COMEX Algorithm for Combinatorial Black Box Optimization
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Solution Overview
Problem
Existing algorithms for black box function optimization over combinatorial domains, such as Bayesian Optimization of Combinatorial Structures (BOCS) and Combinatorial Bayesian Optimization using the Graph Cartesian Product (COMBO, are computationally expensive and impractical for moderate to large numbers of variables, as they require a significant amount of time to determine the next sample for evaluation.
Innovation Solution
The proposed method introduces a computationally efficient algorithm called Combinatorial Optimization with Monomial Experts (COMEX) that uses a multilinear polynomial surrogate model with exponential weight updates and simulated annealing to optimize black box functions over the Boolean hypercube, reducing computational time by several orders of magnitude compared to state-of-the-art algorithms.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing algorithms like BOCS and COMBO are used for black box function optimization over combinatorial domains, then optimization accuracy is improved, but computational time increases significantly
Solution Approach 1:
The algorithm segments the combinatorial optimization problem into smaller subproblems by working with local search neighborhoods and incremental modifications. Instead of evaluating the entire search space, it divides the problem into manageable steps where each iteration focuses on local improvements, thereby reducing computational time while maintaining optimization accuracy.
Solution Approach 2:
The algorithm performs preliminary actions by pre-computing and storing information about the black box function evaluations and their relationships. It prepares data structures in advance that allow for efficient querying and comparison during the optimization process, reducing the time needed for each iteration while preserving accuracy.
2Measurement precision
If exhaustive search is performed to find the optimal solution, then solution quality is improved, but computational complexity becomes intractable
Solution Approach 1:
The algorithm applies local quality by focusing computational resources on locally optimal solutions rather than attempting to evaluate all possible solutions globally. It uses local search strategies that improve solutions incrementally by making small, targeted modifications, achieving high solution quality without the intractable complexity of exhaustive search.
Solution Approach 2:
The algorithm employs partial action by performing optimization steps that are sufficient to reach a high-quality solution without completing a full exhaustive search. It stops when a satisfactory solution is found or when computational resources are exhausted, avoiding the unnecessary complexity of evaluating every possible solution when a good enough solution suffices.
Data Source
AI summary
Aspects of the present invention disclose a method, computer program product, and system for optimizing a result for a combinatorial optimization problem. The method includes one or more processors receiving a black-box model. The method further includes one or more processors learning a multilinear polynomial surrogate model employing an exponential weight update rule. The method further includes one or more processors optimizing the learnt multilinear polynomial surrogate model. The method further includes one or more processors applying the black-box model to the optimized solution found by the multilinear polynomial surrogate model. In an additional aspect, the method of learning an optimized multilinear polynomial surrogate model employing an exponential weight update rule further includes one or more processors calculating utilizing data from the black-box model, an update of the coefficients of the multilinear polynomial surrogate model.