AI + Operations Research Consulting · Singapore

We Design Optimization Algorithms
for Your Hardest Operational Problems

Using AI-driven automated algorithm design, we solve the combinatorial optimization challenges that stump commercial solvers — across energy dispatch, production scheduling, fleet routing, network planning, revenue management, portfolio optimization, and beyond — without months of manual algorithm engineering.

Book a Consultation → See Case Study ↓

The Challenge

Why real-world OR problems remain unsolved

Commercial solvers and textbook algorithms were not designed for the messy, large-scale realities of industrial operations. Three fundamental barriers stand in the way.

Commercial solvers hit a wall at industrial scale

Tools like Gurobi and CPLEX work well on textbook instances. But real industrial problems — involving thousands of jobs, vehicles, or assets with complex constraints — exceed what any off-the-shelf solver can handle within practical time limits.

Custom algorithms take months of expert effort

When solvers fall short, the only option is a hand-crafted heuristic. Designing one demands deep OR expertise, careful problem analysis, and months of iterative engineering — a process most organizations simply cannot afford to repeat for every new challenge.

Algorithms don't transfer across problems

A metaheuristic tuned for one scheduling problem rarely generalizes to another — even structurally similar ones. Every new problem variant restarts the design process from scratch, with no reuse of prior investment in algorithm development.

Our Approach

ORaI: LLM-driven automated algorithm design

Most AI methods try to solve optimization problems directly — and fail on anything novel or large-scale. ORaI takes a different path: we use large language models to design the algorithms themselves, producing a portfolio of complementary heuristics that collectively cover your problem's full landscape of instances and runtime requirements.

Stage 01

Modular Problem Decomposition

We encode your problem as modular components — state representation, action space, and a domain tool library. This separation means our LLM focuses purely on decision logic, not on re-learning your domain from scratch. It also enables generalization: the same structure works across radically different problem types.

Stage 02

Complementary Portfolio Evolution

An LLM-driven evolutionary process iteratively generates, evaluates, and selects heuristics under explicit runtime budgets. Rather than producing a single algorithm, it constructs a complementary portfolio — heuristics that collectively dominate across instance types, from fast emergency decisions to deep overnight optimization.

Delivery

Production-Ready Algorithm Portfolio

You receive clean, executable Python code — a set of algorithms that outperform both human-designed heuristics and existing LLM-based methods, and that generalize zero-shot even to problems no prior method has encountered. No problem-specific pretraining required.

Zero-shot generalization to structurally novel problems absent from any training corpus

Any domain applicable to any combinatorial optimization problem — scheduling, routing, assignment, planning, and beyond

Full spectrum from real-time emergency decisions to high-quality overnight strategic planning

How It Works

From a plain description to a production-ready algorithm

You don't need to know operations research. Just describe your problem as you would to a colleague — we handle all the modelling, solving, and delivery.

Describe your challenge in plain language

Tell us about your operational scenario, objectives, and constraints — no formulas, no technical background required. A paragraph is all it takes to start.

AI automatically models your problem

We translate your description into a rigorous combinatorial optimization problem — defining state space, objective function, and constraint structure. What typically takes senior OR experts weeks, our system does automatically.

LLM-driven algorithm evolution & selection

Large language models iteratively generate, evaluate, and select heuristics under explicit runtime budgets — building a portfolio of complementary algorithms that collectively cover every instance type and time horizon your problem demands.

Receive your complete solution

You receive production-ready Python algorithm code, a detailed performance benchmark report, and full technical support to integrate the solution into your existing systems.

Example scenario

“We operate 150 delivery vehicles across Southeast Asia, serving 600–800 drop points daily. Our routing software takes 2 hours to compute and still needs heavy manual adjustment — during peak season we can't even finish before drivers need to depart.”

ORaI delivery · completed in 3 weeks

23%

reduction in total transport cost

8 min

route planning time (down from 2 hrs)

4×

peak-season load capacity improvement

Zero-shot generalisation · no historical training data required

Describe your problem for furhter consultation →

Application Domains

OR optimization applies across every major industry

From energy grids to e-commerce platforms, operations research drives decisions at every scale. ORaI's automated algorithm design works across all of them.

