Rolling Horizon Optimisation
Solve the near horizon, commit the first decisions, slide forward, re-optimise -- trading global optimality for tractability, at the cost of suboptimality near each window boundary.
Read →Large Neighbourhood Search
A metaheuristic that escapes local optima by repeatedly destroying a large portion of the current solution and rebuilding it using an exact solver.
Read →Predict-then-Optimize
A two-phase workflow where an ML model forecasts uncertain parameters passed to an optimisation solver, creating a risk of decision infeasibility if forecast accuracy metrics don't align with decision error.
Read →Non-Anticipativity
A structural constraint in multi-stage stochastic models that forces decisions to be made using only information available at the time — preventing inadvertent peeking at the future.
Read →Big-M Formulation
Use a large constant to linearise disjunctive logic in mixed-integer models by scaling constraints with binary variables, at the cost of numerical fragility.
Read →Lexicographic Optimisation
Rank multiple objectives in strict sequential order: optimise the first criterion absolutely, then fix its optimal value and optimise the second criterion within that constraint.
Read →Integrality Gap
The fractional gap between the optimal value of an LP relaxation and the optimal value of the integer problem — a measure of how weak the relaxation is.
Read →Column Generation
An algorithmic technique for solving large LPs and MIPs by iterating between a restricted master problem and a pricing subproblem that identifies the most improving variable to add.
Read →Two-Stage Robust Optimisation
Optimise a here-and-now decision against the worst-case realisation of uncertain parameters in a given uncertainty set, where a recourse action is allowed after uncertainty is revealed.
Read →Pareto Optimality
A solution is Pareto optimal when no objective can be improved without worsening at least one other objective. The Pareto front is the set of all such non-dominated solutions.
Read →Constraint Programming
Specify what constraints must hold over a set of decision variables; let a solver propagate those constraints and search for an assignment that satisfies all of them.
Read →Stochastic Programming
Minimises expected cost across a probability distribution of scenarios rather than a single forecast — producing decisions that are good on average rather than guaranteed for the worst case.
Read →Mixed Integer Programming
Optimisation where some decisions must be whole numbers — enabling yes/no choices, assignment decisions, and logical conditions that continuous LP cannot model.
Read →Branch and Bound
Solves integer programmes exactly by recursively splitting on fractional variables while pruning branches where the LP relaxation proves no improving integer solution can exist.
Read →Benders Decomposition
Solves large MIPs by fixing complicating integer variables, solving the resulting LP exactly, and feeding back optimality and feasibility cuts until the two subproblems converge.
Read →Lagrangian Relaxation
Moves hard coupling constraints into the objective with a penalty multiplier, creating a decomposable problem that provides a lower bound and often near-optimal solutions.
Read →Scenario Recourse Inequalities
Valid cuts for two-stage stochastic MIPs that encode optimal recourse policy choices as integer constraints, enabling exact solution with provable optimality certificates.
Read →Vehicle Routing Problem
Find the cheapest way to assign customers to a fleet of vehicles and sequence each vehicle's stops, subject to capacity and time constraints.
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