  Finding the best solution is a common objective in combinatorial optimization
(CO). In practice, directly handling constraints is often challenging,
incorporating them into the objective function as the penalties. However,
balancing these penalties to achieve the desired solution is time-consuming.
Additionally, formulated objective functions and constraints often only
approximate real-world scenarios, where the optimal solution is not necessarily
the best solution for the original real-world problem. One solution is to
obtain (i) penalty-diversified solutions with varying penalty strengths for the
former issue and (ii) variation-diversified solutions with different
characteristics for the latter issue. Users can then post-select the desired
solution from these diverse solutions. However, efficiently finding these
diverse solutions is more difficult than identifying one. This study introduces
Continual Tensor Relaxation Annealing (CTRA) for unsupervised-learning
(UL)-based CO solvers, a computationally efficient framework for finding these
diverse solutions in a single training run. The key idea is to leverage
representation learning capability to automatically and efficiently learn
common representations and parallelization. Numerical experiments show that
CTRA enables UL-based solvers to find these diverse solutions much faster than
repeatedly running existing UL-based solvers.
