Optimization Apparatus Escaping Local Minima via Adaptive Energy Offset
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Solution Overview
Problem
Discrete optimization problems, such as the traveling salesman problem and knapsack problem, are challenging due to their exponential calculation time and tendency to get stuck in local minimums, making it difficult to find an optimum solution efficiently.
Innovation Solution
An optimization apparatus that includes a state holding unit, an energy calculation unit, a temperature control unit, and a transition control unit, which adds an offset to the energy change to facilitate state transitions based on temperature and random numbers, with the offset being larger at local minima than at non-minimal energy states and reset when the energy change exceeds a threshold.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of time
If simulated annealing is used to solve discrete optimization problems, then the calculation time is reduced compared to exhaustive methods, but the algorithm frequently gets stuck in local minimums and fails to find the global optimum
Solution Approach 1:
The patent applies preliminary anti-action by introducing an escape mechanism before the algorithm gets permanently stuck in local minimums. When a local minimum is detected (through repeated visits or energy threshold checks), the system proactively applies a perturbation to jump out of the local minimum, preventing the algorithm from wasting excessive time trapped in suboptimal states.
Solution Approach 2:
The patent utilizes parameter changes by dynamically adjusting the energy threshold and perturbation magnitude during the annealing process. The energy threshold is gradually lowered as the algorithm progresses, while perturbation strength is modulated based on the current state, allowing the system to escape local minimums effectively while converging to the global optimum.
2Reliability
If the energy threshold is lowered to escape local minimums, then the algorithm can find better solutions, but the calculation time increases due to more frequent state transitions
Solution Approach 1:
The patent applies dynamics by making the energy threshold and perturbation parameters adaptive rather than static. The energy threshold dynamically decreases as the annealing progresses, and perturbation is applied conditionally based on the current energy state and iteration count. This dynamic adjustment allows efficient escape from local minimums while minimizing unnecessary transitions.
Solution Approach 2:
The patent implements periodic action through the annealing schedule itself, where perturbation is applied at specific intervals and energy thresholds are adjusted periodically. This structured periodic approach ensures that escape attempts occur at optimal moments in the optimization process, balancing solution quality with computational efficiency.
Data Source
AI summary
When a transition control unit stochastically determines whether to accept one of a plurality of state transitions, using a temperature, an energy change, and a random number, depending on a relative relationship between the energy change and thermal excitation energy, the transition control unit adds an offset to the energy change, controls the offset so as to be larger at a local minimum, at which the energy is locally minimized, than at a solution at which the energy is not minimized, and resets the offset to zero when the energy change value is larger than a threshold.