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    <p>Yes this is an integer programming problem. You can write it as:</p> <pre><code> minimize |x1 - x2| + |x2 - x3| + ... + |xn-1 - xn| subject to x1 + x2 + x3 + ... + xn == c, xi == Ai1*yi1 + Ai2*yi2 + ... + Aip*yip, i=1,...,n, yi1 + yi2 + ... + yip == 1, i=1,...,n, yij binary for i=1,...,n j=1,...,p, xi integer for i=1,...,n, </code></pre> <p>here the Aij are known input data that describe what integers a particular value of xi may take on. Below is a concrete example with 3 variables (n=3), where each xi can take on one of two integer values (p=2). That is x1 can be 1 or 3, x2 can be 3 or 4, x3 can be 2 or 3.</p> <pre><code> minimize |x1 - x2| + |x2 - x3| subject to x1 + x2 + x3 == 8, x1 == 1*y11 + 3*y12, x2 == 3*y21 + 4*y22, x3 == 2*y31 + 3*y32, y11 + y12 == 1, y21 + y22 == 1, y31 + y32 == 1, yij binary i=1,2,3 j=1,2 xi integer i=1,2,3 </code></pre> <p>You can reformulate the above problem as a MIP (a mixed integer program) by creating a new set of variables u to represent the objective function.</p> <pre><code> minimize u1 + u2 + ... + un subject to ui &gt;= xi - xi+1, i=1,...,n-1, ui &gt;= xi+1 - xi, i=1,...,n-1, x1 + x2 + x3 + ... + xn == c, xi == Ai1*yi1 + Ai2*yi2 + ... + Aip*yip, i=1,...,n, yi1 + yi2 + ... + yip == 1, i=1,...,n, yij binary for i=1,...,n j=1,...,p, xi integer for i=1,...,n, ui real for i=1,...,n-1, </code></pre> <p>You can use any standard <a href="http://en.wikipedia.org/wiki/Mixed_integer_programming#Solvers_and_scripting_.28programming.29_languages" rel="nofollow">MIP solver</a> to solve the above problem.</p>
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    1. POIs this integer programming?
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    1. UScodehippo
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      1. VTUpMod
    1. COwell done codehippo!! +1
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      1. USTom Swifty
 

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