Energy

Reactive power scheduling, unit commitment, electricity market pricing & clearing

Aerospace & Defense

Spacecraft trajectory optimization, test resource scheduling, combat resource allocation & logistics

Aviation

Flight scheduling, disruption recovery, network planning, route & revenue management

Transportation

Metro/rail maintenance scheduling, crew rostering, smart port scheduling & coordination

Industry 4.0

Production scheduling, S&OP, smart manufacturing, inventory & warehouse network optimization

Retail

Smart site selection, staff rostering, revenue management & inventory optimization

E-Commerce

Marketing strategy optimization, ad budget allocation & traffic distribution

Warehousing & Logistics

Route optimization, network planning, replenishment, wave scheduling & pick path optimization

Finance

Portfolio optimization, quantitative market computation & risk management

Academia & Research

OR & management, automation, CS, mechanical, industrial, electrical & chemical engineering

Case Studies

State-of-the-art performance across 4 combinatorial optimization benchmarks

ORaI is evaluated on Job Shop Scheduling (JSSP), Traveling Salesman Problem (TSP), Capacitated Vehicle Routing (CVRP), and a novel Port Scheduling Problem (PSP) — benchmarked against classical solvers, learning-based methods, and existing LLM-based frameworks.

JSSP

1.95%

avg gap · best overall

vs 11.30% HeurAgenix · 9.49% OR-Tools

TSP

1.11%

avg gap · best overall

vs 8.29% HeurAgenix · 7.55% LEHD

CVRP

6.35%

avg gap · best LLM method

vs 17.33% HeurAgenix · 8.87% EoH-S

PSP

0.83%

avg gap · zero-shot novel problem

vs 22.61% Gurobi 30 min · 14.54% HeurAgenix

Performance comparison across JSSP, TSP, CVRP, and PSP — average quality gap vs. average runtime

Average quality gap (%) vs. average runtime across all four benchmark problems. Lower-left is best. ORaI (★) consistently achieves the best quality–time trade-off across all domains.

Job Shop Scheduling Problem (JSSP)

15 standard benchmark instances: small (la10–la14, 10 jobs × 5 machines), medium (swv18–ta69, 20 jobs × 10–15 machines), large (ta73–ta77, 20 jobs × 15–20 machines). Gap = (Solution − Optimal) / Optimal × 100%. Time in seconds. Lower gap is better.

Scale	Instance	OR-Tools		Iterated Greedy		FunSearch		EoH		EoH-S		HeurAgenix		ORaI
Scale	Instance	Gap	Time	Gap	Time	Gap	Time	Gap	Time	Gap	Time	Gap	Time	Gap	Time
Small	la10	0.00	0.48	0.00	60.02	12.65	0.34	6.75	0.12	0.00	0.07	5.64	0.05	0.00	0.08
	la11	0.00	0.87	0.00	60.07	12.05	0.54	6.35	0.18	6.14	0.13	29.05	0.08	0.99	0.11
	la12	0.00	0.68	0.00	60.05	11.25	0.54	5.60	0.18	15.98	0.13	23.77	0.09	0.07	0.11
	la13	0.00	3.16	0.00	60.05	16.40	0.96	10.06	0.14	0.35	0.12	16.26	0.08	0.35	0.11
	la14	0.00	0.31	0.00	60.07	15.60	2.75	9.45	0.85	0.00	0.13	15.87	0.08	0.00	0.11
Medium	swv18	1.40	60.02	15.64	60.07	18.25	5.26	11.39	3.40	2.35	3.22	1.12	1.61	2.35	2.18
	swv20	4.68	60.02	16.12	60.07	17.60	5.34	10.75	3.40	5.65	3.12	6.80	1.51	2.54	2.17
	ta53	18.18	60.01	32.14	60.05	16.90	7.00	10.10	8.40	4.48	7.56	5.74	4.09	0.93	5.45
	ta60	18.07	60.01	44.47	60.07	19.45	10.50	12.25	9.45	5.03	8.21	11.51	4.11	2.03	5.43
	ta69	25.17	60.01	43.24	60.05	22.80	31.25	14.25	28.70	9.34	16.64	8.90	8.51	1.97	10.91
Large	ta73	16.41	60.03	35.25	60.07	22.10	31.25	13.60	28.70	7.22	80.30	3.90	31.22	4.68	38.84
	ta74	13.54	60.02	34.14	60.05	26.40	62.00	17.95	57.75	2.64	90.74	13.59	32.13	0.79	40.61
	ta75	15.30	60.03	25.58	60.07	25.60	62.00	17.25	57.75	12.63	82.76	12.56	32.19	3.20	41.05
	ta76	18.42	60.03	28.13	60.07	29.30	93.00	20.60	86.80	6.92	85.82	6.19	32.39	5.55	38.40
	ta77	11.20	60.03	30.12	60.05	28.60	93.00	19.90	86.80	9.55	80.18	8.64	32.21	3.78	42.58
Average		9.49	40s	20.32	60s	19.66	27s	12.42	25s	5.88	31s	11.30	12s	1.95	15s

