Quantum-Inspired Immune Clonal Algorithm for solving large-scale capacitated arc routing problems

Abstract

In this paper, we present an approach to Large-Scale CARP called Quantum-Inspired Immune Clonal Algorithm (QICA-CARP). This algorithm combines the feature of artificial immune system and quantum computation ground on the qubit and the quantum superposition. We call an antibody of population quantum bit encoding, in QICA-CARP. For this encoding, to control the population with a high probability evolution towards a good schema we use the information on the current optimal antibody. The mutation strategy of quantum rotation gate accelerates the convergence of the original clone operator. Moreover, quantum crossover operator enhances the exchange of information and increases the diversity of the population. Furthermore, it avoids falling into local optimum. We also use the repair operator to amend the infeasible solutions to ensure the diversity of solutions. This makes QICA-CARP approximating the optimal solution. We demonstrate the effectiveness of our approach by a set of experiments and by Comparing the results of our approach with ones obtained with the RDG-MAENS and RAM using different test sets. Experimental results show that QICA-CARP outperforms other algorithms in terms of convergence rate and the quality of the obtained solutions. Especially, QICA-CARP converges to a better lower bound at a faster rate illustrating that it is suitable for solving large-scale CARP.

Robust Optimization in Uncertain Capacitated Arc Routing Problems: Progresses and Perspectives [Review Article]

“…For example, the uval instances contain no more than 50 vertices and 97 edges. Meanwhile, in the studies of DCARP, several sets of static CARP instances created based on real-world transport networks (e.g., Flanders district of Belgium [56], [57], Beijing and Hefei of China with up to 3584 tasks [58], [59]) have been used. Moreover, only [18], [34], [35], [53] focused on multi-objective DCARP and considered instances of small size only in their case studies.…”

Divide-and-conquer large scale capacitated arc routing problems with route cutting off decomposition

“…The divide-and-conquer strategy has achieved great success in a range of problems, such as continuous optimization [45,46,47], vehicle routing [48,49] and job shop scheduling [50,51,52]. Also for LSCARP, there have been a variety of divide-and-conquer approaches [18,20,22,23,24] based on decomposing the problem into smaller sub-problems by grouping the routes together of the best-so-far solution. Specifically, in these algorithms, the entire search process is divided into cycles.…”

“…To evaluate the effectiveness of the proposed RCO operator for LSCARP, we conduct experiments to compare RCO-RDG-MAENS and RCO-SAHiD with their original counterparts as well as other state-of-the-art algorithms on a range of LSCARP instances. In addition to RDG-MAENS and SAHiD, we also compare with VNS [8], TSA1 [34], ILS-RVND [31], IRDG-MAENS [22], QICA-CARP [23], ESMEANS [24], Fast-CARP [54] and PS [56].…”

“…Therefore, all the existing divide-and-conquer approaches (e.g. [20,22,23,24,21]) adopt the adaptive decomposition. They start with a randomly/heuristically generated task subsets, and gradually improve the decomposition during the search process based on the updated information.…”

Quantum Optimization and Quantum Learning: A Survey

“…In addition, [96] uses a repair operator to amend the infeasible solutions so as to ensure the diversity. [97] utilizes nonfeasible solutions to improve the constrained multi-objective optimization.…”