## 2 Related Work
To overcome the fuzziness that arises from an ill definition of the classes, some authors rely on feature embedding to automatically identify clusters of instances based on their similarity in the resulting feature space [10; 17; 24]. Several studies exist that deal with the identification of these features, at least for the most relevant problem types. These features can be used for both algorithm selection as well as algorithm configuration problems. Ref. [25] describes what is perhaps the most widely applied set of MIP problem features currently available in the literature. The availability of features to model problem instances gave place to the first prominent incursions into the PIAC for vast configuration spaces, such as ISAC [10] or Hydra [11; 12]. These methods make use of portfolios of complementary algorithm configurations \(\{\theta_{1}^{n},\theta_{2}^{n},\dots\}\), where each configuration in the portfolio dominates over a given instance class \(I\in\{I^{1},I^{2},\dots\}\). As such, the differences between portfolio-based approaches to PIAC lie in the way the portfolios are identified and the mechanism to map a given instance to its most similar instance class. Regardless of these differences, portfolio-based methods have achieved significant gains in performance on widely adapted (heterogeneous) benchmark sets. However, as some authors point out, this is not without significant limitations [17; 18]. In fact, some of the recognized drawbacks of portfolio-based methods are as follows:  
1. [label=()]
2. Once again, they are related to generalization, as it is possible to find unique configurations outside of the portfolio with better performance than the best \"average\" configurator of the class for individual instances within the class,
3. the expensive Exploration of the configuration space, since each new configuration explored needs to be evaluated against all (or a representative set of) the available problem instances. This is nonetheless a very expensive approach that limits the set of configurations that can eventually be explored (although some arguments in favor of this approach appear in the literature as a countermeasure to over-tuning [10; 16]). 4. Consequently, it becomes rather expensive to augment the portfolio (if, e.g., a new instance class or a new configuration with possible performance gains is identified), since adding a new configuration would require its evaluation in a large number of instances. In response to these issues, [18] proposed a PIAC method that makes use of deep embedding, and case-based reasoning [26] for prediction. As such, a repository or case base of training instances, algorithm configurations (identified by solving SIAC on each individual instance) and pertinent algorithm performance is constructed. At runtime, a look-up methodology assigns the algorithm to a new (unseen) problem instance, the best configuration found for the closest instance available in the case base. Regardless of the embedding mechanism used, the case-based reasoning approach described in [18] helps overcome _(i)_ by solving SIAC for each individual instance available (rather than solving the PSAC on the entire set or on a given class, as is the case for portfolio-based methods). Consequently, the approach allows for the exploration of a larger set of possible configurations (cf. _(ii)_), and makes it easier to augment the model (cf. _(iii)_) thanks to the focus on individual instances. Additionally, the authors in [18] report better performance (up to 38% increase in performance) when compared with that of Hydra on a homogenous instance set. However, it is worth noting that the authors evaluate their method using the best value (cost) of the objective value found by the algorithm as the performance metric. This way of working is mostly relevant if a large majority of the problem instances times out, i.e., an instance cannot be solved to optimality within a certain time span.