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