**1. Introduction**

The technological assembly process is the final and the most important stage of the production process, which determines its labor consumption and the final production costs. For this reason, the development of the most favorable technology to join parts with the given conditions is a difficult task with multi-criteria but is extremely important. Optimization or improvement of assembly at the production planning stage concerns the determination of components having a direct impact on this process.

One of the most important problems at this level is the determination of the most advantageous sequence [1–5] of the assembly and components of the production cycle but also the problem of assembly line balancing (ALB) in linear systems, which in principle are also part of activities occurring at the production process stage. These issues are fundamentally related to the degree of process automation but also to the production conditions in a given enterprise. It should be emphasized that in recent times the issues of determining the assembly sequence based on artificial intelligence methods were not very frequent, despite the rapid development of this field of knowledge and the significance of the problem [2,6,7].

Planning the assembly sequence is crucial because it relates to many of its aspects, including the number of necessary tool changes, the number of assembly directions, or even the design of mounting brackets and other instrumentation, for the analyzed assembly sequence. It also has a major impact on the overall efficiency of the process. These features of the assembly process, along with many others, have a decisive impact on the efficiency of its course, but some of them may also be criteria for assessing assembly sequences for its improvement or optimization. Assembly sequence planning (ASP) consists of determining the feasibility and at the same time, finds the most advantageous, under certain criteria: order of combining assembly units, parts, and assemblies into more complex units, which leads to obtaining a final product or a product that meets all design and functional assumptions. Due to the high complexity of the issue of choosing the appropriate assembly

sequence from among all acceptable choices and at the same time remaining feasible is a difficult and complex task. This is due to a large number of possible combinations of the assembly order, as the theoretical number of variants increases exponentially with the number of parts joined. In many industrial cases, when planning the assembly process, no analysis of the sequence or selection of assembly sequences is performed, and this choice is often based only on the engineering knowledge of people directly involved in planning the assembly process, although this area often contains large reserves allowing for improvement and optimizations. This state of affairs results mainly from the difficulty of evaluating even the already generated ones, due to the constraints of the constructional nature of assembly sequences.

In the literature on the subject, the assessment and selection of the most favorable sequence are made according to various criteria, depending on the specificity of plants, availability of devices, etc. Such criteria may be: assembly time, number of changes in assembly direction, number of tool changes, degree of difficulty in reaching the next process state, degree of complexity of assembly unit movements, degree of difficulty in reaching the next process state, the necessary number of reorientations of the base unit during assembly, stability of assembly units, correctness of the assembly course itself, technological production capacity, and economy of the process. Sequence evaluation criteria may also include aspects of safety, reliability, weight, operating economy, technology, ergonomics, aesthetics, or ecology. Importantly, selected data regarding the criteria for evaluating assembly sequences can be obtained automatically from CAD assembly models, for example, the direction of joining parts obtained in this way is related to the number of changes in assembly direction for a specific sequence. Very important for this process are assembly features, which also have a direct impact on the assembly order of parts. Figure 1 presents a summary of the most commonly used criteria for optimizing the assembly process in the selection of assembly sequences in the published and analyzed scientific studies.

**Figure 1.** Criteria for the evaluation of assembly sequences in the analyzed scientific publications concerning ASP issues.

The assembly sequence planning problem belongs to a general class of optimization problems known as NP-complete. For this kind of problem, it is necessary to query the whole set of permissible solutions to ensure that the optimal assembly sequence is found. Nevertheless, because this search strategy is very time consuming and impractical in many industrial applications which are complex, have multiple criteria, and often contain issues that prove difficult to optimize, other heuristic techniques are often applied to find a

solution close to the optimal one. One solution is also artificial neural networks, which is an information processing paradigm inspired by the natural biological nervous system. The very topic of assembly sequence planning using neural networks was covered in recent years by only a limited number of publications [8,9].

The input vector in neural network is multiplied by the synaptic weights, which are the weight vector. This activity is related to the implementation of the function of the postsynaptic potential and the determination of the value of the y signal calculated based on the sum of input signals multiplied by synaptic weights. The models of artificial neurons can be perceived as mathematical models. What we consider to be the first model of a neural network is the neuron model proposed by W. McCulloch and W. Pitts in 1943 and inspired by the biological model, following the pattern [9]:

$$\text{Transfer function} \Rightarrow y = f(\sum\_{i=1}^{k} x\_i w\_i + w\_0) \tag{1}$$

Usually, the signal path between neurons (processing units) is as shown in Figure 2, where *xn* are the neuron input signals (or the external system input data), *wn* are the weights of the edge-connections (synapses), *wo* is the neuron's sensitivity threshold (i.e., bias), and *f* (·) is a simple non-linear function, e.g., a sigmoid or logistic one. Activation (transfer) (AF) functions are possible for each of the hidden and output layers [3].

