Stochastic State Transition Control for Discrete Optimization
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Discrete optimization problems, such as the traveling salesman problem and knapsack problem, face challenges in finding optimal solutions due to their NP difficulty, leading to exponentially increasing computation time and often resulting in suboptimal approximate solutions, with existing methods like simulated annealing struggling to converge to the optimal solution within a finite number of iterations.
Innovation Solution
An optimization device and method that controls state transitions based on the Boltzmann distribution using a Markov process, incorporating a transition controller that generates multiple state transition candidates, calculates energy changes, and determines acceptance probabilities according to thermal excitation energy and temperature, ensuring convergence to the optimal solution while minimizing solution quality deterioration.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If exhaustive method is used to obtain optimal solution reliably, then solution quality is improved, but calculation time increases exponentially
Solution Approach 1:
The patent changes the parameter of acceptance probability from a fixed deterministic value to a stochastic value that varies according to the Boltzmann distribution. This allows the system to occasionally accept worse solutions (with probability exp(-ΔE/T)) to escape local minima, while still converging to the global optimum with probability 1 given sufficient iterations, thus achieving optimal solution quality without exhaustive search.
Solution Approach 2:
The patent introduces an intermediary mechanism - the Boltzmann-based acceptance criterion - that mediates between exploration (accepting worse solutions) and exploitation (accepting better solutions). This intermediary allows the system to navigate the trade-off between solution quality and computation time by providing a probabilistic bridge that enables escape from local minima while maintaining convergence guarantees.
2Productivity
If simulated annealing with deterministic acceptance is used, then calculation speed is improved, but convergence to optimal solution cannot be guaranteed due to trapping in local minima
Solution Approach 1:
The patent makes the acceptance criterion dynamic by introducing stochasticity that adapts to the energy landscape. Instead of a static deterministic rule, the acceptance probability dynamically adjusts based on the energy difference ΔE and temperature T, allowing the system to be more exploratory at higher energies and more exploitative at lower energies, thus ensuring convergence while maintaining computational efficiency.
Solution Approach 2:
The patent implements feedback through the Boltzmann acceptance criterion, where the acceptance decision is based on feedback from the energy change ΔE. The system continuously monitors energy changes and adjusts acceptance probabilities accordingly, creating a feedback loop that guides the search toward the global optimum while allowing temporary deviations to escape local minima.
3Loss of time
If temperature is lowered rapidly in simulated annealing, then calculation time is reduced, but solution quality deteriorates due to insufficient exploration
Solution Approach 1:
The patent applies preliminary action by establishing the Boltzmann-based acceptance criterion before the optimization process begins. This preliminary stochastic framework is in place from the start, ensuring that even during rapid cooling, the system maintains the capability to accept worse solutions with appropriate probability, thus preserving exploration ability throughout the entire optimization trajectory without requiring slow cooling schedules.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The approach guarantees convergence to the optimal solution and suppresses solution quality deterioration by bringing the energy distribution closer to the Boltzmann distribution, improving the efficiency of finding good solutions in discrete optimization problems.
Implementation Method 1
a transition controller that, based on a temperature value, an energy change value, and a random number value, determines stochastically whether to accept any of a plurality of state transitions according to a relative relationship between the energy change value and the thermal excitation energy
Implementation Method 2
determines stochastically whether to accept any of a plurality of state transitions according to a relative relationship between the energy change value and the thermal excitation energy
Data Source
Figure 1
Figure 2
Figure 3
AI summary
An optimization device includes: a state holding unit configured to hold values of a plurality of state variables included in an evaluation function representing energy; a calculation unit configured to calculate a change value of the energy for each of a plurality of state transitions occurred in response to a change in any of the values of the plurality of state variables; a temperature control unit configured to control a temperature value indicating a temperature; and a transition control unit including: a plurality of first selection circuits each configured to randomly select an intermediate candidate from a predetermined number of state transitions based on a propriety of acceptance of each of the predetermined number of state transitions, the propriety being obtained by comparing thermal excitation energy with an energy change for a corresponding state transition, the thermal excitation energy being calculated using each of independent random numbers a number of which is same as the predetermined number; and a second selection circuit configured to randomly select one state transition from intermediate candidates selected by the plurality of first selection circuits.