The design for additive manufacturing (DfAM) principles allow industries to use many computational tools to optimize designs such as topology optimization, generative design, compositionally heterogeneous multimaterial component design, embedded graded lattices, tailored porous functional structure integration, and functional part consolidation [1]. Compared to conventional manufacturing, additive manufacturing has higher degrees of design freedom. AM eliminates the need for intermediate tooling, thus increasing complexity without additional cost increase for a light weight design achieved by eliminating the multiple production steps in AM being a dieless manufacturing method [2]. This added complexity is usually eliminated in conventional manufacturing due to cost overruns. But this additional complexity comes free in AM and any computational optimization of design for manufacturing using traditional manufacturing methods seemed to greatly increase cost due to difficulty in manufacturing [3]. Engineers and designers are confronted with multiple solutions of computational tools such as generative design, topology optimization and lack of decision support to help them select a design variant for manufacturing techniques such as additive manufacturing (AM) is a limiting factor to achieve efficiency and cost objectives. So, identification of appropriate designs for manufacturing in AM regarding economic and technical aspects need advanced training and education [4]. Hence in this work we propose a MCDM approach to identify the most appropriate design from the computationally optimized design variants.
Multiple variants of a single design are made feasible by leveraging the unique design capabilities of the DfAM. For example, several design variants can be generated for a given design problem in generative design and Topology Optimization (TO). In such cases, it is difficult for the users to select an appropriate design variant. To assist such users, we propose a composite measure of geometric complexity and economic benefits using multicriteria decisionmaking. Enrico et al. [5] created a tool for selecting the best design variant by merging it with a topologicaloptimization algorithm. Rohan et al. [6] proposed a method for selecting design variants using three categories: DfAM use, manufacturing efficiency, and inventiveness. This helps users to avoid part failures when choosing a design variant. Another method for selecting design variants proposed by Yicha et al. [7] is to examine the limits of process planning.
Different part selection strategies based on quantitative measures exist that can be used for selecting design variants. Some of these studies were compared in terms of cost, complexity, and functionality. Table 1 lists the different method for selecting suitable parts for AM. Only a few methods have used both cost and complexity to evaluate the suitable part and most of the approaches are proposed for part selection. Hence, there is a need to develop an alternative approach that combines all the cost measures (preprocessing, processing, and postprocessing costs) and shape complexity measures, for selecting a suitable design variant.
A part selection guide was developed by Pham and Gaul [8] to identify the strengths and weaknesses of different AM processes by comparing process parameters such as layer thickness, process accuracy, and printing speed. Bib et al. [9] proposed a software tool for generating quotes to calculate printing time and cost. Based on this cost analysis, users decide on part selection. Campell and Bernie [10] created a database that discusses the capabilities of various AM systems, and users can use this database to select an AM process for their part. Materialize [11] uses bounding box volume, geometric complexity, production volume, and function to decide the candidacy of a part.
Most existing part selection frameworks rely on questionnaires and demand expert process knowledge. Under these circumstances, the need for a decisionsupport system for part selection in the AM process is justified.
Table 1 Comparison of different part selection strategies for additive manufacturing
Defining reliable complexity measurements is the first step in creating such systems. To this end, we proposed four measures for assessing the suitability of design variants.
Definition 1
The external shape complexity metric () is the shape complexity of a design variant's external shape and is determined by comparing views taken from various viewpoints around it. A higher number suggests a more complex shape. [24].
Definition 2
The internal structural complexity metric () is the shape complexity of the internal structure taken from the intersection of parallel planes with the 3D model at various heights from the base. A greater value suggests a more complex shape. [24].
Definition 3
Costbenefit ratio (C br ) is the ratio of the benefit in the processing cost after optimization to the total processing cost of an unoptimized part in the MAM using LPBF process. It represents the cost savings of the optimization effort. The probability of selecting a design variant is higher for an optimized design variant with a larger Cbr.
Definition 4
Incremental cost is the additional cost incurred in processing the design variant compared to the unoptimized design variant in MAM using LPBF. The design variant with the high incremental cost is not preferred for manufacturing using AM.
The assumptions in the proposed work while calculating the incremental cost and costbenefit ratio are given below

All design variants in the case studies were realized using Ti6Al4V in metal additive manufacturing (MAM) using laser powder bed fusion (LPBF) EOS M270.

The type of support structure used for all the case study design variants is area support with poly line (a support structure variant in Autodesk Netfabb)
The above metrics are evaluated for the case study involving selection of a design variant of a triple clamp presented in the earlier work of the authors [24]. The details of the design variants and its ranking based on the metric are shown Fig. 1. Ranking these design variants using shape complexity metric or cost factors individually yields different results (detailed methodology for calculating these measures are discussed in section 2). It can be observed that design variants with high complexity are not economically feasible, but those with high economic benefits have a high incremental cost. Therefore, selecting design variants using these metrics independently does not provide holistic insights into the technical feasibility and economic viability of the variations of the design. Even though TC3 has high shape complexity and economic benefits compared to other design variants, the incremental cost is high which is undesirable in selection of a design variant (refer Fig. 1(be)). So, relying on a single metric will lead to lopsided decision making. In view of this, it can be observed that an aggregated metric provides a balanced approach to selecting a design variant.
Concerning the current problem, metric aggregation should consider the importance of each metric because the technical feasibility and economic viability of the design variant need to be considered together for the effective selection of the design variant [25]. Therefore, decisionmaking without considering the interrelationship of these criteria will lead to the selection of a technically feasible design that is economically not viable or vice versa. To avoid this, we use an FPWMSM operator developed based on the concepts of Fuzzy Numbers (FN), power average operator, and Maclaurin Symmetric Mean (MSM) operator. In the FPWMSM, the decision values are converted into fuzzy numbers before aggregation, which converts all measures into a unified range. The weights for aggregating the measures were calculated using the MSM operator, which is known as the dynamic weight. The operator can also consider the interaction between the criteria and reduce the risk associated with decisionmakers by considering the risk factor [26]. Therefore, a composite complexity metric considering both complexity and cost factor is introduced in this work.
Definition 5
The composite complexity metric (c co ) is an aggregated metric calculated using a fuzzy powerweighted Maclaurin symmetric mean operator of shape complexity metrics and cost factors.
A multicriteria decisionmaking method (Fig. 2(a)) is required to aggregate these metrics (Fig. 2(b)) that may be used to choose the most suitable design variant. In this study, a fuzzy powerweighted Maclaurin symmetric mean (FPWMSM) operatorbased multicriteria decisionmaking technique has been adopted and is presented in the next section.