Solver Technology

The Engine That Thinks in Tensors

Discover how Helix AI's patented solver architecture delivers 18-600x faster optimization while guaranteeing 100% constraint satisfaction across all domains.

Evo Architecture

A lean, layered pipeline where English prompts enter at the top, emerging as GPU-accelerated decisions at the bottom—every step auditable and evolvable.

Compact Symbology

Express problems as concise chains like D_m(5k) → C*(60,30m) → O*(50). Each token is a handle to GPU primitives.

Millisecond compilation to GPU kernels

Fused Execution

No eager loops—symbols auto-fuse (distance + contraction = single kernel launch). Data stays GPU-resident.

10-50x speedup vs traditional solvers

Learned Composites

MetaLearner analyzes runs and invents hybrids like O* = 2opt ⊗ swap (22% faster). System self-evolves.

Continuous improvement without human tuning

HelixDelta Streaming

Parse problems as DAGs. When data changes (+100 orders), re-execute only downstream symbols in <50ms.

Batch problems become real-time

100% Constraint Satisfaction

Provably correct solutions verified by mathematical proofs, not heuristics or approximations.

Enterprise-grade reliability

Multi-Domain Universality

148 symbols span optimization, transformers, SSMs, GNNs, forecasting, and diffusion models.

Single platform for all optimization domains

Solver Lineup

Each solver optimized for specific problem characteristics. Choose the right tool for your workload.

Hybrid Solver

Core Two-Phase Architecture

Combines constraint programming for hard constraints with GPU-accelerated neural constraint optimization for soft constraints.

SPEEDUP
18-46x faster than OR-Tools

Phase 1: Hard Constraint Satisfaction

  • Pre-compiles hard constraints to binary indicator masks
  • Uses OR-Tools CP-SAT for constraint satisfaction
  • Guarantees 100% feasibility before optimization
  • Performance: 64-133ms for 86-124 constraints

Phase 2: Soft Constraint Optimization

  • Pre-compiles soft constraints to energy tensors
  • GPU-accelerated Graph Neural Networks (GNN)
  • Operates exclusively within feasible subspace
  • Iterative refinement (typically 2 iterations)

Best For

  • Generic optimization with hard and soft constraints
  • Real-time applications requiring <1s solve time
  • Problems requiring 100% constraint satisfaction
  • Multi-domain optimization
  • Dynamic staffing and instant updates

Performance Metrics

Solve Time (GPU)
Target: <1s
Achieved: 0.1079s
✓ Exceeded
Solve Time (CPU)
Target: <1s
Achieved: 0.0458s
✓ Exceeded
Hard Constraint Satisfaction
Target: 100%
Achieved: 100%
✓ Met
Solution Correctness
Target: 100%
Achieved: 100%
✓ Met

Proteomics Solver

VRP-Optimized

Uses biological metaphors (DNA codons → amino acids → proteins) to create fast, interpretable Vehicle Routing Problem solutions.

SPEEDUP
100-600x faster than PyVRP

Biological Metaphor

  • Codons represent heuristic operations (constructive, improving, destructive)
  • Proteins represent complete solution strategies
  • Fully interpretable strategy strings (e.g., 'SAV-TOP-ORP-RLC')
  • Human-readable and auditable routing logic

Strategy Optimization

  • Fast strategies: 0.01-0.02s (real-time routing)
  • Balanced strategies: 0.02-0.04s (general VRP)
  • Quality-intensive strategies: 0.04-0.08s (best quality)
  • Adaptive strategy selection based on time budget

Best For

  • Vehicle routing problems
  • Real-time delivery optimization
  • Last-mile logistics
  • Fleet management
  • Dynamic routing with instant updates

Performance Metrics

Solve Time
Target: 10.0s
Achieved: 0.01-0.06s
✓ 100-600x faster
Solution Quality
Target: Baseline
Achieved: 6-8% better
✓ Superior
Interpretability
Target: Low
Achieved: High
✓ Excellent

MultiStart Solver

Quality Enhancement

Parallel exploration of multiple solution space regions to find high-quality solutions with statistical confidence.

SPEEDUP
Configurable quality-time tradeoff

Multi-Region Exploration

  • Launches N parallel solution searches
  • Each region explores local optima
  • Intelligent sampling from diverse starting points
  • Probabilistic convergence guarantees

Quality Aggregation

  • Aggregates best solutions from all regions
  • Performs post-processing and local search
  • Provides confidence intervals on solution quality
  • Typically 1.5-2.5x improvement over single-start

Best For

  • Quality-critical optimizations
  • Portfolio optimization
  • High-stakes scheduling
  • When time budget allows
  • Problems where solution quality directly impacts revenue

Performance Metrics

Quality Improvement
Target: Baseline
Achieved: 1.5-2.5x better
✓ Excellent
Time Trade-off
Target: Linear
Achieved: Configurable
✓ Flexible

Incremental Solver

Fast Updates

Efficiently solves modified problems by reusing computation from previous solutions, enabling real-time adjustments.

SPEEDUP
50-90% faster than full re-solve

Delta Detection

  • Detects which constraints/variables changed
  • Identifies affected portions of solution
  • Preserves unchanged solution segments
  • Minimal re-computation overhead

Incremental Optimization

  • Re-solves only affected regions
  • Warm-starts with previous solution
  • Typical improvement: 50-90% faster than full re-solve
  • Ideal for streaming/real-time data

Best For

  • Real-time order management
  • Live traffic-aware routing
  • Streaming optimization problems
  • Incremental demand updates
  • Sub-second re-optimization

Performance Metrics

Update Time (10 new items)
Target: Full solve
Achieved: 50-90% faster
✓ Exceptional
Memory Usage
Target: Full solve
Achieved: State-efficient
✓ Optimized

How Helix Compares

Benchmarks against industry-standard alternatives.

vs OR-Tools

Solve Time (1000 jobs)
Traditional
2-5 seconds
Helix AI
0.1079 seconds
18-46x faster

vs PyVRP

VRP Solve Time
Traditional
10.0 seconds
Helix AI
0.01-0.06 seconds
100-600x faster

vs Custom CUDA

Development Time
Traditional
6-12 months
Helix AI
Days to weeks
80% engineering cost reduction

Enterprise Guarantees

100% Constraint Satisfaction

All solutions are mathematically verified to satisfy every hard constraint. No approximations, no violations.

Provable Correctness

Unlike LLMs which can hallucinate, our outputs are verified by mathematical proofs. Enterprise-grade reliability.

GPU-Accelerated

Fused tensor kernels deliver 10-50x speedups. Real-time performance at scale on modern hardware.

Patent-Protected

7-patent fortress covering symbology, composites, streaming, and evolution. Defensible moat.

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