Problem and Solve¶

Problem¶

Problem is the LP container. Lifecycle:

p = Problem()
v = p.add_var(...)                     # register a variable
p.set_objective(c * v, sense="min")    # set an objective
p.add_cstr(name, over=…, sense=…,      # add a constraint family
           lhs_terms=…, rhs_terms=…)
sol = p.solve()                         # build LP, hand to HiGHS, return Solution

Constraints are stored as protos and only materialize into LP rows when solve() (or WarmProblem) is invoked.

Adding a constraint¶

p.add_cstr(
    name="balance",
    over=node_time_index,         # (n, d, t) frame; one LP row per row here
    sense="==",                   # one of "<=", ">=", "=="
    lhs_terms={                   # named contributions on the LHS
        "inflow":  Sum(v_in,  over=…),
        "outflow": Sum(v_out, over=…),
        "delta":   v_state - Lag(v_state, …),
    },
    rhs_terms={                   # named contributions on the RHS
        "demand": p_demand,
    },
)

Each term's open dims must be a subset of over's columns. Constants (int, float) and Param are accepted on either side. Var / Expr on the RHS are moved to the LHS automatically.

Row counts¶

p.cstr_row_count("balance") returns the number of LP rows the constraint produced. p.cstrs_named("balance") returns the CstrRecord for the constraint family — useful when you need to look up row indices for warm updates or duals.

Solution¶

Solution is what Problem.solve() returns:

sol = p.solve()
sol.optimal              # bool
sol.obj                  # float — objective value (with offset applied)
sol.value("v")             # polars frame: (*dims, value)
sol.value_wide("v", …)    # wide-form frame for time-indexed vars
sol.constraint_dual("balance")   # polars frame: (key, dual)
sol.col_dual             # numpy array of reduced costs
sol.highs                # the live highspy.Highs instance — for advanced use

Numerics: HiGHS's optimality status is reported on sol.optimal. For non-optimal terminations, inspect sol.highs.getModelStatus() directly.

Solver options¶

Pass HiGHS options at construction time:

p.set_solver_options({"presolve": "off", "solver": "simplex"})

or per-solve:

sol = p.solve(options={"time_limit": 60.0})

The per-call options overrides the stored options. Keys must match HiGHS canonical names; values must be the type HiGHS expects (str/int/float/bool).