Multiple Solutions: Dice problem

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Problem type: MIP (small)

Keywords: Multiple solutions, Incumbent callback, Solution pool, GMP

Description: This example demonstrates several approaches to get multiple solutions when solving a MIP problem. These approaches are:

  • Using the incumbent (solver) callback;

  • Using the solution pool (supported by CPLEX, Gurobi and ODH-CPLEX);

  • Repeatedly solve the problem forbidding the previous solutions.

In the dice problem a set of three dice has to be designed by assigning an integer number to each face such that on average die 1 beats die 2, die 2 beats die 3, and die 3 beats dice 1. The goal is to maximize the number of total wins on average. The dice problem has many solutions.

References: Bosch, R.A., Mindsharpener - Monochromatic Squares, OPTIMA Newsletter 71 (2004), Mathematical Optimization Society, pp. 6-7