MCMC Combinatorial Optimization Search With Adaptive Constraint Weights
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Solution Overview
Problem
The efficiency of Markov-Chain Monte Carlo (MCMC) search methods for combinatorial optimization problems is hindered by inappropriate weight values for constraint conditions, leading to either excessive constraint violations or reduced state transitions.
Innovation Solution
A data processing device and method that adjusts the weight values (λk) of constraint terms based on constraint violations and energy evaluations during the search, increasing λk for violated constraints and decreasing it when energy improvement is observed, thereby optimizing the search efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the weight value of a constraint term is increased to reduce constraint violations, then constraint satisfaction improves, but state transitions are reduced and search efficiency deteriorates
Solution Approach 1:
The patent applies dynamics by making the weight value of constraint terms variable rather than fixed. The weight value is dynamically adjusted during the MCMC search process based on constraint violation status and energy changes, allowing the system to adaptively balance constraint satisfaction with search efficiency at different stages of the optimization process
Solution Approach 2:
The patent implements parameter changes by modifying the weight value of constraint terms based on specific conditions. When constraint violations occur, the weight value is increased; when energy improvement is observed without violations, the weight value is decreased. This dynamic parameter adjustment resolves the contradiction between constraint satisfaction and search efficiency
2Productivity
If the weight value of a constraint term is decreased to promote state transitions, then search efficiency improves, but constraint violations increase
Solution Approach 1:
The patent applies feedback by continuously monitoring constraint violation status and energy changes during the search process. Based on this feedback, the weight value of constraint terms is adjusted in real-time, creating a closed-loop control system that adapts the balance between exploration and constraint satisfaction
Solution Approach 2:
The patent makes the constraint weight dynamic rather than static, allowing it to respond to the current state of the search process. The weight increases when constraints are violated and decreases when they are satisfied, enabling the system to adaptively prioritize constraint satisfaction or exploration based on actual search conditions
Data Source
AI summary
A data processing device includes a memory configured to store evaluation function information of an evaluation function of a combinatorial optimization problem represented by a sum of a quadratic cost term and a linear cost term that is a sum of constraint terms weighted by a coefficient that represents a weight of each of constraint conditions, and a processor configured to search for a solution to the combinatorial optimization problem based on the evaluation function information, increase a value of the coefficient in a case of constraint violation at a first time point during the search, and determine whether to decrease or maintain the value of the coefficient based on a value of the quadratic cost term at the first time point and a value of the evaluation function obtained before the first time point in a case where the constraint conditions are satisfied at the first time point.