Mobjective

Mobjective is a conceptual framework for multi-criteria optimization that generalizes traditional scalarization approaches by introducing a modular objective aggregator. In Mobjective, each criterion is treated as a component of a vector-valued objective, and an aggregator function combines these components into a single scalar objective. The aggregators are parameterized to reflect decision-maker preferences, allow different norms, and support adaptive weighting schemes.

Core idea: An aggregator A(o1,...,on; θ) maps the vector of objective values o to a real number, where θ denotes weights, priority orders, or reference points. By solving the optimization problem min A(o1,...,on; θ) subject to constraints, and by varying θ, the method traces a set of Pareto-efficient solutions. Mobjective thus unifies linear, nonlinear, and lexicographic scalarization under a single framework and accommodates both static preferences and dynamic, context-dependent weighting.

Advantages and limitations: It provides a flexible way to encode complex preferences, supports hierarchical or category-based objectives, and can be implemented with existing optimization solvers. Limitations include sensitivity to the choice of aggregator and potential non-convexities, which can affect tractability and the interpretability of results.

Applications: The concept appears in theoretical studies of decision theory, engineering design, operations research, and AI planning, where there are several competing objectives and explicit trade-offs are required.

See also: multi-objective optimization, Pareto efficiency, scalarization, decision support systems.