Ising Solver QUBO Variables for Constrained Routing
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Solution Overview
Problem
Conventional Ising solver systems are inadequate for solving Traveling Salesman Problem (TSP) and Vehicle Routing Problem (VRP) with realistic constraints such as time windows and capacitated vehicles, as they cannot effectively handle complex constraints like time and capacity limitations.
Innovation Solution
The introduction of dynamic penalty terms and QUBO variables representing inter-city travel steps, capacitated variables, and state changes allows for the formulation of TSP and VRP in the Ising solver system, enabling the description of time and capacity constraints, and allowing for optimal route search considering multiple capacities and constraints.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If conventional Ising solver systems are used for TSP and VRP, then the solver can handle basic routing, but it cannot effectively handle complex constraints such as time windows and capacitated vehicles
Solution Approach 1:
The patent segments the constraint handling by introducing separate QUBO variables for different aspects: x variables for route selection, y variables for time step tracking, and z variables for capacitated variable tracking. This segmentation allows each variable type to handle specific constraints independently, improving adaptability while managing formulation complexity through systematic organization.
Solution Approach 2:
The patent adds temporal dimension by introducing time step variables y that track the progression of travel between cities. This dimensional extension transforms the static routing problem into a dynamic one where time constraints can be explicitly modeled, enabling the solver to handle time window constraints without excessive formulation complexity.
2Adaptability or versatility
If dynamic penalty terms and QUBO variables representing inter-city travel steps are introduced, then the solver can formulate TSP and VRP with time constraints, but the formulation complexity increases
Solution Approach 1:
The patent applies preliminary action by pre-defining the structure of QUBO variables and their relationships before solving the optimization problem. The interaction terms between variables are predetermined based on the problem constraints, allowing the solver to directly apply the formulation without complex runtime calculations, thus balancing adaptability with manageable formulation complexity.
3Measurement precision
If the solver formulation includes multiple QUBO variables and interaction terms, then the accuracy of optimal route search improves, but the computational complexity increases
Solution Approach 1:
The patent merges multiple constraint satisfaction requirements into a unified QUBO formulation where interaction terms between variables collectively enforce all constraints. By combining route selection, time tracking, and capacity monitoring into a single integrated formulation, the solver achieves high solution accuracy while avoiding the need for separate complex solving mechanisms.
Data Source
AI summary
An ising solver system that searches an optimal route of a vehicle from plural routes passing through plural locations. In the ising solver system, the search of the optimal route uses a Hamiltonian. The Hamiltonian includes an equation representing an interaction between Quadratic Unconstrained Binary Optimization (QUBO) variables depending on a relation between a departure location and an arrival location or capacitated variable of the ising solver. The capacitated variable corresponds to one of the QUOBO variables and includes a variable constraint, and the location-to-location travel step number corresponds to an accumulated movement time of the vehicle.