for ind in 1:9 # Each row, OR each column These constraints are all very similar, so much so that we can actually add them at the same time. Next we'll add the constraints for the rows and the columns. # can be in this cell, so the sum must be equal to sum(x for k in 1:9) = 1) We'll actually start with something obvious to us as humans, but what we need to enforce: that there can be only one number per cell. The meaning of each variable is as follows: x = 1 if and only if cell (i,j) has number k, where i is the row and j is the column.Ĭreate a model sudoku = Model(HiGHS.Optimizer)Ĭreate our variables x, Bin) We will define a binary variable (a variable that is either 0 or 1) for each possible number in each possible cell. We'll use JuMP to create the model, and then we can solve it with any integer programming solver. We can model this problem using 0-1 integer programming: a problem where all the decision variables are binary. Mixed-integer linear programming formulation You can think of it as an optimization problem with an objective of 0. Solving a Sudoku isn't an optimization problem with an objective its actually a feasibility problem: we wish to find a feasible solution that satisfies these rules. Here is a partially solved Sudoku problem: The numbers 1 to 9 must appear in each column.The numbers 1 to 9 must appear in each row.The numbers 1 to 9 must appear in each 3x3 square.Your solution must satisfy the following rules: The goal is to place the digits 1 to 9 on a nine-by-nine grid, with some of the digits already filled in. This tutorial was originally contributed by Iain Dunning. Solving a problem using MathOptInterface.Simple semidefinite programming examples.Optimal control for a Space Shuttle reentry trajectory.

Computing the duals of a mixed-integer program.Mixed-integer linear programming formulation.Sensitivity analysis of a linear program.

Sudoku strategy tutorial