Monte Carlo Algorithm Using Approximated Objective Function
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Solution Overview
Problem
Existing optimization algorithms face challenges in efficiently computing solutions for large-scale optimization problems due to the high computational cost of evaluating objective functions, leading to resource-intensive processing time and environmental impact.
Innovation Solution
A computing device is configured to receive an exact objective function and an approximated objective function, using a Monte Carlo algorithm with fast-step and correction iterations to estimate an optimal state, where fast-step acceptance probabilities are based on the approximated function and correction probabilities on both functions, allowing for efficient computation of optimal states.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If exact objective function evaluation is performed for every Monte Carlo iteration, then solution accuracy is improved, but computational cost and processing time increase significantly
Solution Approach 1:
The Monte Carlo algorithm is segmented into two distinct phases: a fast-step phase using the approximated objective function for rapid exploration, and a correction phase using the exact objective function for precision refinement. This segmentation allows the system to benefit from both speed and accuracy without paying the full computational cost throughout the entire process.
Solution Approach 2:
The approximated objective function is used in advance during the fast-step iterations to identify promising regions of the state space and generate candidate solutions. This preliminary action reduces the search space for subsequent exact evaluation, minimizing the number of expensive exact function calls needed.
2Reliability
If exact objective function evaluation is performed for every Monte Carlo iteration, then solution reliability is improved, but resource utilization increases
Solution Approach 1:
The exact objective function is evaluated only partially - specifically during the correction phase after the fast-step phase has identified candidate solutions. This partial evaluation approach provides sufficient reliability for the final solution while avoiding the excessive resource consumption of evaluating the exact function at every iteration.
Solution Approach 2:
The approximated objective function serves as an intermediary that bridges the gap between rapid exploration and reliable solution finding. It enables the algorithm to perform most iterations with low computational cost while still ensuring solution reliability through selective exact evaluation in the correction phase.
3Measurement precision
If Monte Carlo algorithm performs many iterations to ensure convergence, then solution precision is improved, but computational complexity increases
Solution Approach 1:
The iterative process is segmented into fast-step iterations (using approximated function) and correction iterations (using exact function). This segmentation reduces computational complexity by distributing the iteration burden across two different evaluation strategies rather than using the expensive exact function throughout.
Solution Approach 2:
The algorithm dynamically changes the parameter being optimized - using the approximated objective function during fast-steps and switching to the exact objective function during correction steps. This parameter change allows the system to maintain solution precision while reducing overall computational complexity.
Data Source
AI summary
A computing device including a processor configured to receive an exact objective function over a state space. The processor may receive an approximated objective function that approximates the exact objective function. The processor may compute an estimated optimal state of the exact objective function. Computing the estimated optimal state may include, starting at an initial state, computing a preliminary estimated optimal state by performing a plurality of fast-step iterations of a Monte Carlo algorithm with respective fast-step acceptance probabilities determined based at least in part on the approximated objective function. Computing the estimated optimal state may further include performing a correction iteration that has a correction-step acceptance probability determined based at least in part on respective values of the approximated objective function and the exact objective function computed at the preliminary estimated optimal state. The processor may output the estimated optimal state.