Abstract-This paper presents a theory and an empirical evaluation of Higher-Order Quantum-Inspired Genetic Algorithms. Fundamental notions of the theory have been introduced, and a novel Order-2 Quantum-Inspired Genetic Algorithm (QIGA2) has been developed. Contrary to all QIGA algorithms which represent quantum genes as independent qubits, in higherorder QIGAs quantum registers are used to represent genes strings, which allows modelling of genes relations using quantum phenomena. Performance comparison has been conducted on a benchmark of 20 deceptive combinatorial optimization problems. It has been presented that using higher quantum orders is beneficial for genetic algorithm efficiency, and the new QIGA2 algorithm outperforms the old QIGA algorithm tuned in highly compute-intensive metaoptimization process.
I. INTRODUTIONR ESEARCH on quantum-inspired computational intelligence techniques was started by Narayann [1] in 1996, and the first proposal of Quantum-Inspired Genetic Algorithm (QIGA1) has been presented by Han and Kim in [2]. QuantumInspired Genetic Algorithms belong to a new class of artificial intelligence techniques, drawing inspiration from both evolutionary [3] and quantum [4] computing. Current literature on the subject consists of about a few hundreds scientific papers. Only a few papers attempt to theoretically analyse the properties of that class of algorithms. Among those there are i.a. [22,28], which has been emphasized in conclusions of recent comprehensive surveys [18,29].In QIGA algorithms, representation and genetic operators are based on computationally useful aspects of both biological evolution and unitary evolution of quantum systems. QIGA algorithms use quantum mechanics concepts including qubits and superposition of states. QIGA algorithms have been successfully applied to a broad range of search and optimization problems [5,6,7]. The algorithms have demonstrated their particular efficacy for solving complex optimization problems. Recent years have witnessed successful applications of Quantum-Inspired Genetic Algorithms in a variety of fields, including image processing [8,9,10], flow shop scheduling [11,12], thermal unit commitment [13,14], power system optimization [15,16], localization of mobile robots [17] and many others.For a current and comprehensive survey of QuantumInspired Genetic Algorithms and the necessary background of Quantum Computing and Quantum-Inspired Computational Intelligence techniques, the reader is referred to [1,2,18,29].This work was supported in part by PL-Grid Infrastructure This paper is structured as follows. In Section 1, an introductory background and the most important references for the subject field have been given. In Section 2, the theory of Higher-Order Quantum-Inspired Genetic Algorithms has been presented. In Section 3, details of the original Order-2 Quantum-Inspired Genetic Algorithm have been provided. In Section 4, experimental results have been provided and evaluated. In Section 5, the article has been briefly summarized, final conclusi...