Hyperparameter tuning in metaheuristics for NP-hard combinatorial optimization problems
Keywords: hyperparameter, optimized operator, metaheuristic
Abstract: Modern metaheuristics have many categorical and numerical parameters, as well
as operators. We investigate the problem of turning such parameters, selecting operators
and the intensity of their search. Learning-based optimization algorithms,
adaptive parameter control and the coordination of different components are theoretically
analyzed and experimentally tested.,In the case of the evolutionary algorithms,
we consider optimized crossover and mutation. Deterministic recombination
operators are used for large neighborhood exploration. A so-called optimal
recombination consists of searching for the best possible offspring as a result of a
crossover operator, which satisfies the property of the gene transmitting recombination.
Dynamic Programming, Branch and Cut or Branch and Bound methods, as
well as specialized enumeration techniques, are successfully used for solving such
sub-problems. We investigate the computational complexity of the optimal recombination
problem, and provide a universal solving method. Moreover, we prove
that “almost all” pairs of parent solutions give polynomially solvable optimal recombination
problems for position-based solution representation. For mutation
we use randomized operators that provide large neighborhoods, where the best
solution can be found in polynomial time. In the case of local search algorithms,
we consider large neighborhoods and analyze the computational complexity of the
corresponding subproblems.
Submission Number: 45
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