New algorithm solves the impossible trade-off between cost and emissions
Researchers have cracked a long-standing problem in operations optimization: how to find the best solution when two competing objectives matter equally. The breakthrough could reshape supply chain planning, facility location decisions, and environmental compliance strategies where companies must balance costs against carbon footprint—and need proof their choices are genuinely optimal.
Originaltitel: A Lagrangian bounding and heuristic principle for bi-objective discrete optimization
<p>Lagrangian relaxation is a common and often successful way to approach computationally challenging single-objective discrete optimization problems with complicating side constraints. Its aim is often twofold; first, it provides bounds for the optimal value, and, second, it can be used to heuristically find near-optimal feasible solutions, the quality of which can be assessed by the bounds. We consider bi-objective discrete optimization problems with complicating side constraints and extend this Lagrangian bounding and heuristic principle to such problems. The Lagrangian heuristic here produces non-dominated candidates for points on the Pareto frontier, while the bounding forms a polyhedral outer approximation of the Pareto frontier, which can be used to assess the quality of the candidate points. As an illustration example we consider a facility location problem in which both CO2 emission and cost should be minimized. The computational results are very encouraging, both with respect to bounding and the heuristically found non-dominated solutions. In particular, the Lagrangian bounding is much stronger than the outer approximation given by the Pareto frontier of the problem's linear programming relaxation.</p>