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John Gatward
2026-03-16 18:03:17 +00:00
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<!DOCTYPE html>
<html>
<link href="style.css" rel="stylesheet" type="text/css">
<script src="https://cdnjs.cloudflare.com/ajax/libs/p5.js/1.2.0/p5.min.js"
integrity="sha512-b/htz6gIyFi3dwSoZ0Uv3cuv3Ony7EeKkacgrcVg8CMzu90n777qveu0PBcbZUA7TzyENGtU+qZRuFAkfqgyoQ=="
crossorigin="anonymous"></script>
<title>Travelling Sales Person</title>
<h1>Travelling Sales Person Problem</h1>
<button id="backButton" onclick="window.location.href='/#tutorials'">Back</button>
<head>
<meta charset="UTF-8">
<div class="pictureContainer">
<img src="https://optimization.mccormick.northwestern.edu/images/e/ea/48StatesTSP.png" alt="TSP Problem"
id="Conway">
</div>
<p>The travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances
between each pair of cities, what is the shortest possible route that visits each city and returns to the origin
city?" </p>
<p>The problem was first formulated in 1930 and is one of the most intensively studied problems in optimization. It
is used as a benchmark for many optimization methods. Even though the problem is computationally difficult, a
large number of heuristics and exact algorithms are known, so that some instances with tens of thousands of
cities can be solved completely and even problems with millions of cities can be approximated within a small
fraction of 1%.</p>
<p>The TSP has several applications even in its purest formulation, such as planning, logistics, and the manufacture
of microchips. Slightly modified, it appears as a sub-problem in many areas, such as DNA sequencing. In these
applications, the concept city represents, for example, customers, soldering points, or DNA fragments, and the
concept distance represents travelling times or cost, or a similarity measure between DNA fragments. The TSP
also appears in astronomy, as astronomers observing many sources will want to minimize the time spent moving the
telescope between the sources. In many applications, additional constraints such as limited resources or time
windows may be imposed.</p>
<h2>These are some of the algorithms I used</h2>
<p>Note the purple route is the best route it's found so far and the thin white lines are the routes it's trying
real time.</p>
</head>
<body>
<div class="canvasBody">
<h3>Random Sort</h3>
<span id="c1"></span>
<p class="canvasText">This canvas sorts through random possiblities. Every frame the program chooses two random
points (cities) and swaps them around. eg say the order was London, Paris, Madrid, the program would swap
London and Paris so that the new order is: Paris, London, Madrid. The program then compares the distance
against the record distance to decide whether the new order is better than the old order. This search method
is the most inefficient way, the worst case scenario is never ending, as the point swaping is random the
program may never reach the optimum route</p><br>
<h3>Lexicographic Order</h3>
<span id="c2"></span>
<p class="canvasText">This canvas sorts through all possible orders sequentially, so after n! (where n is the
number of points) this algorithm is guaranteed to have found the quickest possible route. However it is
highly inefficient always taking n! frames to complete and as n increases, time taken increases
exponentially.</p>
<a target="_blank"
href="https://www.quora.com/How-would-you-explain-an-algorithm-that-generates-permutations-using-lexicographic-ordering">Click
here to learn more about the algorithm</a><br>
<h3>Genetic Algorithm</h3>
<span id="c3"></span>
<p class="canvasText">This canvas is the most efficient at finding the quickest route, it is a mixture of the
two methods above. It starts off by creating a population of orders, a fitness is then generated for each
order in the population. This fitness decides how likely the order is to be picked and is based on the
distance it takes (lower distance is better). When two orders are picked, the algorithm splices the two
together at a random term, it's then mutated and compared against the record distance. This takes the least
amount of time to find the shortest distance as the algorithm doesn't search through permuations that are
obviously longer due to the order.</p><br>
</div>
</body>
<script src="sketch.js"></script>
<footer>
<p>This page was inspired by The Coding Train</p><a
href="https://www.youtube.com/channel/UCvjgXvBlbQiydffZU7m1_aw">Check him out here</a>
</footer>
</html>