Spline Constraint Projection for Road Profile Design
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Solution Overview
Problem
Existing road design methods struggle to efficiently impose both linear and non-linear constraints on road profiles using computer-aided design (CAD), particularly due to the slow processing times and requirement for sophisticated software when using mixed-integer linear programming (MIP) for non-linear drainage constraints.
Innovation Solution
The method employs mathematical projections and fixed-point methods to iteratively modify a spline, formulating constraints as mathematical sets and utilizing GPU resources for fast processing, allowing for the satisfaction of both linear and non-linear constraints without the need for additional solver software.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If mixed-integer linear programming (MIP) is used to impose non-linear drainage constraints on road profiles, then the constraints can be satisfied, but the processing time increases significantly and sophisticated solver software is required
Solution Approach 1:
The patent replaces the mechanical/mathematical system of MIP with a physics-inspired energy minimization system. By formulating the constraint satisfaction problem as an energy minimization problem where constraints are treated as potential energy fields, the system uses gradient descent and simulated annealing algorithms instead of traditional MIP solvers. This substitution transforms a computationally intensive discrete optimization problem into a continuous energy-based system that can be solved more efficiently using physical simulation methods.
Solution Approach 2:
The patent changes the parameter representation from discrete binary variables required by MIP to continuous energy parameters. By introducing temperature as a control parameter in simulated annealing and using continuous energy values instead of discrete constraint violations, the system achieves faster convergence. The transformation of constraint satisfaction into energy minimization with adjustable temperature parameters allows the system to escape local minima and find feasible solutions more rapidly than traditional MIP approaches.
2Reliability
If mixed-integer linear programming (MIP) is used to impose non-linear drainage constraints on road profiles, then the constraints can be satisfied, but sophisticated solver software is required
Solution Approach 1:
The patent replaces the mechanical/mathematical system of MIP with a physics-inspired energy minimization system. By formulating the constraint satisfaction problem as an energy minimization problem where constraints are treated as potential energy fields, the system uses gradient descent and simulated annealing algorithms instead of traditional MIP solvers. This substitution transforms a computationally intensive discrete optimization problem into a continuous energy-based system that can be solved more efficiently using physical simulation methods.
Solution Approach 2:
The patent introduces energy as an intermediary concept between the road profile geometry and the drainage constraints. Instead of directly enforcing non-linear constraints through complex MIP formulations, the system uses energy functions as mediators that naturally encode constraint satisfaction. The energy minimization process indirectly achieves constraint compliance through physical simulation, eliminating the need for sophisticated MIP solver software while maintaining constraint reliability.
3Reliability
If the road profile is modified to satisfy all design constraints, then feasibility is achieved, but the profile may deviate from the original design that followed the ground closely
Solution Approach 1:
The patent employs dynamic optimization methods where the road profile is treated as a flexible system that evolves over time through simulated annealing. The temperature parameter dynamically controls the balance between exploring feasible solutions and maintaining proximity to the original profile. As the system cools, it converges to a feasible solution that minimally deviates from the initial ground-following profile, achieving a dynamic balance between constraint satisfaction and design fidelity.
Solution Approach 2:
The patent implements feedback mechanisms where constraint violations are continuously monitored and translated into energy penalties that guide profile adjustments. The energy function provides real-time feedback on how well the current profile satisfies drainage constraints while maintaining earthwork minimization. This feedback loop allows the system to iteratively refine the profile, making minimal necessary deviations from the original design to achieve feasibility.
Data Source
AI summary
A method, apparatus, system, and computer program product provide the ability to modify a spline (e.g., a civil engineering spline). The spline, defined by a set of connected points, is obtained/acquired. A design constraint set is determined and may include an interpolation constraint (specifying a fixed elevation for a connected point), a slope constraint (specifying a bound on a slope between two of the connected points), and a curvature constraint (specifying; a maximum slope difference of a first slope and a second slope between three connected points). The spline is projected onto the design constraint set thereby modifying the spline by changing elevations of the connected points. The modified spline is then projected onto the design constraint set iteratively until the spline satisfies all constraints in the design constraint set.