Subassembly Detection and Optimal Assembly Sequence Generation through Elephant Search Algorithm

Most of the engineering products are made with multiple components. The products with multiple subassemblies offer greater flexibility for parallel assembly operation and also disassembly operation during its end of life. Assembly cost and time can be minimized by reducing the number of assembly levels. In this paper Elephant search algorithm is used to perform Optimal Assembly Sequence Planning (OASP) in order to minimize the number of assembly levels. Subassembly identification technique is used as an integral part of algorithm to identify the parallel assembly possibilities. The proposed method is implemented on industrial products and a detailed comparative assessment has been made with suitable product illustrations to corroborate the efficiency. KeywordsAssembly sequence planning, Elephant search algorithm, Swarm intelligence.


Introduction
There is an ever increasing demand for producing new products and supplying into market on-time towards fulfilling the customer needs, which made the industries to look towards new fabrication techniques and assembling methods. Product assembling is the major time consuming and expensive process for products with large part counts thus an industrial engineer always tries to reduce the overall fabrication cost and time of products (Bahubalendruni and Biswal, 2016a).
There exist several assembly sequence generation methods intended for different uses, the graphical based methods generally result in a single/multiple feasible assembly sequence (Bahubalendruni et al., 2015a). Some traditional methods and recent computational approaches offer the same by considering the assembly attributes as input (Vigano and Osorio Gomez, 2012;Bahubalendruni and Biswal, 2016b). However, these methods do not assure any optimal assembly sequences, an optimal assembly sequence is a feasible and stable assembly sequence which requires minimum assembly efforts and time . Finding an optimal assembly sequence ensuing multiple assembly constraints including clash information is an extremely challenging task (Gunji et al., 2019). Several researchers implemented numerous optimization algorithms to solve the The recent optimization techniques have been implemented to solve large products (Smith et al, 2001;Chen et al., 2010;Ghandi and Masehian, 2015;Bahubalendruni et al., 2016;Gunji et al., 2018). Hybridized and advanced optimization techniques have also been tried to overcome the limitations with traditional AI techniques and to address the OASP problem effectively (Akpinar et al., 2013;Gunji et al., 2017;Bahubalendruni and Biswal, 2017;Sahoo, 2017;Bahubalendruni and Biswal, 2018a). Also, the hybrid heuristic approaches were implemented for multiple constraints in various realist problems like process planning and plant layout design (Bhunia et al., 2017;Bose and Pain, 2018;Turgay, 2018). Fine tuning the optimization process parameters hybrid algorithms is computationally inefficient. Moreover, the researchers only focused on linear assembly systems where subassembly identification is ignored. The recent research focused on stable subassembly identification for small products made with fewer parts (Bahubalendruni and Biswal, 2018b;Bahubalendruni and Kumar, 2018).
The proposed method aims to apply a new swarm intelligence based optimization algorithm, namely Elephant Swarm Water Search Algorithm (ESWSA), to solve subassembly based optimal assembly sequence planning efficiently for large scale products.

Assembly Attributes
Assembly attributes plays significant role in ensuring the practical possibility of assembly operation while applied during assembly sequence generation. Most of the assembly attribute data can be extracted through Computer Aided Design (CAD) product through user interface (Vigano and Osorio Gomez, 2012;Bahubalendruni and Biswal, 2016;Bahubalendruni and Biswal, 2017;. Most of Application Program Interface (API) of CAD ease the process of automatic attribute extraction without any human error. A 17-part gear box assembly shown in Figure 1 is considered from literature. There are three assembly attributes namely Assembly Contact Matrix (ACM), Collision Free Path Matrix (CFPM) and Assembly Stability Matrix (ASM). ACM is a square matrix of size equal to number of parts in the final product. It represents the surface contact between any pair of parts, the existence of surface contact is "1" and non-existence as "0". A product can have three CFPMs along principal axes (x+, y+ and z+) the transpose of these matrices give the CFPM along the opposite directions (x-, y-and z-), the element value "1" in the matrix represents possibility of collision free path of the part stated in the row in presence of part stated in the column. ASM is a square matrix of size equal to number of parts in the final product. It characterizes the stability of any pair of parts, "3" signifies permanent stability between pair of parts due to external connectors, "2" represents permanent stability between pair of parts due to part mating features, "1" depicts partial stability of part stated in the column in presence of part in the row and "0" denotes unstable pair of parts. The ACM, ASM and CFPM for the reduction gear-box assembly is given in Figure  2.

Elephant Swarm Water Search Algorithm
Elephant Swarm Water Search Algorithm is a swarm based optimization algorithm inspired from the natural phenomenon of Elephants searching for water during dry weather and scarcity of water situations (Mandal, 2018). The communication strategies among swarm is used to find the global optimal solution from local optima. A typical ESWSA for assembly sequence planning is given in Figure 3.

Assembly Sequence Validation and Fitness Value Computations
Initial elephants swarm are generated based on the random numbers; in each swarm, assembly-part numbers are assigned to random numbers in ascending order. A typical assembly sequence generation from random numbers is indicated in Table 1. Liaison become true when each successive part in the sequence must exhibit at least one surface contact with one part in the preceding list. Assembly stability is true when part has at least one stable relation (partial/permanent) with reference to one part the preceding sequence. Geometric feasibility is true when part has at least one collision free path in the existence of all preceding parts. A stable subassembly is a sub-set where all the parts must exhibit permanent stability along with geometric feasibility. The position changes for the parts after every iteration based on the fitness values is given in Table 2.

If dj=dj+1; j (l,k) & k>l If ASM (j,j+1)>=2 j (l,k) & k>l
The group of parts (l,k) creates a stable subassembly The present problem part/subassembly position swapping in the assembly sequence obtained from above fitness vales are depicted in Figure 4. Fitness function is evaluated based on the number of total assembly levels, which is calculated as the sum of maximum number of single assembly operations of the final assembly and subassembly. A typical assembly level calculation for a sequence is listed in the Table 3.   ((6-7) The maximum number of iterations and population of algorithms (swarm) is chosen as 1000, 10 respectively and the probabilistic constant (switching probability) is turned to 0.86 after few iterations and the resulted outcomes are presented in the following section.

Results and Discussions
The product is solved multiple times due to the stochastic nature of optimization algorithm and the resulted assembly sequence is compared with that of solution given by past literature. Dini has proposed a solution while implementing the Genetic Algorithm (GA), the solution has 12 total assembly levels with 4 identified stable subassemblies (Dini and Santochi, 1992). Trigui solved the product with disassembly sequence planning approach and obtained a feasible solution with 7 assembly levels (Trigui et al., 2017). The proposed approach resulted in an assembly sequence with 6 total assembly levels as listed in Table 4.  The rate of convergence of the algorithm is compared with that of basic scheme of Genetic Algorithm and Particle Swarm Optimization (PSO) technique and presented in Figure 5. The time taken to converge the solution by each algorithm is presented in Figure 6. The GA and PSO have taken the more time than ESWSA.

Conclusion
An efficient method to produce optimal assembly sequences by considering all the necessary assembly sequence validity constraints is proposed. The proposed ESWSA is a proven capable to solve both subassembly detection and assembly sequence planning. The previous methods discussed by Dini and Trigui focus on identifying the stable subassemblies and then each subassembly is treated as a single part and further linear assembly sequence is found out. Unlike the previous methods, the proposed method obtains the better fitness value with total number of assembly levels of 5, where subassembly detection is an integral part of assembly sequence generation. A comparative assessment is also presented with that of swarm based optimization technique to corroborate the performance of the proposed method.