# Explained: What is Traveling Salesman Problem (TSP)

• By Rakesh Patel
• Last Updated: January 24, 2023
Key Takeaways:

• A well-known mathematical problem called the Traveling Salesman Problem (TSP) aims to determine the shortest path between a number of places.
• Logistics, transportation, and manufacturing are just a few of the industries where the TSP is useful.
• The number of points, the form of the point set, and the algorithm employed can all have an impact on how the TSP is solved.
• Technology advancements like cloud computing and parallel processing have made it possible to solve the Traveling Salesman Problem effectively for larger and more complicated situations.

Traveling salesman problem is not new for delivery-based businesses. Its recent expansion has insisted that industry experts find optimal solutions in order to facilitate delivery operations.

The major challenge is to find the most efficient routes for performing multi-stop deliveries. Without the shortest routes, your delivery agent will take more time to reach the final destination. Sometimes problems may arise if you have multiple route options but fail to recognize the efficient one.

Eventually, traveling salesman problem would cost you time and result in late deliveries. So, before it becomes an irreparable issue for your delivery company, let us understand the traveling salesman problem and find optimal solutions in this blog.

## What is Traveling Salesman Problem (TSP)?

The traveling Salesman Problem (TSP) is a combinatorial problem that deals with finding the shortest and most efficient route to follow for reaching a list of specific destinations.

It is a common algorithmic problem in the field of delivery operations that might hamper the multiple delivery process and result in financial loss. TSP turns out when you have multiple routes available but choosing a minimum cost path is really hard for you or a traveling person.

### How difficult is it to solve?

It is quite difficult to solve TSP as it is known as NP-hard, which means there is no polynomial time algorithm to solve it for more numbers of addresses. So, with an increasing amount of addresses, the complexity of solving TSP increases exponentially.

So, it is impossible to find TSP solutions manually. Also, many mathematical algorithms and the fastest computers fail to solve TSP.

However, TSP can be eliminated by determining the optimized and efficient path using approximation algorithms or automated processes.

## Common Challenges of Traveling Salesman Problem (TSP)

Being a salesman is not easy, as you need to face various unavoidable challenges in your everyday schedules.

• Firstly, every day, salespeople have to carry out a number of deliveries in a very limited time, so there are a lot of time constraints. To overcome this, you need to plan your routes in a way that you make the most out of them.
• Secondly, there are chances of last-minute changes. Sometimes you get extra and urgent visits to make, while sometimes, some visits are postponed or canceled due to the customer’s unavailability.
• Lastly, a math problem, a combinatorial optimization problem, arises. A combinatorial optimization problem is a problem that is mathematically complex to solve as you have to deal with many variables.

These are major challenges in the Traveling Salesman Problem (TSP) as you are required to create a route with the shortest distances using hundreds and thousands of permutations and combinations that asks for less fuel, fulfill on-time delivery to customers, and are ready to modify routes considering last minute changes.

These are some of the near-optimal solutions to find the shortest route to a combinatorial optimization problem.

### 1. Nearest Neighbor (NN)

The Nearest Neighbor Method is probably the most basic TSP heuristic. The method followed by this algorithm states that the driver must start by visiting the nearest destination or closest city. Once all the cities in the loop are covered, the driver can head back to the starting point.

Solving TSP using this efficient method, requires the user to choose a city at random and then move on to the closest unvisited city and so on. Once all the cities on the map are covered, you must return to the city you started from.

### 2. The Branch and Bound Algorithm

The Branch & Bound method follows the technique of breaking one problem into several little chunks of problems. So it solves a series of problems. Each of these sub-problems may have multiple solutions. The solution you choose for one problem may have an effect on the solutions of subsequent sub-problems.

### 3. The Brute Force Algorithm

The Brute Force Approach takes into consideration all possible minimum cost permutation of routes using a dynamic programming approach. First, calculate the total number of routes. Draw and list all the possible routes that you get from the calculation. The distance of each route must be calculated and the shortest route will be the most optimal solution.

## What are Other Optimal Solutions to the Traveling Salesman Problem?

• Multi-Agent System: Involves distributing the pair of cities into groups. Then assign a single agent to discover the shortest path, covering all the cities in the assigned group.
• Zero Suffix Method: This method solves the classical symmetric TSP and was introduced by Indian researchers.
• Multi-Objective Evolutionary Algorithm: This method solves the TSP using NSGA-II
• Biogeography-based Optimization Algorithm: This method is based on the migration strategy of animals for solving optimization issues.
• Meta-Heuristic Multi Restart Iterated Local Search: This method states that the technique is more efficient compared to genetic algorithms.

Blow Away TSP using Upper

## What are Some Real-Life Applications of Traveling Salesman Problem?

Most businesses see a rise in the Traveling Salesman Problem (TSP) due to the last mile delivery challenges. The last mile delivery is the process of delivering goods from the warehouse (or a depot) to the customer’s preferred location. Considering the supply chain management, it is the last mile deliveries that cost you a wholesome amount.

