# Multiobjective Combinatorial Optimization

# Decision makers have often to face different, and usually conﬂicting, objectives. In these cases, the aggregation of multiple criteria into a single objective function seems a natural approach, but the rules for aggregation may be arbitrary and the resulting problem may be oversimpliﬁed.

Decision makers have often to face different, and usually conﬂicting, objectives. In these cases, the aggregation of multiple criteria into a single objective function seems a natural approach, but the rules for aggregation may be arbitrary and the resulting problem may be oversimpliﬁed.

# Providing the decision maker with a single “optimal” solution may be not adequate to capture the complexity of the actual decision to be made. In contrast, a shortlist of “non-dominated” solutions, i.e. solutions that cannot be improved in one objective without deteriorating at least another one, may effectively support the decision process. With this respect, multi-objective optimization tools are of interest.

Providing the decision maker with a single “optimal” solution may be not adequate to capture the complexity of the actual decision to be made. In contrast, a shortlist of “non-dominated” solutions, i.e. solutions that cannot be improved in one objective without deteriorating at least another one, may effectively support the decision process. With this respect, multi-objective optimization tools are of interest.