Academic Laboratory

AI as a convergent optimization structure

OptFin studies a foundational idea: a knowledge-bearing AI can repeatedly compress a hard graph problem into a smaller certified operation, bring back a feasible improvement from that abyss, and continue until lower and upper bounds converge toward a provable optimum.

Read the theory Launch the V3 simulator See the research agenda

An AI does not only answer. It restructures.

The OptFin view is that intelligence emerges when an agent can enter a hard graph, isolate the active frontier, reduce the search to a minimal valid operation, and return with a certified contribution to the global solution.

The result must be feasible, not poetic.

Every candidate must carry a status: OPTIMAL, FEASIBLE_WITH_GAP, INFEASIBLE, or UNSOLVED. A laboratory is only serious when feasibility is checked and the objective is reproduced.

Exactness lives locally, power lives globally.

We combine exact subgraph solvers, branch-and-bound, dynamic programming, and hybrid metaheuristics so that small critical regions are solved exactly while global search remains scalable.

Theory

The OptFin structural hypothesis

OptFin starts from a strong proposition: a sufficiently informed AI can identify a dominant local structure inside a large optimization graph, collapse it into a single certified operation, solve or tightly bound that operation, and reinsert the result into the original graph without losing global validity.

Repeating that cycle induces a layered decomposition. The lower bound rises through exact local certificates. The upper bound falls through feasible reconstructions and repair. Intelligence appears when both fronts converge under proof, not when one of them merely sounds persuasive.

Step 1

Locate the active frontier

Detect the arcs, variables, residues, or assignments that dominate cost.

Step 2

Collapse the subgraph

Rewrite the decisive region as a bounded exact problem with explicit guards.

Step 3

Recover a certified move

Lift the local optimum back into the global instance and recompute feasibility.

Step 4

Drive bounds to convergence

Track gap, certificates, repairs, and stopping criteria until proof is honest.

Architecture

A superstructure for exactness, repair, and proof

Global layer

Instance parser and domain model
Incumbent manager and feasibility checker
Bound tracker with proof registry
Portfolio scheduler for exact and heuristic lanes

Critical subgraph engine

Dynamic programming on compressed neighborhoods
Branch-and-bound with aggressive pruning
Exact enumeration for tiny decisive kernels
Restricted master or cut generation when structure allows

Recovery layer

Feasible reconstruction and repair
Hybrid metaheuristics for global polish
Status semantics for agents and APIs
Runtime guards for memory, time, and fallback safety

Exact where it matters

Critical kernels are solved exactly or with certified gaps. We do not waste exact methods where structure is too loose to justify them.

Feasible at every stage

The system should always retain a valid incumbent. A research platform must survive hard instances without collapsing the whole run.

Proof before product claims

PMAFIN, Solvida, and agent orchestration should inherit this engine only after objective values, feasibility, and gaps are reproducible.

Research Programs

Where the lab applies the theory

Operations Research

ROADEF and large-scale industrial benchmarks

Historical ROADEF families remain the stress test for the OptFin thesis: assignment, machine reassignment, routing, packing, outage planning, and adaptive segment routing.

Molecular Design

Exact subgraph refinement for pMHC binders

Generative models can explore candidate structures; OptFin can certify and refine the decisive contact subgraphs governing specificity and off-target risk.

Agent Systems

Optimization as the common decision API

Luna, Solvida, and future agents should not improvise critical actions. They should call OptFin when a decision has a measurable objective, constraints, and proofs.

Proof Standard

The lab standard for a real result

An OptFin result is real only when the instance, objective value, feasibility status, runtime, lower bound, upper bound, optimality gap, and checker evidence are preserved together. Anything else is still only a promising narrative.

Field Requirement

Feasibility Independent checker or verifiable constraints

Objective Explicit value with reproducible evaluation

Bound status Lower bound, upper bound, and certified gap

Trace Solver path, fallback path, and stopping reason

OptFin Mission

Build the academic core first. Then let every system inherit certainty.

OptFin.org is the public face of a research program: operations research, AI structure, certified decomposition, and convergence by proof. The aim is not to decorate optimization. It is to make optimality claims worthy of belief.