High-Speed Dynamic Programming Solver

I need the advanced solvers to beat the benchmark baseline solvers.

Here are TSP solvers what I want to update.

1. Multi-TSP (Multiple Salesmen)

What it is:
- Multiple salesmen (trucks) visit cities
- Each city visited by exactly one salesman
- Goal: Minimize the longest route (balance workload)

Real-world example:
- Amazon delivery with 5 trucks
- 2000 delivery addresses
- Each truck visits some addresses
- Want to balance work between trucks


2. Constrained Multi-TSP (Capacity Limits)

What it is:
- Multiple trucks with limited capacity
- Each city has a demand (package weight)
- Goal: Visit all cities while respecting capacity limits

Real-world example:
- Moving company with 3 trucks
- Each truck can carry maximum 1000kg
- Each house has different weight of items
- Must deliver everything without overloading trucks

Example:
```
Truck1: Capacity 1000kg → [House1(300kg), House2(400kg), House3(300kg)]
Truck2: Capacity 1000kg → [House4(500kg), House5(500kg)]
Truck3: Capacity 1000kg → [House6(800kg), House7(200kg)]
``
---

3. Time Windows Multi-TSP

What it is:
- Constrained Multi-TSP + time windows
- Each city has opening hours
- Goal: Visit cities within their time windows

Real-world example:
- Package delivery with time windows
- House1: Open 9AM-11AM
- House2: Open 2PM-4PM
- House3: Open 10AM-12PM
- Must visit each house during their open hours

Example:
```
Truck1: 9:00AM → House1(9-11AM) → House3(10-12AM) → 11:30AM
Truck2: 2:00PM → House2(2-4PM) → 3:30PM
```

4. Portfolio Reallocation

What it is:
- Completely different problem!
- Not TSP - it's about financial optimization
- Goal: Minimize number of swaps to rebalance portfolio

Real-world example:
- You have 100 stocks in your portfolio
- Want to rebalance to target percentages
- Goal: Make minimum number of trades (swaps)

Example:
```
Current: Apple(30%), Google(20%), Tesla(50%)
Target: Apple(40%), Google(30%), Tesla(30%)
Solution: Sell 20% Tesla, Buy 10% Apple, Buy 10% Google
Swaps: 2 trades needed
```

The most priority is to update solver 1 and solver 2.

In my github repo, I set all installation and benchmark codebase and solver evaluate script.

https://github.com/marco1202-dev/graph_problems.git

Only apply if you have the deep knowledge in graph algorithm. I don't care where you are from but I want to save time.

Result acceptance: if I run the evaluate script and it say "nImprovement 25% better than benchmark", I will pay immediately without checking others.