# An Improved Variable Neighborhood Search for the Reconfigurable Assembly Line Reconfiguring Problem
## 1 Introduction  
Throughout the past several decades, the manufacturing industry has been confronted with an increasing variety of products and the consequent reduction in production volumes, together with the continuous shortening of products' life cycle [1]. In this context, the design of manufacturing systems becomes a complex engineering task that entails manufacturing strategy decisions, has long-term impacts, and involves a major commitment of financial resources [2]. Hence, [PERSON] et al. [3] proposed the solution of the Reconfigurable Manufacturing System (RMS). In terms of response functionality, the RMS can change the variety and quantity of manufactured products through phased reconfiguration; in terms of response time, since the RMS is initially designed and developed for a product family, when there is a need to manufacture a new product within the family, the RMS can undergo less reconfiguration, which greatly reduces the time needed to reconfigure the manufacturing system. Assembly accounts for 40-60% of the total manufacturing time and over 30% of the total manufacturing cost of a product, making the Reconfigurable Assembly System (RAS) an important component of the RMS. Since the majority of RASs in the discrete assembly industry adopt the line layout, the design of the Reconfigurable Assembly Line (RAL) is the key [4]. Past researchers have conducted extensive studies on the initial design of the RAL. However, research on the reconfiguration phase of the RAL is limited, with most literature focusing on the Assembly Line Rebalancing Problem (ALRBP), which reallocates operations without considering the selection of specific manufacturing resources. These findings arechallenging to apply in engineering practice because they do not account for actual resource selection. Moreover, the existing methods use matrix encoding, which is not suitable for modeling complex process information that includes resources. In fact, in the design of assembly line in the discrete assembly industry, most operations require selecting a resource from a specific set of optional resources, while fewer operations can select flexible resource such as robots. Therefore, there is a need to optimize the utilization of both the resources from old assembly line and new resources based on the allocation of new product operations to stations. This challenge is defined as the Reconfigurable Assembly Line Reconfiguring Problem (RALRP). This paper stems from the research project \"Configuration Design and Reconfiguration Optimization of RAL\", which divides the design of RAL into three stages: (1) product family formation for RALs, (2) configuration design of RALs, and (3) reconfiguration optimization of RALs. Firstly, various products are classified into product families based on co-line production, allowing a RAL to offer production flexibility for each category of product family. Secondly, the initial design of a RAL is based on the existing product varieties within a product family, ensuring capacity and a certain level of reconfigurability. Finally, when products within the product family are updated, the RAL is reconfigured and optimized to meet new operation requirements. This study aimed to solve the reconfiguration optimization of RAL. The innovation of this paper is as follows. 1. A mixed integer linear program (MILP) is developed to formulate the RALRP for product update. 2. An efficient data structure is proposed to model product and assembly line, which includes more detailed process information. 3. An improved Variable Neighborhood Search (VNS) is proposed to reduce reconfiguration cost for Reconfigurable Assembly Line. The rest of this paper is organized as follows. Section 2 gives a literature review about the Reconfigurable Assembly Line Reconfiguring Problem and solution methods. Section 3 describes the problem and proposes a mathematical model. The data structure of the problem is detailed in Section 4. The proposed algorithm is introduced in Section 5.