We investigate two modified Quantum Evolutionary methods for solving real value problems. The Quantum Inspired Evolutionary Algorithms (QIEA) were originally used for solving binary encoded problems and their signature features follow superposition of multiple states on a quantum bit and a rotation gate. In order to apply this paradigm to real value problems, we propose two quantum methods Half Significant Bit (HSB) and Stepwise Real QEA (SRQEA), developed using binary and real encoding respectively, while keeping close to the original quantum computing metaphor. We evaluate our approaches against sets of multimodal mathematical test functions and real world problems, using five performance metrics and include comparisons to published results. We report the issues encountered while implementing some of the published real QIEA techniques. Our methods focus on introducing and implementing new rotation gate operators used for evolution, including a novel mechanism for preventing premature convergence in the binary algorithm. The applied performance metrics show superior results for our quantum methods on most of the test problems (especially for the more complex and challenging ones), demonstrating faster convergence and accuracy.
We investigate two modified Quantum Evolutionary methods for solving real value problems. The Quantum Inspired Evolutionary Algorithms (QIEA) were originally used for solving binary encoded problems and their signature features follow superposition of multiple states on a quantum bit and a rotation gate. In order to apply this paradigm to real value problems, we propose two quantum methods Half Significant Bit (HSB) and Stepwise Real QEA (SRQEA), developed using binary and real encoding respectively, while keeping close to the original quantum computing metaphor. We evaluate our approaches against sets of multimodal mathematical test functions and real world problems, using five performance metrics and include comparisons to published results. We report the issues encountered while implementing some of the published real QIEA techniques. Our methods focus on introducing and implementing new rotation gate operators used for evolution, including a novel mechanism for preventing premature convergence in the binary algorithm. The applied performance metrics show superior results for our quantum methods on most of the test problems (especially for the more complex and challenging ones), demonstrating faster convergence and accuracy.
Quantum-Inspired Evolutionary Algorithms (QIEAs) represent a novel fusion of quantum computing principles and classical evolutionary strategies, offering a powerful approach to solving complex optimization problems. This chapter provides a comprehensive overview, detailing foundational concepts, implementation techniques, and potential applications of QIEAs. By leveraging quantum phenomena such as superposition and entanglement, QIEAs enhance the exploitation and exploration capabilities of traditional evolutionary algorithms (EAs), thus enabling an efficient search of vast solution spaces. The study examines key components of QIEA, including quantum encoding, rotation gates, and entanglement operations, and compares its performance with classical EAs. By analyzing real-life examples of combinatorial optimization problems (COPs) such as the minimum spanning tree (MST), traveling salesman problem (TSP), and graph coloring, the chapter demonstrates QIEA’s superior efficiency and solution quality. Despite implementation challenges, QIEA shows promise in various domains, including machine learning, finance, healthcare, telecommunications, and e-commerce. Future research directions are outlined, emphasizing the need for simplified quantum-inspired operators, hybrid quantum-classical systems, and interdisciplinary collaboration. This chapter highlights the transformative potential of QIEA, setting the stage for further advancements and applications in optimization and computational efficiency.
A novel evolutionary algorithm based on quantum computing concepts is applied to engineering optimization problems. Quantum computing mimics behavior of atoms in processing information. Quantum inspired algorithm is a concept, which employs certain elements of quantum computing to use in a wider class of search and optimization problems. The main parts of a quantum-inspired algorithm are the qubits (quantum equivalent of bits) and the quantum gates. Qubits hold the information in a superposition of all the states, while the quantum gates evolve the qubit to achieve the desired objective, which is, in optimization the maximum or the minimum. The paper addresses the ability of the Quantum-Inspired Evolution Algorithm (QIEA) to solve practical engineering optimization problems. QIEA, which is developed by authors, is based on their previous work and it is extended to acquire the floating-point representation of the information. The RQIEA is tested on a four benchmark engineering optimization problems. The results showed that the new algorithm has the ability to compete and even overcome other well known methods.
As a novel evolutionary algorithm, a quantum-inspired evolutionary algorithm (QIEA) is attracting increasing attention, due to its good global search capability and rapid convergence. A quantum rotation gate (QR-gate) is the key operator in a QIEA. In the literature, there are many versions of QR-gates. How to evaluate and choose a QR-gate is very worth discussing. This paper focuses on a comparison and analysis on six QR-gates. The performances of QIEAs with the six QR-gates are tested on a practical problem, image sparse decomposition. Experimental results show that the QR-gate5 is superior to other five versions of QR-gates in terms of the quality of solutions and computing time.
This paper proposes a novel evolutionary algorithm inspired by quantum computing, called a quantum-inspired evolutionary algorithm (QEA), which is based on the concept and principles of quantum computing, such as a quantum bit and superposition of states. Like other evolutionary algorithms, QEA is also characterized by the representation of the individual, evaluation function, and population dynamics. However, instead of binary, numeric, or symbolic representation, QEA uses a Q-bit, defined as the smallest unit of information, for the probabilistic representation and a Q-bit individual as a string of Q-bits. A Q-gate is introduced as a variation operator to drive the individuals toward better solutions. To demonstrate its effectiveness and applicability, experiments were carried out on the knapsack problem, which is a well-known combinatorial optimization problem. The results show that QEA performs well, even with a small population, without premature convergence as compared to the conventional genetic algorithm.
From recent research on combinatorial optimization of the knapsack problem, quantum-inspired evolutionary algorithm (QEA) was proved to be better than conventional genetic algorithms. To improve the performance of the QEA, this paper proposes research issues on QEA such as a termination criterion, a Q-gate, and a two-phase scheme, for a class of numerical and combinatorial optimization problems. A new termination criterion is proposed which gives a clearer meaning on the convergence of Q-bit individuals. A novel variation operator H/sub /spl epsi// gate, which is a modified version of the rotation gate, is proposed along with a two-phase QEA scheme based on the analysis of the effect of changing the initial conditions of Q-bits of the Q-bit individual in the first phase. To demonstrate the effectiveness and applicability of the updated QEA, several experiments are carried out on a class of numerical and combinatorial optimization problems. The results show that the updated QEA makes QEA more powerful than the previous QEA in terms of convergence speed, fitness, and robustness.
This paper proposes a novel type of quantum-inspired evolutionary algorithm (QiEA) for numerical optimization inspired by the multiple universes principle of quantum computing, which is based on the concept and principles of quantum computing, such as a quantum bit and superposition of states. Numerical optimization problems are an important field of research with several applications in several areas: industrial plant optimization, data mining and many others, and although being successfully used for solving several optimization problems, evolutionary algorithms still present issues that can reduce their performances when faced with task where the evaluation function is computationally intensive. In order to address those issues the QiEA represent the most recent advance in the field of evolutionary computation. This work present some application about combinatorial and numerical optimization problems.