A novel Quantum-Inspired Estimation of Distribution Algorithm (QIEDA) is proposed to solve the Travelling Salesman Problem (TSP). The QIEDA uses a modified version of the W state quantum circuits to sample new solutions during the algorithm runtime. The algorithm behaviour is compared with other state-of-the-art population-based algorithms. QIEDA convergence is faster than other algorithms, and the obtained solutions improve as the size of the problem increases. Moreover, we show that quantum noise enhances the search of an optimal solution. Because quantum computers differ from each other, partly due to the topology that distributes the qubits, the computational cost of executing the QIEDA in different topologies is analyzed and an ideal topology is proposed for the TSP solved with the QIEDA.

Many real-world optimization problems involve two different subsets of variables: decision variables, and those variables which are not present in the cost function but constrain the solutions, and thus, must be considered during optimization. Thus, dependencies between and within both subsets of variables must be considered. In this paper, an estimation of distribution algorithm (EDA) is implemented to solve this type of complex optimization problems. A Gaussian Bayesian network is used to build an abstraction model of the search space in each iteration to identify patterns among the variables. As the algorithm is initialized from data, we introduce a new hyper-parameter to control the influence of the initial data in the decisions made during the EDA execution. The results show that our algorithm improves the cost function more than the expert knowledge does.

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