# Travelling Salesman Problem: Complexities Resolved

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.

Whether you are a logistics manager responsible for fleet efficiency, a delivery service operator aiming to minimize costs and attain on-time deliveries, or a field service manager striving to maximize daily appointments, the core challenge remains the same–navigating multiple destinations in the shortest, most efficient way possible and that’s what the travelling salesman problem is all about

Failing to solve the TSP efficiently can lead to wasted time, increased fuel costs, late deliveries, and ultimately, dissatisfied customers.

If you’ve landed on this blog, you’re likely dealing with the complexities of multi-stop route planning and are seeking actionable insights to enhance your operations.

So, without any further ado, let’s get started with the blog to explore the intricacies of the Traveling Salesman Problem, and common challenges faced, review popular and advanced solutions, and discuss real-life applications.

## What is a Traveling Salesman Problem (TSP)?

The traveling Salesman Problem (TSP) is a combinatorial problem that involves finding the shortest and most efficient route to reach a list of specific destinations.

It is a common algorithmic problem in delivery operations that might hamper multiple delivery processes and result in financial loss. TSP occurs when multiple routes are available, but choosing a minimum-cost path is difficult for you or a traveling person.

## What is the Traveling Salesman Problem with Time Windows (TSPTW)?

The Traveling Salesperson Problem with Time Windows (TSPTW) is the process of finding the quickest path for a salesperson to visit a group of customers within a predetermined amount of time.

This problem applies to various sectors, such as transportation, logistics, and manufacturing, where following deadlines is crucial for ensuring on-time service or delivery and boosting efficiency.

TSPTW is a version of the traditional Traveling Salesman Problem (TSP) with time window constraints. Meeting these constraints guarantees that clients are served quickly and effectively.

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## 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, salespeople have to carry out several deliveries in a very limited time every day, so there are many time constraints. To overcome this, you need to plan your routes so that you make the most of them.
• Secondly, there is a chance of last-minute changes. Sometimes, you get extra urgent visits, while sometimes, some visits are postponed or canceled due to the customer’s unavailability.
• Lastly, a math problem, a combinatorial optimization problem, arises. This problem is mathematically complex to solve as it involves 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 ask for less fuel, fulfill on-time delivery to customers, and are ready to modify routes considering last minute changes.

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Upper’s route planning lets you prioritize urgent deliveries, ensuring your most important packages reach their destinations first to maintain customer reliability and assurance.

## 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.

These are some of the near-optimal solutions to finding 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

All these challenges suggested above are manual and time-consuming, often requiring significant computational resources and expertise. Fortunately, technological advancements have provided more efficient methods and tools for solving the traveling salesman problem.

## Other Optimal Solutions to the Traveling Salesman Problem

In addition to the popular methods mentioned, several advanced techniques and algorithms have been developed to tackle the TSP more effectively. Here are some of the most noteworthy:

• Multi-agent system: This 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 to solve optimization issues.
• Meta-heuristic multi-restart iterated local search: This method states that the technique is more efficient than genetic algorithms.

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

TSP has numerous practical applications, particularly in logistics and supply chain management:

• Delivery services: Companies like Amazon and FedEx use TSP algorithms to optimize delivery routes, reducing time and fuel costs.
• Manufacturing: Efficiently scheduling the sequence of operations in manufacturing processes to minimize setup times and costs.
• Field Service Businesses: Optimizing routes for sales personnel and field service technicians to maximize the number of daily visits.

## 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, with route management software like Upper, there is much more beyond simply finding the shortest and most optimal route. It has all the solutions you need when talking about TSP.

Let’s have a look at a few of them:

### 1. Automated route optimization

Upper Route Planner leverages advanced algorithms to automatically determine the most efficient routes, saving you time and reducing the risk of human error. This automated route optimization ensures that your deliveries are always optimized for the shortest distance and minimal travel time.

Upper makes handling large-scale deliveries easy. You can easily import an Excel or CSV file with multiple addresses, streamlining the process of planning routes for hundreds of stops. This bulk import feature is particularly useful for businesses handling high volumes of deliveries daily.

### 3. Electronic proof of Delivery (ePOD)

Upper’s electronic proof of delivery feature helps you capture and store delivery confirmations securely. You can take snapshots of delivered items, collect electronic signatures, and add relevant notes. This feature helps in avoiding disputes and maintaining a transparent record of all deliveries.

### 4. Real-time driver tracking

Gain complete visibility over your delivery operations with Upper’s real-time driver tracking. Monitor the progress of your drivers on the field, ensuring that deliveries are on schedule and addressing any issues promptly. This real-time insight helps you manage your fleet more effectively and improve customer satisfaction.

### 5. Urgency-based route planning

Upper allows you to prioritize deliveries based on urgency. Whether you have time-sensitive packages or urgent customer requests, Upper’s intelligent routing system ensures that these deliveries are planned and executed with the highest priority, enhancing overall efficiency.

### 6. Customer communication

Build trust and loyalty with your customers by informing them about their deliveries. Upper enables you to send live delivery updates via live customer notifications, informing them about delays or unexpected stops. This transparency helps manage customer expectations and improve their experience.

### 7. Comprehensive reporting and analytics

Upper provides detailed reports and analytics to help you understand and improve your delivery operations. Analyze route efficiency, driver performance, and delivery times to identify areas for improvement and make data-driven decisions.

If Not Now, Then When?

Why not take advantage of the Upper’s free trial and experience the powerful routing solutions for traveling salesman issues?

## 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.

## Conclusion

If you are a business owner dealing with TSPs and want to get rid of them, we recommend using a TSP solver like Upper Route Planner. The online route planner can pluck 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 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 ensures your tradesman doesn’t go wrongfooted and quickly wraps up pending deliveries.

Author Bio
Rakesh Patel

Rakesh Patel, author of two defining books on reverse geotagging, is a trusted authority in routing and logistics. His innovative solutions at Upper Route Planner have simplified logistics for businesses across the board. A thought leader in the field, Rakesh's insights are shaping the future of modern-day logistics, making him your go-to expert for all things route optimization. Read more.