NP-hard decision problems

The hardest decisions in industry are the same handful of problems.

Which securities to hold. What to load on the truck. Which jobs run on which machine. Underneath the industry language they are the same mathematics — and they are the problems computers are worst at. heurics is building a general engine for them.

What “NP-hard” means in practice

Too many possibilities to ever check, and no shortcut to the best one.

Some problems get harder in a way that no faster computer can rescue. Add one more item and the number of possible answers doesn’t grow — it multiplies. Choosing 30 things out of 100, a small problem by industrial standards, already allows more combinations than there are grains of sand on Earth.

So nobody checks them all. In practice a business gets one of two things: an exact solver that can prove its answer is the best one, but only up to a certain size, or a rule of thumb that answers instantly and leaves value on the table that nobody can measure. Most real decisions are made in the gap between the two.

30 of 100 a modest selection problem — a portfolio, a shift, a load plan
3 × 1025 ways to make that one choice
~900,000 yrs to try them all at a trillion per second

Where they show up

Every industry has one, and usually calls it something else.

These are not exotic edge cases. They are the recurring, high-value decisions at the centre of the operation — the ones made every day, often under a deadline.

Asset management

Portfolio construction

Hold a few hundred securities out of thousands to track a benchmark, under limits on count, size, sector and tradable lot.

Insurance & pensions

Asset-liability matching

Buy a set of bonds whose cashflows meet decades of liabilities, under capital and eligibility rules.

Structured credit

Collateral selection

Assemble a pool of loans that satisfies a whole matrix of rating, diversity and concentration tests at once.

Cloud & data centres

Workload placement

Pack workloads onto machines so that as little capacity as possible is stranded across half-used servers.

Logistics

Routing & load building

Decide what goes on which vehicle, in what order, under capacity, time windows and driver hours.

Manufacturing

Scheduling & cutting

Sequence jobs across machines, and cut the required shapes from stock with the least waste.

Energy

Unit commitment

Choose which generators run in which hour, under start-up costs, ramp limits and reserve requirements.

Workforce & healthcare

Rostering

Cover every shift and every skill requirement while respecting rest rules, contracts and fairness.

What we’re building

One engine for the whole family, fast enough to use inside the working day.

heurics is a general-purpose engine for these problems. Rather than a bespoke model per problem, the same engine takes the decision, the objective and the rules that cannot be broken, and searches for the best answer it can find in the time available — on ordinary hardware, not a cluster.

Answers you can act on

Every answer respects every hard rule, at every moment of the search. Stop the clock whenever you like and what is on the table is usable.

Scale past where solvers stop

The interesting sizes are the ones where an exact solver stops proving anything. That is the range we build for, and we measure ourselves against the best available answer there.

Speed that changes the workflow

An overnight run gets done once. A run that takes seconds gets done ten different ways before the decision is made — which is where the real value sits.

Some of the problems above already fit the engine well; others are work in progress, and we would rather tell you which is which than sell you a general claim.

Benchmarks

Tested on the field’s own problems, not ones we invented.

We run against the public benchmark libraries and academic protocols these problems are judged by, plus real production data where we can get it — including a full production trace from a hyperscale cloud. Where a commercial solver can still prove the best answer, we check that we reach the same one. Past that size, we compare against the strongest published result.

Families benchmarked so far:

portfolio selection index tracking knapsack multidimensional knapsack bin packing graph colouring max-cut quadratic assignment fleet placement

Why this matters more than a demo. A benchmark someone else designed, with a protocol someone else published and a result someone else already achieved, is the only kind of test that can embarrass us.

The write-ups keep the methodology and the limitations next to the numbers, and we are glad to walk anyone through them.

Let’s connect

Got a problem in mind?

If something on this page sounded like a decision you make every week, we would like to hear about it — how it is solved today, what it costs when it goes wrong, and what you would do differently if the answer arrived in seconds. Half an hour, nothing to sit through.

connect@heurics.com