## 1 Introduction  
Decision support systems (DSSs) are interactive information systems intended to help decision makers utilize data and models in order to identify and solve problems and make decisions [1, 2, 3]. Typically, decision support models are static and provide the users with an output for a given input (Step 1 and Step 2 in Figure 1). However, besides the output, users are often interested in alternatives that are close to their initial input and enable a change, usually a positive one, in the output of the model (see Step 1 and Step 2--with BAG-DSM in Figure 1). To solve that specific problem, we developed BAG-DSM, a surrogate-based stochastic optimization method for searching the decision space and generating alternativesthat fulfill certain criteria with regard to the provided initial state (current alternative) and that guarantees evaluation of the outcome to the desired level. Hierarchical multi-attribute models are a type of decision model used in DSSs that decompose the problem into smaller and less complex subproblems and represent it by a hierarchy of attributes and utility or aggregation functions. Such decision models are especially useful in solving complex decision problems [4; 5; 6; 7]. DEX [8] is a qualitative hierarchical multi-attribute method whose models are characterized by using qualitative (symbolic) attributes and decision rules. The method is supported by DEXi [8], an interactive computer program for the development of qualitative multi-attribute decision models and the evaluation of alternatives. DEXi has been used to analyze decision problems in different domains. According to [8], DEXi was used in healthcare for the assessment of breast cancer risk, assessment of basic living activities in community nursing, risk assessment in diabetic foot care, and advising about medication therapy for Parkinson's disease. In agriculture, DEXi [8] was used for assessing the impact of cropping systems on soil quality, assessing the ecological and the economic impact of genetically modified crops, assessing livestock systems, and predicting insect pest damage to crops. Some other recent applications were carried out in the fields of electricity production [9], risk assessment [10], sustainability development [11], and knowledge management [12]. Besides modeling expert knowledge and evaluating existing alternatives, DEXi can be used for what-if analysis, i.e., the process of changing the values of certain attributes in an existing alternative and analyzing how those changes affect the outcome. The what-if analysis has the ability to investigate the differences within a given set of alternatives but lacks the ability to generate the alternative set itself. The provided set of alternatives comprises alternatives that the decision maker chooses to investigate based on corresponding expert knowledge about the underlying decision problem and the set of attributes. However, imposing a condition to consider the desired evaluation of the outcome, which differs from the actual evaluation, makes the what-if analysis intractable. Therefore, a useful extension of such analysis would be to provide the possibility to search for new alternatives or to generate them under a certain set of conditions that strongly relate to or depend on the initial or current state of the modeled system in order to obtain a desirable outcome--an evaluation of the modeled phenomenon. The solutions should satisfy the criteria of least deviation from the initial state, where the deviation is defined with a geometric or set-based distance measure(s) from a given alternative (initial state). This task is important for practical decision support. The qualitative nature of DEX models, along with the set of input attributes and their domains (sets of nominal values that each attribute receives a value from), defines the combinatorial nature of the underlying search task that evolves in a complex combinatorial optimization problem, where the dimensionality of its search space affects the complexity.