Traveling Salesman Problem (TSP)

15 TSPLIB benchmark instances: small (29–152 cities), medium (417–666 cities), large (1000–1889 cities). Gap = (Solution − Optimal) / Optimal × 100%. Time in seconds. Lower gap is better. † Results from cited papers.

Scale	Instance	OR-Tools		POMO†		LEHD†		FunSearch		EoH		EoH-S		HeurAgenix†		ORaI
Scale	Instance	Gap	Time	Gap	Time	Gap	Time	Gap	Time	Gap	Time	Gap	Time	Gap	Time	Gap	Time
Small	kroD100	0.00	300.16	4.52	0.10	2.47	0.12	4.91	0.50	4.20	0.80	3.94	0.27	6.19	0.28	0.05	0.34
	kroE100	0.29	300.18	4.35	0.10	2.53	0.12	14.70	0.50	6.80	0.80	4.56	0.27	6.46	0.28	0.06	0.34
	pr107	0.00	300.17	4.87	0.10	2.68	0.13	15.50	1.50	3.68	0.80	2.62	0.34	3.65	0.36	0.88	0.45
	bayg29	0.00	300.04	3.14	0.10	1.95	0.08	12.80	0.40	3.20	0.02	2.24	0.01	1.37	0.01	0.93	0.01
	pr152	0.85	300.36	5.27	0.20	2.81	0.18	23.21	3.20	7.49	1.10	2.05	0.88	2.41	1.07	0.93	0.33
Medium	d657	4.82	306.22	25.14	19.22	5.63	26.85	25.40	180.50	19.50	85.00	7.41	68.29	9.30	85.83	1.37	97.50
	ali535	6.18	305.27	22.52	11.45	4.89	24.92	28.60	95.80	22.30	42.00	11.72	36.92	11.25	53.93	1.24	48.87
	fl417	2.01	302.59	17.58	15.45	4.42	23.28	21.50	48.20	15.80	22.50	3.67	16.76	3.07	20.31	1.29	24.89
	gr666	3.82	308.17	26.14	14.25	5.87	27.41	24.10	185.60	18.90	90.00	7.74	69.97	14.98	87.26	0.01	91.67
	u574	4.76	305.45	23.84	13.52	5.14	25.36	13.23	118.40	17.40	62.80	9.65	44.96	10.46	55.75	1.51	64.89
Large	fl1400	5.61	333.18	45.47	34.44	13.76	38.76	25.20	1850.20	18.50	820.50	2.67	668.68	7.48	766.62	0.88	188.00
	rl1889	9.17	356.91	75.14	64.53	16.48	72.18	22.50	2680.80	25.80	2100.00	12.33	1702.32	12.12	1926.51	2.80	248.93
	vm1748	9.37	354.16	95.85	59.52	15.92	65.43	28.90	1720.45	21.20	1680.30	7.26	1339.19	12.27	1556.55	1.58	212.26
	u1432	5.54	332.78	98.71	46.95	15.83	52.37	23.70	1015.80	17.60	950.60	9.47	727.12	11.63	831.10	1.83	205.46
	dsj1000	7.85	317.28	40.46	39.53	12.91	48.94	19.80	480.25	13.40	380.70	8.18	240.09	11.69	319.75	1.26	169.32
Average		4.02	315s	32.87	21s	7.55	27s	20.27	559s	14.38	416s	6.37	328s	8.29	380s	1.11	90s

