then goes on to propose a "construct" that he claims to be a counter-example to recently published linear programming formulations of the Traveling Salesman Problem (TSP) and the Quadratic Assignment Problems (QAP), respectively. In this paper, we show that Hofman's construct is flawed, and provide further proof that his "counter-example" is invalid.Comment: 2 page; 1 table; clarification of some unclear statement

Why Linear Programming cannot solve large instances of NP-complete problems in polynomial time

This article discusses ability of Linear Programming models to be used as solvers of NP-complete problems. Integer Linear Programming is known as NP-complete problem, but non-integer Linear Programming problems can be solved in polynomial time, what places them in P class. During past three years there appeared some articles using LP to solve NP-complete problems. This methods use large number of variables (O(n^9)) solving correctly almost all instances that can be solved in reasonable time. Can they solve infinitively large instances? This article gives answer to this question

Path Planning Algorithms for Robotic Aquaculture Monitoring

Aerial drones have great potential to monitor large areas quickly and efficiently. Aquaculture is an industry that requires continuous water quality data to successfully grow and harvest fish. The Hybrid Aerial Underwater Robotic System (HAUCS) is designed to collect water quality data of aquaculture ponds to reduce labor costs for farmers. The routing of drones to cover each fish pond on an aquaculture farm can be reduced to the Vehicle Routing Problem. A dataset is created to simulate the distribution of ponds on a farm and is used to assess the HAUCS Path Planning Algorithm (HPP). Its performance is compared with the Google Linear Optimization Package (GLOP) and a Graph Attention Model (AM) for routing problems. GLOP is the most efficient solver for 50 to 200 ponds at the expense of long run times, while HPP outperforms the other methods in solution quality and run time for instances larger than 200 ponds