Hybrid Evolutionary–Optimization Methods for Furnace Design Decisions in Glass Container Industry

This paper studies the Glass Container Industry Problem regarding a New Furnace (GCIP--NF), in which a plant must decide the melting capacity of a new furnace and the set of moulding machines. We propose a mixed-integer linear programming (MILP) model that captures furnace capacity, machine configuration and demand satisfaction. The binary design variables are evolved by genetic-algorithm variants (simple and multi-population schemes), while a linear relaxation is solved for the continuous variables. A Greedy Filter heuristic discards infeasible configurations and provides warm starts for the linear subproblems, yielding hybrid matheuristics. The methods are evaluated on 200 instances generated from data and grouped into small and large cases. For small instances, Branch-and-Cut finds optimal solutions and smaller optimality gaps, whereas Greedy Filter–enhanced genetic algorithms produce near-optimal solutions with lower computational times. For large instances, the exact method often fails to find feasible solutions within the time limit, while genetic algorithms yield similar objective values; Greedy Filter–based variants achieve the best time performance. A 10-year Return on Equity (ROE) analysis shows that the choice of furnace–machine configuration can produce differences above 1.3 percentage points per year, underscoring the impact of the proposed approaches.