networkconstrained

Network-constrained refers to systems or problems in which feasible decisions are limited by an underlying network structure. The network is typically represented as a graph, with nodes corresponding to locations and edges to links such as roads, pipes, or communication lines. Each edge may have attributes like capacity, cost, or travel time, and decisions must respect these constraints as well as flows that conserve at network nodes. This concept is used across disciplines including transportation, energy, telecommunications, and logistics.

In mathematical terms, network-constrained problems often involve decision variables defined on edges or paths, subject to flow conservation at nodes, capacity limits on edges, and demand satisfaction. Additional routing, connectivity, or accessibility requirements may be imposed. The objective can vary, encompassing cost minimization, throughput maximization, reliability improvements, or a combination of performance metrics.

Common problem classes include network flow problems (such as max flow and min-cost flow), shortest-path problems with constraints, vehicle routing with network considerations, and network design or facility location problems embedded in a graph. These models frequently feature mixed integer and linear components, reflecting binary decisions like edge activation or route selection.

Solution approaches range from exact methods (linear and integer programming, decomposition techniques) to heuristics and metaheuristics for large-scale or complex networks. Stochastic programming and robust optimization address uncertainty in demand, travel times, or link failures, while time-expanded or dynamic networks capture temporal changes.

Applications span urban transit planning, power and water distribution, telecommunications routing, and supply chain logistics. Challenges include scalability, network dynamics, uncertainty, and resilience against disruption.