Capacitated Vehicle Routing Problem (CVRP)

15 X-series benchmark instances: small (X-n106–X-n251), medium (X-n317–X-n439), large (X-n641–X-n957). Gap = (Solution − Optimal) / Optimal × 100%. Time in seconds. Lower gap is better. † Results from cited papers.

Scale	Instance	PyVRP		POMO†		LEHD†		FunSearch		EoH		EoH-S		HeurAgenix†		ORaI
Scale	Instance	Gap	Time	Gap	Time	Gap	Time	Gap	Time	Gap	Time	Gap	Time	Gap	Time	Gap	Time
Small	X-n106	1.60	300.01	7.23	0.13	5.82	0.18	30.50	3.85	25.20	3.15	8.80	2.50	21.91	2.84	7.96	0.46
	X-n157	2.32	300.05	7.89	0.21	5.47	0.29	12.50	8.10	10.80	6.65	8.68	5.25	8.87	5.97	8.47	0.97
	X-n181	2.17	300.06	8.34	0.26	6.15	0.36	25.80	10.80	21.50	8.85	10.20	7.00	18.03	7.95	7.68	1.89
	X-n219	0.69	300.07	16.47	2.85	6.28	3.92	22.40	26.60	18.90	21.85	4.50	17.25	15.42	19.61	1.97	6.83
	X-n251	4.27	300.08	17.82	4.17	11.63	5.74	32.50	34.30	27.80	28.15	14.50	22.20	22.14	25.26	9.29	4.24
Medium	X-n317	1.11	300.13	19.56	7.38	12.71	10.15	14.80	79.55	12.50	65.25	6.20	51.50	9.56	58.59	2.49	11.04
	X-n359	6.15	300.19	20.73	9.64	13.38	13.27	24.60	91.35	20.80	74.90	11.50	59.20	16.84	67.25	8.26	9.47
	X-n376	0.73	300.18	21.18	15.83	13.19	14.91	16.50	130.50	13.80	107.05	4.80	84.60	11.24	96.10	1.91	25.55
	X-n401	5.42	300.16	22.41	18.76	15.94	17.57	22.60	117.35	19.20	96.25	9.50	76.00	15.42	86.41	7.94	12.81
	X-n439	5.31	300.24	24.35	26.52	14.67	22.76	16.80	113.75	14.20	93.30	9.50	73.70	11.24	83.84	7.38	17.41
Large	X-n641	6.09	300.44	38.67	48.47	16.83	52.93	34.20	830.10	29.50	680.60	11.50	537.50	23.20	611.26	8.19	39.89
	X-n655	1.16	300.54	39.84	50.25	17.29	55.43	29.50	343.20	25.20	281.40	6.80	222.40	20.12	252.81	2.51	108.14
	X-n701	8.68	300.98	42.19	67.83	18.46	65.87	23.40	380.75	19.80	312.25	7.20	246.70	15.75	280.45	6.75	56.37
	X-n801	4.02	300.79	45.73	72.71	19.75	86.33	35.80	1700.55	30.60	1394.70	8.90	1101.80	24.22	1252.16	7.35	73.86
	X-n957	4.06	300.93	52.38	95.38	22.91	131.24	38.50	2205.75	32.80	1809.15	10.50	1429.10	26.02	1624.12	7.09	183.92
Average		3.59	300s	25.65	28s	13.37	32s	25.36	405s	21.51	332s	8.87	262s	17.33	298s	6.35	37s

Port Scheduling Problem (PSP) — Novel Zero-Shot Benchmark

18 benchmark instances: small (20–100 vessels), medium (150–250 vessels), large (300–500 vessels). Gap measured vs. best solution found across all methods. FunSearch, EoH, and EoH-S all failed to produce feasible algorithms for this novel problem.

