The meaning of a real optimality claim
A result is not real because it is numerically attractive. It is real when feasibility is checked, the objective is reproducible, the bound status is clear, and the stopping condition can be audited.
OptFin Research Notes
A professional blog for optimization and operations research
This journal is the public working notebook of OptFin Research Lab: exact methods, decomposition, branch-and-bound, packing, routing, scheduling, stochastic models, robust optimization, AI structure, and proof standards for real-world decisions.
Linear Programming
Mixed-Integer Optimization
Scheduling
Vehicle Routing
Machine Reassignment
Packing and Loading
Network Flow
Column Generation
Benders and Lagrangian
From O(n) to one decisive operation
The OptFin hypothesis is that intelligence appears when the decisive local structure can be isolated, collapsed, solved or tightly bounded, and then lifted back into the original graph without breaking global validity.
Why historical challenge families still matter
Assignment, packing, routing, outage planning, machine reassignment, and adaptive segment routing remain the strongest regression suite for any ambitious optimization engine.
Exact locally, heuristic globally, honest everywhere
Exactness does not need to dominate the whole instance. It needs to dominate the decisive kernels while global search preserves good incumbents, repairs feasibility, and improves upper bounds safely.
Problem Catalog
Optimization families that belong in the OptFin academic lab
- Linear programming and convex optimization
- Mixed-integer programming and combinatorial optimization
- Set covering, partitioning, and packing
- Assignment and generalized assignment
- Knapsack and multiple knapsack
- Cutting stock and bin packing
- Graph coloring and clique structure
- Network flow, multi-commodity flow, and survivability
- Vehicle routing, arc routing, and pickup-delivery
- Timetabling, rostering, and machine scheduling
- Maintenance planning and outage planning
- Facility location and service territory design
- Stochastic, robust, and online optimization
- Game-theoretic and bilevel optimization
- Branch-and-bound and branch-and-cut
- Dynamic programming on compressed state spaces
- Lagrangian relaxation and column generation
- Benders decomposition and dual methods
- Metaheuristics, VNS, ILS, and tabu search
- Hybrid AI + OR decision systems
- Certified lower-bound / upper-bound convergence