A Hybrid Quantum Evolutionary Algorithm with Improved Decoding Scheme for a Robotic Flow Shop Scheduling Problem

Hindawi Mathematical Problems in Engineering Volume 2017, Article ID 3064724, 13 pages https://doi.org/10.1155/2017/3064724 Research Article A Hybrid Quantum Evolutionary Algorithm with Improved Decoding Scheme for a Robotic Flow Shop Scheduling Problem Weidong Lei,1 Hervé Manier,2 Marié-Ange Manier,2 and Xinping Wang1 1 School of Management, Xi’an University of Science and Technology, Xi’an 710054, China Université Bourgogne Franche-Comté, UTBM, OPERA, 90100 Belfort, France 2 Correspondence should be addressed to Weidong Lei; Received 8 October 2016; Accepted 28 February 2017; Published 16 April 2017 Academic Editor: Calogero Orlando Copyright © 2017 Weidong Lei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We aim at solving the cyclic scheduling problem with a single robot and flexible processing times in a robotic flow shop, which is a well-known optimization problem in advanced manufacturing systems. The objective of the problem is to find an optimal robot move sequence such that the throughput rate is maximized. We propose a hybrid algorithm based on the Quantum-Inspired Evolutionary Algorithm (QEA) and genetic operators for solving the problem. The algorithm integrates three different decoding strategies to convert quantum individuals into robot move sequences. The Q-gate is applied to update the states of Q-bits in each individual. Besides, crossover and mutation operators with adaptive probabilities are used to increase the population diversity. A repairing procedure is proposed to deal with infeasible individuals. Comparison results on both benchmark and randomly generated instances demonstrate that the proposed algorithm is more effective in solving the studied problem in terms of solution quality and computational time. 1. Introduction Since the 1970s, with the development of the robotics and automation technologies, computer-controlled robots instead of workers have been gradually used in many manufacturing industries to perform high frequency or dangerous transportation jobs. The advantages of robotic or automated manufacturing systems include higher production rate, better product quality, and more efficient use of materials, improved safety, and reduced labor intensity. Besides, highly robotic or automated manufacturing systems can effectively meet the requirement of mass production and respond to global competition. In automated manufacturing systems, the production line with transporting device usually consists of several processing machines arranged in a line and one or more robots for transporting parts among machines, as shown in Figure 1. Due to the industrial applications [1], the part processing time on each machine is usually flexible and imposed with a pair of minimum and maximum time bounds. Besides, the cyclic production mode is usually adopted in such systems because of easy implementation in a mass production environment. This leads to a repetitive schedule performed by the robot in every certain time. The duration of the robot to perform the repetitive schedule is called the cycle time or cycle length [2]. For such problem, scheduling of robot movements is very critical because the line productivity and the product quality extremely depend on it. Therefore, the decision concerns how to sequence the robot movements such that the cycle time is minimized, which is equivalent to maximizing the throughput rate of the production line in steady-state. Note that such scheduling problems in different industrial contexts may have different appellations, such as hoist scheduling problem [3], robotic cell, or robotic flow shop scheduling problem [4, 5]. Lei and Wang [6] first proved that the cyclic flow shop scheduling problem with a single robot and flexible processing times is NP-complete. Many researchers have been constantly dedicated to this area and proposed various efficient methods for solving the relevant problems. The first fundamental work in this area was done by Phillips and Unger [7], who formulated a Mixed Integer Programming (MIP) model for solving the single robot cyclic scheduling 2 Mathematical Problems in Engineering Robot arm Treatment track Part Input station Processing machines Output station Figure 1: A typical robotic production line. problem with one degree, which means that each machine is emptied exactly once within a cycle. After that, various exact methods or heuristics were developed for the related problem in the literature [2, 8–10]. Moreover, Liu et al. [11] developed an MIP model for solving the problem with complex lines (i.e., including multifunction stations and parallel stations). Che and Chu [12] developed an efficient branch-and-bound (B&B) algorithm for the same problem as Liu et al. [11]. Besides the above studies, researchers have also examined the problem with multiple robots. For instance, Lei and Wang [13] and Zhou and Liu [14] proposed various heuristic algorithms based on zone-partition approach for solving different kinds of multiple robots cyclic scheduling problems. Manier et al. [15] first formulated a mathematical model with disjunctive constraints and then proposed a branch-andbound like algorithm for finding the optimal schedules for multiple robots. Manier and Lamrous [16] proposed an evolutionary approach to minimize the number of robots on parallel tracks. Moreover, Che and Chu [17] and Leung et al. [18] presented a specific B&B algorithm and an MIP approach for the multiple robots scheduling problem with unidirectional part flow, where the part processing route is the same as the machine arrange sequence. Recently, Elmi and Topaloglu [19] proposed an MIP model for the multiple robots scheduling problem with multidegree. Since a higher degree of cyclic schedule would generally improve the production rate, different MIP approaches were suggested for the single robot cyclic scheduling problem with 2 degrees, which means that each machine is emptied exactly 2 times during a cycle [20]. Feng et al. [21] proposed an MIP approach for the dynamic hoist scheduling problem with multiparts. Che et al. [22] proposed a B&B algorithm for the problem with k-degree cycles. More recently, Elmi and Topaloglu [23] developed a metaheuristic algorithm based on ant colony optimization for solving the robotic flow shop scheduling problem with multidegree. Furthermore, Li and Fung [24] proposed an MIP approach for the single robot multidegree cyclic scheduling with reentrance. In recent years, Quantum-Inspired Evolutionary Algorithm (QEA) has been receiving much attention from researchers. It can be seen as a probability optimization algorithm based on the concepts and principles of quantum computation [25, 26]. Since 1990s, QEA has been successfully applied to solve several well-known optimization problems, such as travell (...truncated)