Scale	Instance	Gurobi			GPIH		HeurAgenix		ORaI
Scale	Instance	10 min	20 min	30 min	Gap	Time	Gap	Time	Gap	Time
Small	20_2_3_T12	0	0	0	21.19	1s	8.54	1s	3.41	1s
	40_3_4_T12	0	0	0	13.83	1s	8.97	1s	3.15	1s
	60_5_8_T12	0	0	0	10.09	1s	7.57	1s	3.01	1s
	80_10_15_T48	5.45	3.41	0	20.95	1s	14.56	1s	2.51	1s
	100_15_30_T24	10.64	6.59	0	21.41	1s	9.51	3s	2.84	6s
	100_15_30_T48	19.04	19.04	2.80	19.45	1s	11.25	5s	0	7s
Medium	150_20_40_T24	6.04	1.36	2.22	19.53	2s	5.64	11s	0	18s
	150_20_40_T48	51.21	10.61	10.61	18.54	3s	6.31	25s	0	53s
	200_20_40_T24	25.53	6.53	6.53	23.54	4s	8.64	24s	0	78s
	200_20_40_T48	43.98	43.98	8.94	25.14	5s	9.69	48s	0	118s
	250_20_50_T24	28.26	8.59	8.59	24.53	4s	11.35	52s	0	202s
	250_20_50_T48	70.07	70.07	34.64	18.25	5s	15.64	61s	0	310s
Large	300_25_60_T24	63.41	34.67	22.08	17.55	4s	21.25	58s	0	402s
	300_25_60_T48	66.93	66.93	66.93	35.51	6s	23.14	69s	0	502s
	400_30_80_T24	76.20	76.20	29.12	39.15	7s	20.12	68s	0	690s
	400_30_80_T48	70.99	70.99	70.99	45.54	8s	19.34	80s	0	884s
	500_40_100_T24	82.65	82.65	82.65	38.51	7s	31.52	81s	0	870s
	500_40_100_T48	60.87	60.87	60.87	35.64	9s	28.59	93s	0	987s
Average		37.85	31.25	22.61	27.31	4s	14.54	38s	0.83	285s

† Results taken from original papers (HeurAgenix, POMO, LEHD)

How We Work

Tailored engagements, from proof-of-concept to production

Every client challenge is different. We offer three engagement models designed to match where you are — whether you are exploring feasibility, deploying at scale, or building a long-term optimization capability.

2 – 3 weeks

Pilot Assessment

Validate whether your problem is a strong fit for AI-driven algorithm design — with a working demonstration before any larger commitment.

Deep-dive problem scoping session
State-action-tool framework design
Small-scale ORaI demonstration run
Performance benchmark report
Engagement roadmap and recommendations

Get in Touch

Most Requested

4 – 8 weeks

Full Deployment

End-to-end algorithm design, optimization, and delivery — from problem formulation to a production-ready algorithm portfolio running in your environment.

Everything in Pilot Assessment
Full ORaI evolutionary design process
Complementary algorithm portfolio (executable code)
Integration support for your existing systems
Post-delivery technical support

Ongoing

Ongoing Partnership

A continuous optimization partnership for organizations with evolving operational challenges — new problem variants, algorithm refinement, and strategic advisory.

Continuous algorithm refinement
New problem variant support
Regular strategy review sessions
Priority response and dedicated access
Annual performance audit

Let's Talk

Get In Touch

Tell us about your optimization challenge

Email us with a description of your operational context and optimization objectives — we typically respond within 1–2 business days.

huatian.gong@ntu.edu.sg

In your email, briefly describe your operational scenario, objectives, and constraints — we will arrange an introductory call as soon as possible.

Send an Email →

Typically responds within 1–2 business days

We Design Optimization Algorithmsfor Your Hardest Operational Problems