**Figure 2.** Schematic representation of the artificial neural network.

These studies are aimed at showing the possibility of predicting the assembly time of mechanical products based on variable factors influencing this parameter. The advantage of using artificial neural networks over other optimization algorithms is the ability to predict the assembly time without knowing the mathematical model that describes this phenomenon. This allows to obtain adequate results, also in the conditions of having incomplete production data. This procedure is indirectly aimed at indicating the assembly sequence by selecting the least time-absorbing solution. The article focuses on the application of artificial neural networks as a universal tool of artificial intelligence to support predictive tasks in the area of assembly of machine and device parts. The authors did not find any articles in which the issue of minimizing assembly time, which is important from the point of view of production efficiency, is solved with the use of art neural networks or other methods corresponding to the current trends in the use of artificial intelligence methods. Difficulties in developing an assembly time prediction procedure are mainly focused on providing an appropriate number of examples teaching the neural network. This was achieved by experimentally testing the operation of the network after each set of 100 examples was prepared. The criterion for accepting the network model for further analysis was the achievement of network efficiency during verification at a level greater than 90%. This publication should contribute to a better explanation of the relationship between the determinants of the technological process and its time consumption.

This paper discusses a modelling scheme known as artificial neural networks. The neural network approach has been used for analyzing all feasible assembly sequences. This network structure is suitable for this kind of problem. Proposed assembly planning system is a graph-based approach in the representation of product.

## **2. Related Works**

One of the most important issues in determining the assembly sequence is the appropriate data structure, which means graph representations, mainly directed graphs or hypergraphs. This kind of structure can be considered as formalisms to encode the feasible assembly sequences. To determine all feasible sequences an appropriate graph search algorithm is necessary. The commonly used algorithm for directed graphs or hypergraphs is a heuristically guided search algorithm A\*. Although exhaustive search is the simplest and most popular strategy ensuring the complete of the task, it is quite often impractical. This approach is usually used in cases where the number of parts is small (simple assembly objects). In the case when the number of parts increases, these strategies may have limitations due to the problem of combinatorial explosion.

Studies on ASP have implemented different heuristics optimization algorithms such as genetic algorithm, simulated annealing, evolutionary algorithm, ant colony optimization algorithm, and immune and other heuristic methods [10–17].

In paper [10] to solve the assembly sequence planning of a certain type of product, first of all, the rule of nomenclature is designed. Secondly, geometric feasibility and coherence are designed as constraint conditions and these two are combined with each other as the objective function. Finally, authors proposed a novel method under the name of immune particle swarm optimization algorithm. The results show that the immune particle swarm algorithm can be effective and useful in solving the problem of planning the assembly sequence.

Authors of [12] address assembly sequence planning problem and propose an improved cat swarm optimization (CSO) algorithm and redefine some basic CSO concepts and operations according to ASP characteristics. The feasibility and the stability of this improved CSO are verified through an assembly experiment and compared with particle swarm optimization.

Paper [13] proposes an ASP algorithm based on the harmony search (HS), which has an outstanding global search ability to obtain the global optimum. To solve the sequence planning problem, an improved harmony search algorithm is proposed in four aspects: (1) an encoding of harmony is designed based on ASP problems; (2) an initial harmony memory (HM) is established using the opposition-based learning (OBL) strategy; (3) a particular way to improvise a new harmony is developed; and (4) a local search strategy is introduced to accelerate the convergence speed. The proposed ASP algorithm is verified by two experiments.

In paper [17], an attempt is made to generate optimal feasible assembly sequences using design for assembly concept by considering all the assembly sequence testing criteria from obtained feasible assembly sequences. To generate all sets of assembly sequences a simulated annealing technique is used. Sequences consist of n − 1 levels during assembly, which are reduced by the DFA concept. DFA uses functionality of the assembled parts, material of the assembled parts, and liaison data to reduce the number of levels of the assembly by considering the directional changes as the objective function.

In this article, an assembly sequence planning system is proposed. The neutral network structure is suitable for this kind of problem. The network is capable of predicting the assembly time, which allows one to choose the best assembly sequence from all the feasible sequences.
