Multi-Objective Lexicographic Mixed-Integer Linear Programming: an Infinity Computer Approach

In this chapter we show how a lexicographic multi-objective linear pro- gramming problem (LMOLP) can be transformed into an equivalent, single-objective one, by using the Grossone Methodology. Then we provide a simplex-like algorithm, called GrossSimplex, able to solve the original LMOLP problem using a single run of the algorithm (its theoretical correctness is also provided). In the second part, we tackle a Mixed-Integer Lexicographic Multi-Objective Linear Programming prob- lem (LMOMILP) and we solve it in an exact way, by using a Grossone-version of the Branch-and-Bound scheme (called GrossBB). After proving the theoretical correctness of the associated pruning rules and terminating conditions, we show a few experimental results, run on an Infinity Computer simulator.