At the same time, you need to sacrifice financial loss in order to maintain your current position in the market. Suppose last mile delivery costs you \$11, the customer will pay \$8 and you would suffer a loss. This is because of pre-defined norms which may favor the customer to pay less amount.

This hefty last mile delivery cost is the result of a lack of Vehicle routing problem(VRP) software. VRP finds you the most efficient routes so that operational costs will not get increase. So, by using the right VRP software, you would not have to bother about TSP.

Such delivery management software uses an automated process that doesn’t need manual intervention or calculations to pick the best routes. Hence, it is the easiest way to get rid of the traveling Salesman Problem (TSP).

## How TSP and VRP Combinedly Pile Up Challenges?

The traveling Salesman Problem is an optimization problem studied in graph theory and the field of operations research. In this optimization problem, the nodes or cities on the graph are all connected using direct edges or routes. The weight of each edge indicates the distance covered on the route between the two cities.

The problem is about finding an optimal route that visits each city once and returns to the starting and ending point after covering all cities once.

The TSP is often studied in a generalized version which is the Vehicle Routing Problem. It is one of the most broadly worked on problems in mathematical optimization. VRP deals with finding or creating a set of routes for reducing time, fuel, and delivery costs.

### Is there any real world solution to TSP and VRP?

Many solutions for TSP and VRP are based on academics which means they are not so practical in everyday life. The reason is that many of them are just limited to perfection, but need a dynamic programming-based solution. So, if businesses really want to get rid of them, they need a TSP solver integrated with route optimization software.

The right TSP solver will help you disperse such modern challenges. It offers in-built route planning and optimization solutions in such a way that your tradesman doesn’t get stranded while delivering the parcel. Also, it is equipped with an efficient algorithm that provides true solutions to the TSP. As a result, the delivery manager can create a route plan hassle-free in a few minutes.

## Can a Route Planner Resolve the Traveling Salesman Problem (TSP)?

In the general case, the Traveling Salesman Problem (TSP) involves finding the shortest optimized and possible route that includes a set of stops and returns to the starting point. The number of possible routes increases exponentially as the number of locations increases. Finding the best solution becomes difficult computationally, even for moderately sized problems.

But, Upper Route Planner, a route optimization software, is built differently. Upper has all the solutions you need when talking about TSP.

For example, if you are in charge of planning delivery routes with more than 500 stops in them, all you need to do is import an Excel or CSV file with multiple addresses into Upper, review, allot delivery drivers, optimize, and dispatch with a single click. This delivery route planning solution saves you hours of time spent on planning delivery routes and optimizing them.

Also, once the delivery is completed, Upper lets you collect proof of delivery. This is how the Upper Route Planner is a simple solution to the Traveling Salesman Problem.

Upper Route Planner

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## FAQs

TSP stands for traveling Salesman Problem, while VRP is an abbreviation form of vehicle routing problem (VRP). In the delivery industry, both of them are widely known by their abbreviation form.

Yes, you can prevent TSP by using the right route planner. The online route planner helps you get the optimized path so that your delivery agents don’t have to deal with such challenges. In addition, they don’t struggle with multiple routes. Instead, they can progress on the shortest route.

The new method has made it possible to find solutions that are almost as good. This was done by the Christofides algorithm, the popular algorithm in theoretical computer science. This algorithm plugs into an alternate version of the problem that finds a combination of paths as per permutations of cities. It made the round trip route much longer. The round trip produced by the new method, while still not being efficient enough is better than the old one.

The vehicle routing problem (VRP) reduces the transportation costs as well as drivers’ expenses. It helps you serve more customers with fewer fleets and drivers. Thus, you don’t have any variation in the time taken to travel.

## Create Optimized Routes Using Upper and Bid Goodbye to Traveling Salesman Problem

As a business owner, If you are dealing with TSP and want to get rid of them, we recommend using a TSP solver like Upper Route Planner. The online route planner is capable of plucking out the most efficient routes no matter how big your TSP is. It has an in-built sophisticated algorithm that helps you get the optimized path in a matter of seconds.

Therefore, you won’t fall prey to such real-world problems and perform deliveries in minimum time. Upper’s delivery route planner offers a dedicated driver app that makes sure your tradesman doesn’t go wrongfooted and quickly wraps up pending deliveries. Don’t just agree with our words, book a demo on Upper and disperse TSP once and for all.

Author Bio
Rakesh Patel

Rakesh Patel is the founder and CEO of Upper Route Planner, a route planning and optimization software. With 28+ years of experience in the technology industry, Rakesh is a subject matter expert in building simple solutions for day-to-day problems. His ultimate goal with Upper Route Planner is to help delivery businesses eliminate on-field delivery challenges and simplify operations such as route planning, scheduling, dispatching, take a proof of delivery, manage drivers, real time tracking, customer notifications and more. He loves sharing his thoughts on eliminating delivery management challenges via blogs. Read more.