# Superpower your local deliveries — all within your Shopify admin

Streamline every step of your delivery operations and let your customers know when their orders are arriving. Save time and delight your customers with your new delivery superpowers.

## "The best routing app for Shopify merchants."

###### - Official Shopify Retail Blog -

## Create a delightful delivery experience for your customers...

From custom order tracking pages to delivery notifications, EasyRoutes lets you craft the perfect delivery experience for your customers.

**...all without ever leaving your Shopify Admin.**

## Save (a lot) of time planning local delivery routes...

Create multiple optimized routes in one click, schedule and assign routes, and add last-minute orders…

**...all without ever leaving your Shopify Admin.**

## Make life easier for your delivery drivers

Create routes with EasyRoutes and deliver with them EasyRoutes Delivery Driver for iOS and Android. Our delivery driver app puts all the information and tools your driver needs right at their fingertips.

**...all without ever leaving your Shopify Admin.**

### 🏆 EasyRoutes is a 2x Shopify Staff Pick

## The Traveling Salesman Problem

## Introduction

The traveling salesman problem (TSP) is a classical problem in computer science and operations research. It has been called "the single most studied and difficult to solve optimization problem" and "the world's hardest math problem". In its simplest form, the TSP involves finding the shortest possible route that visits each site exactly once and returns to the origin city.

## Introduction

The traveling salesman problem (TSP) is an optimization problem that involves determining the shortest route that visits each vertex of a graph exactly once and returns to the starting point. The traveling salesman problem was introduced in 1930 by Karl Menger and represents one of the most famous problems in combinatorial optimization.

The TSP belongs to a class of problems called NP-complete, meaning they are all mathematically equivalent: if any one can be solved efficiently then all can be solved efficiently. It has also been called "the granddaddy of all optimization problems".

Although there are no known efficient or polynomial algorithms for solving TSPs, it is possible to approximate solutions through heuristics such as simulated annealing (SA), genetic algorithms (GA), ant colony optimization (ACO), scatter search etc.

## The Problem

The traveling salesman problem is a classic computer science problem that asks you to find the shortest route to visit a set of cities. The problem itself is not easy to understand, but it's important because it has many applications in other areas of computer science. In fact, there are entire classes on the traveling salesman problem at major universities around the world!

The traveling salesman problem is an example of a NP-complete problem: one that is too hard for computers to solve in any reasonable amount of time unless given vast amounts of processing power (or some other form of assistance). Fortunately, there are ways around this limitation—and we'll talk about them later in this article.

## Previous Research

In the 1940s and 50s, mathematicians started to use the traveling salesman problem as a model for studying other types of combinatorial problems. In 1957, Graham, Morton and Rothschild proved that there is no algorithm that guarantees finding an optimal solution for all instances of TSP in polynomial time. This means that TSP is not only hard to solve but also intractable (meaning it cannot be solved by any known algorithm). The reason why this is so important is because if we can't solve this problem then it's likely other problems will also be NP-complete which means they are also intractable.

## Recent Research Efforts

In recent years, researchers have been focused on using AI and machine learning to solve the TSP. One prominent example is the use of convolutional neural networks (CNNs) to find optimal routes through collections of images. In a related project, researchers tried applying CNNs to generate driving directions that would allow a car to drive itself through cities while minimizing time and distance traveled.

Another approach uses genetic algorithms (GA) instead of neural networks as a way around the issue of needing pre-existing data: if you can't get your hands on enough relevant examples yourself, then just ask nature! By combining this technique with simulated annealing and MCMC sampling techniques, they were able to achieve near-optimal results on "synthetic" instances with hundreds or even thousands of cities—far exceeding what had previously been achieved without access to such large datasets....

## Future Research Efforts

The traveling salesman problem is an unsolved problem in mathematics that is commonly stated as "find the shortest route through a weighted graph". Graphs are diagrams of mathematical objects called vertices (or nodes) and edges connecting these vertices. The weights on the edges are typically real numbers. In this context, the TSP has multiple names: it's also known as the traveling salesman tour problem or the Euclidean traveling salesman problem.

The original motivation for studying this type of problem was to determine whether there was an efficient way of calculating an optimal tour through a set of cities so that you could minimize your distance traveled and make fewer stops than if you had simply visited each city once before returning home (see also Bellman-Ford algorithm). However, today it has more applications in fields ranging from transportation planning to DNA sequencing to artificial intelligence research.

## Takeaway

This problem is difficult to solve, but the future is bright for this area of research. While we don’t have a good algorithm yet, researchers are making progress in solving it.

## This problem is difficult to solve, but the future is bright for this area of research.

The Traveling Salesman Problem is an open problem, meaning it hasn't been solved yet. There are many research efforts underway and there is a lot of future research in this area. The future is bright for this area of research, and we're excited by the prospect that one day it will be solved—and then we'll all have to find something else to do with our lives!

## Conclusion

The Traveling Salesman Problem is one of the oldest and most difficult problems in computer science. The goal is to find a route that visits each city exactly once and returns to the starting point. This problem has applications in many different fields, including logistics, manufacturing and even military operations! Previous research efforts have focused on developing heuristics for solving TSPs or designing algorithms that run faster than others in certain cases (like when there are no negative edge costs). However, recent research has focused on identifying key properties of graphs which make them easier (or harder) to solve by using some sort of “neighborhood structure” property. We hope that this review will help you understand why these types of approaches work well on certain types of problems while others don't work at all.

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