Solver concepts and interface choices

From paths to a routing solution

Pricing finds resource-feasible source-to-sink paths with low reduced cost. A master chooses quantities of route columns to satisfy customer or other shared rows. Column generation alternates master LP solves with pricing. Cuts add valid inequalities; branch-and-price searches integer decisions across a tree.

These layers return different objects. A cheap feasible path is not a full fleet plan. A converged root LP can be fractional. A feasible integer incumbent is an upper bound in minimization; pricing supplies lower-bound information under its configured guarantee. Compare the two only when both concern the same model, distance convention, and inherited node restrictions.

Select the workflow

Need	CLI	Python	Reading
Feasible heuristic routing plan	`hgs`	HGS seeding within root solve	CLI
Routing root LP	`solve`	`solve_root`	pyBaldes routing
Single-network integer routing tree	`solve --tree`	Not exposed by `solve_root`	Routing tree
Custom RCSP pricing	Through a model	`Solver`	Pricing
Shared-master root / integer search	`multi-pricing` / `multi-pricing --tree`	`NetworkProblem.solve(tree=...)`	Multi-pricing

A network model can represent several route families. Its branching capabilities and integer-domain contract differ from the specialized routing tree. A shared master is part of the core framework, while specialized routing formulations are organized under extensions. See source layout.

Three meanings to keep separate

Route feasibility checks a path against resource and node restrictions. Pricing exactness establishes a minimum over the configured pricing domain, which may be an NG relaxation. Independent certification validates bounds or witnesses using its supported arithmetic/model contract. A pricing exactness flag alone does not establish an independent master certificate.

The selected bound_mode is numerical by default. Certified mode keeps missing certificates unknown rather than substituting numerical estimates. JSON uses null for unknown bounds. See Python results and the CLI bound fields.

Resources and route domains

Scalar resources combine arc consumption, initial states, and vertex windows. Disposable coordinates may wait; equality coordinates do not. Coupled resources express additional domains and state-dependent costs on the same physical graph. Their definitions are distinct from scalar coordinate IDs. See scalar resources, coupled resources, and multiple windows.

NG memory is a relaxation of elementary routing: a priced path can revisit a customer when the memory permits it. Complete supported enumeration can transfer an elementary route universe into a master. A bounded collection attempt is not complete just because it returned routes. Inspect enumeration coverage before using a finite-pool MIP as a proof. See enumerated MIP and network transfer.

Reproduce an objective

Match instance data, customer subset, rounding, explicit matrix, NG construction, cuts, backend, bound mode, and limits. CLI coordinate distances default to truncated tenths; Python follows the instance's convention. Root benchmark reproduction requires --rounding none. Compare objective values only after those choices match, and report limits and proof scope with every result.