For sufficiently large problems it could take years to find the optimal

For sufficiently large problems it could take years

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is growing relative to the size of the problem. For sufficiently large problems, it could take years to find the optimal solution. Frane Saric, CTO at OptimoRoute, confirms that point: “Exact methods like integer linear programming (ILP) are rarely used in practice because they are extremely slow and can solve only very small problems with a few orders”. Hence, routing solutions often rely on heuristics to be able to quickly return good enough but not necessarily optimal solutions. now for the solution of the given problem consider the following graph. Let the given graph be: Follow the steps below to find the shortest path between all the pairs of vertices. Create a matrix A1 of dimension n*n where n is the number of vertices. The row and the column are indexed as i and j respectively. i and j are the vertices of the graph. Each cell A[i][j] is filled with the distance from the ith vertex to the jth vertex. If there is no path from ith vertex to jth vertex, the cell is left as infinity. Fill each cell with the distance between ith and jth vertex
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Now, create a matrix A1 using matrix A0. The elements in the first column and the first row are left as they are. The remaining cells are filled in the following way.
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  • Fall '17
  • Tahir Iqbal
  • Travelling salesman problem, Vehicle routing problem, Frane Saric

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