cooptimization

Cooptimization, or co-optimization, refers to the simultaneous optimization of multiple interdependent components, subsystems, or decision problems to achieve a better overall performance than optimizing each part in isolation. It is used when decisions in one component affect others and when a global objective depends on the combination of choices across components.

Formally, cooptimization involves selecting decisions x in X and y in Y to optimize a joint objective f(x, y) subject to constraints g(x, y) ≤ 0. The coupling between x and y means that solving the problems separately can miss advantageous trade-offs. Cooptimization problems can be single-objective or multi-objective, in which case solutions seek Pareto efficiency rather than a single optimum.

Applications span engineering design, computer systems, energy and infrastructure, and operations planning. In engineering, co-design or hardware-software co-optimization aligns hardware architectures with software workloads. In energy systems, co-optimization may couple generation, transmission, storage, and demand response to minimize cost or emissions. In supply chains, simultaneous planning of production, inventory, and distribution can reduce total cost and improve service levels.

Common solution approaches include problem decomposition and Lagrangian relaxation to exploit structure, hierarchical or bilevel optimization for coupled decision levels, alternating optimization to iteratively update one set of variables while keeping others fixed, and various metaheuristics for large, nonconvex problems. The tractability of cooptimization depends on objective properties, constraint coupling, and data availability.

Related ideas include co-design, multiobjective optimization, and joint optimization. Cooptimization remains an active area in operations research, computer science, and systems engineering, reflecting the importance of cross-component interactions in complex systems.