## 1 Introduction  
Optimization is often a part of today's engineering design process for new or improved products. The reason is that the number of possible configurations and the multitude in variants of feasible parts and components creates a huge multidimensional design space, which in turn requires an optimization method for finding high-quality solutions. In this paper, we consider the box-type boom (BTB) crane, as designed at Liebherr-Werk Nenzing (LWN) [1] and shown in Figure 1. The main design task involves the middle section where a boom configuration must be determined which fulfills structural and manufacturing requirements (see also [2, 3]). For the respective design space, a total enumeration of the design variants is not feasible. To efficiently search within the design space, the design task can be formulated as two optimization problems. To solve the respective optimization problems appropriate optimization algorithms need to be selected.  
The selection of an appropriate algorithm is rather challenging given the plethora of available optimization algorithms. For the BTB optimization problems, heuristics derived from the manual process, a metaheuristic, and an approach based on a series of linear programs are considered as viable candidates. To select the most suitable algorithm for a problem from a set of candidates, a comparison of the algorithms is required. This is frequently done by using results from empirical comparisons on benchmarks [4; 5] since the no-free-lunch theorem [6; 7] implies that there is no universal best algorithm. Such benchmarks compare the algorithms based on the obtained solution quality and the necessary computational requirements.  
For end-users of such algorithms, however, further criteria which are not considered in such benchmarks are of almost equal importance. Examples of such criteria are the adaptability of the algorithm, required expert knowledge to tune algorithmic parameters or to comprehend the solution creation process, and system integration requirements. Utilizing an analysis tool from quality function deployment (QFD) [8], this paper describes the design of a decision matrix (DM) that allows systematically discussing the strengths and weaknesses of various algorithms. The elements within the developed DM are derived by experts from the fields of optimization and engineering design and incorporate end-user requirements and criteria based on the performance measures used in benchmarks.  
The DM applied is tailored to the BTB design task and the considered optimization algorithms. To validate the proposed DM within a proof-of-concept, two scenarios for applying the DM are considered: (1) as a tool for selecting an algorithm before applying the algorithm; and (2) as a performance indicator for a comparison of algorithms applied to a benchmark. The first scenario represents the typical application scenario within the design process since it is rarely feasible to implement all suitable algorithms and make a comparison afterward. The second scenario highlights that the DM can be combined with current benchmarks.  
The paper is organized as follows. Section 2 provides an overview of the related work with regard to the QFD method and the algorithm selection problem. In Section 3, the components of the DM are described. Section 4 introduces the BTB design task and its optimization potential. The two optimization problems considered, the algorithms applied, the results obtained, and the evaluations based on the DM are addressed in detail in Sections 5 and 6. In Section 7, the results of applying the introduced decision matrix as well as the methodology itself is discussed. The paper is concluded in Section 8.