# Revisiting Problem-Solution Co-Evolution in the Context of Team Conceptual Design Activity
## 2 Materials and Methods
### Measures and Visualisations  
Fine-grain investigation of team design activity captures the process in the form of a segmented protocol, where each segment corresponds to ASE state transitions performed within or in between the problem and the solution space. Hence, the protocol does not describe the state of the explored design space but rather the transitions between the states (as shown in Figure 2). Each transition \begin{table}
\begin{tabular}{c c} \hline \hline
**Analysis** & Analyse [20], [38], [40], [41], [47], [50], [60], [61]; Simulate [38], [50], [62]; \\ Clarify [41], [63]; Acquire [64]; Calculate [62]; Compare [62]; Correct [63]; \\ Interpret [64]; Understand [14]; Read [65]; Repeat [65]; Request [65] \\ \hline
**Synthesis** & Synthesise [20], [38], [40], [47]; Generate [14], [41], [50], [60], [61], [62], [66]; Define [28], [42]; Elaborate [60], [65]; Gather [61], [68]; \\ Modify [65], [67]; Add [65]; Create [28]; Compose [50]; Formulate [40]; \\ Model [61]; Patch [62]; Propose [65]; Refine [62]; Refine [50]; \\ \hline
**Evaluation** & Evaluate [8], [14], [20], [38], [38], [40], [41], [47], [61], [62], [65], [67]; \\ Decide [14], [28], [41], [61]; Select [8], [67]; Accept [41], [62]; Verify [60]; \\ Reject [62]; Suspended [62]; Qualify [65]; Justify [65] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mapping of various fine-grain design process notions from design literature onto analysis, synthesis, and evaluation as transitions between the states of the explored design space. Figure 2: An example of an activity protocol excerpt where both the problem and the solution space are populated with design entities (in some state i). Analysis, synthesis, and evaluation of problem- (circles) and solution-related (squares) design entities as transitions between the states of the explored design space (i, i + 1,... ). Co-evolution episodes correspond to synthesis moves between the spaces. Legend: PA—problem analysis, PS—problem synthesis, PE—problem evaluation, SA—solution analysis, SS—solution synthesis, SE—solution evaluation. poses an incremental change to the explored design space, either in its problem (circles) or solution (squares) portion. Sequences of transitions within either the problem or the solution space represent the evolution of the respective space, whereas sequences of transitions in between the two spaces represent the co-evolution of the design problem and solutions. In order to simplify the capturing of activity protocols, the ASE transitions can be further categorised based on the space they pose change to. For example, ASE taking place within problem space were labelled as \"problem analysis\" (PA), \"problem synthesis\" (PS), and \"problem evaluation\" (PE). Likewise, ASE within the solution space were labelled as \"solution analysis\" (SA), \"solution synthesis\" (SS), and \"solution evaluation\" (SE). These transitions were, from here on, conceptualised as six basic state transitions. An example of an activity protocol excerpt that could be sampled from the overall activity process is shown in Figure 2. Of particular interest are the transitions that introduce new entities in one space following the transitions within the other; that is, when problem space exploration results in solution synthesis or when solution space exploration results in problem synthesis. These transitions can be treated as potential co-evolution episodes, as highlighted in Figure 2.  
The state-transition model was intended for capturing ASE in the problem and solution space by means of experimental studies (as demonstrated in [43]) as well as a support for predicting the most probable sequences of state transitions during team design activities. Both purposes require identifying and formulating the variables of interest, as well as their measures and a reliable and valid manner of measurement [69]. In terms of fine-grain investigation of the design process, the variables and measures are typically based on the design protocols.