Optimal Stopping Heuristic Optimizer for Benchmarking
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Solution Overview
Problem
Current benchmarking methodologies for optimization algorithms are inadequate due to the interdependence of solution quality and computational effort, lacking a consistent and unbiased measure, especially when the global optimum is unknown.
Innovation Solution
The introduction of optimal stopping theory to formulate a cost-per-call for randomized optimization algorithms, allowing for the computation of expected total cost and providing a flexible figure of merit that avoids biases and arbitrariness in benchmarking, applied to MAX2SAT problems and compared across different solvers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If one uses a quality-first benchmarking approach fixing a minimum target quality, then solution quality is ensured, but the benchmarking becomes biased and requires arbitrary choices about target setting
Solution Approach 1:
The patent changes the benchmarking parameter from fixed quality targets to a dynamic cost function that combines solution quality and computational effort. Instead of setting arbitrary quality thresholds, the system uses a cost function C = Q(x*) + c·T that objectively balances both dimensions, eliminating the need for subjective target selection while ensuring solution quality through the optimization framework.
2Loss of time
If one uses a time-first benchmarking approach fixing computation time, then computational effort is controlled, but solution quality comparison becomes biased by window length selection
Solution Approach 1:
The patent transforms the benchmarking approach by changing from fixed time windows to a cost function that incorporates both time and quality. The cost function C = Q(x*) + c·T allows different algorithms to be compared on their ability to minimize total cost rather than being constrained by arbitrary time limits, eliminating bias from window length selection while controlling computational effort through the cost parameter c.
3Manufacturing precision
If one increases the number of solver calls to improve solution quality, then better solutions are found, but computational effort increases
Solution Approach 1:
The patent implements feedback by using the quality distribution estimated from previous solver calls to dynamically determine when to stop calling the solver. The system continuously monitors the quality improvement and compares it against the cost parameter c, stopping when further calls would increase total cost rather than decrease it. This feedback mechanism optimizes the trade-off between solution quality and computational effort.
Solution Approach 2:
The patent makes the stopping criterion dynamic by adapting it based on the observed quality distribution during the optimization process. Rather than using a fixed number of calls or fixed time limit, the system dynamically adjusts the stopping point based on how quickly quality improves and the relative cost parameter, allowing the optimal number of calls to be determined by the problem characteristics and cost preferences.
Data Source
AI summary
An optimally stopped heuristic optimizer includes a processor. The processor heuristically generates a sequence of proposed solutions for solving a discrete optimization problem associated with an objective function, and for each additional proposed solution of the sequence, derives an estimate of a quality distribution that is based on the sequence including the additional proposed solution. The quality distribution assigns a probability to each of the proposed solutions according to quality of the proposed solution. The processor further, responsive to a most recent additional proposed solution of the sequence having quality better than a quality threshold that is defined by the estimate corresponding to the sequence including the most recent additional proposed solution, commands a stop such that further proposed solutions to the discrete optimization problem are no longer generated, and identifies and outputs a selected one of the sequence having best quality.