Critiquing-based recommender systems enhance decision-making by guiding users through a product space to ifnd items that meet their preferences. By incorporating feedback in the form of critiques that constrain feature value spaces, these systems refine user profiles to provide more accurate and tailored recommendations. This paper presents a novel approach that integrates critiquing into constraint solving, ofering particular benefits for configurable products where finding optimal configurations is complex. We conducted a preliminary ofline evaluation of unit-critiquing in the prototype system to gain initial insights into the approach's eficiency and lfexibility. The results suggest that this method has the potential to eficiently generate relevant recommendations, highlighting its promise for addressing challenges in configurable product recommendations.
In recent decades, critiquing has gained broad recognition as an efective approach in
preferencebased search and recommender systems. This method allows users to express preferences and provide
feedback on various product aspects without specifying exact values [
Constraint solving approaches enable the compact representation of complex problems [7]. These
methods are widely employed in constraint-based recommender systems, which suggest products and
services based on a given set of constraints [8]. Such systems include a recommender knowledge base,
defined by various sets of variables and constraints, which are the core components of a constraint
satisfaction problem (CSP) [
In this paper, we present a recommendation approach that applies critiquing while interacting with a constraint solver from the Choco [10] library. The core idea is that user-specified critiques can be directly translated into constraints, which are then processed by the solver. This approach leverages constraint solving technology to identify valid configurations meeting user requirements [ 11]. Additionally, our approach incorporates a search heuristic that considers user preferences which can positively impact Variables of the set PROD describing the properties of a tennis racket. results. In Section 6, we discuss the advantages of our approach. Finally, Section 7 concludes the paper with a discussion of open research issues.
For demonstration purposes, we present a critiquing-based recommendation scenario within the domain
of tennis rackets. Our approach, similar to constraint-based recommender systems, frames the task of
selecting products that meet user preferences and needs (referred to as the recommendation task) as a
CSP [
For example, extremely narrow rackets require higher stifness (see Table 3). • F: a set of filter constraints based on the user profile. For example, a user with a history of arm injuries requires a racket with lower stifness to help prevent discomfort or injury (see Table 4). • PROD: a single constraint in disjunctive normal form (DNF) that defines the product catalog by specifying elementary restrictions on the possible values of variables in PROD (see Formula 1). Here, is the set of all products, and represents the value of product with respect to the PROD = ⋁︁ (︁ ⋀︁
︁)
∈ ∈
(1)
• C: a set of constraints specified by the user during interaction with the system to reflect the
user’s critiques. For example, this set might include a constraint like brand ̸= Dunlop, excluding
Dunlop from the variable brand. Initially empty, this set is updated as critiques are applied (see
Given this definition, a solution to a recommendation task is an assignment of the variables in PROD
and C, such that none of the constraints in KB, F, PROD, and C are violated [
In this section, we present the key components involved in generating recommendations and describe their core principles.
Acquiring and modeling user preferences is essential in critiquing-based recommender systems. One
common approach is to translate preferences directly into constraints to guide the search process [
In our approach, we employ MAUT to model user preferences. Specifically, each tennis racket variable is assigned an importance and preference value, as well as a preference metric (see Section 3.4), initially set to nearer-is-better. These preferences are dynamically updated through user interactions (i.e., critiquing, see Section 3.2), and play a key role in adjusting the search heuristic (see Section 3.3) and determining the best recommendation when multiple or no solutions meet the user criteria (see Sections 3.4 and 3.5). Additionally, the selection and presentation of attribute-oriented system-suggested critiques are influenced by current user preferences (see Section 3.2). These concepts address the adaptive needs of the critiquing process, making the system more flexible and responsive to changes in user preferences.
To support critiquing, a hybrid system incorporating both user-initiated and system-suggested critiquing
is proposed in [
In our working example, user-initiated critiquing is facilitated by the navigation panel described
in [
After the user selects or specifies critiques, these are translated into corresponding constraints. The
system then performs the following steps on all variables in the set PROD (see Section 2):
1. Update Importance: the system updates the importance of variables depending on whether they
are constrained in the current cycle or not (modified from [
if is critiqued , otherwise where v is a variable and represents an importance factor, set to 1.5 in our working example. 2. Store Preference Metrics: the system stores the preference metrics (see Section 3.4) for variables based on critiques’ impact on their domains. For example, if the user specifies a critique such as "Heavier", the metric more-is-better is assigned to the variable representing the racket’s weight.
For each variable not constrained in the current cycle, the default metric nearer-is-better is applied. Furthermore, as demonstrated in [13], monitoring successive critiques can significantly enhance recommendation eficiency. Consequently, we maintain a model that includes critiques selected by the user in previous cycles. Before adding a new critique (constraint) to the set (see Section 2), we first remove any existing critiques from the model that are inconsistent with the new one.
To find valid configurations, we deploy a custom search heuristic over the search space. As noted in [ 8], identifying valuable products and services within a set of constraints is often necessary in systems operating within domains where millions of potential recommendations are available. Consequently, we limit the number of solutions provided by the constraint solver to 15. The following describes the custom variable and value-order selectors used by the system: • Variable-order Selector: this selector prioritizes variables that are deemed more important at a given moment. For instance, if (weight) > (stifness ), then the variable weight will be selected before stifness . This approach ensures that the instantiation of less important variables does not afect those with higher importance. Additionally, if constraints are relaxed (see Section 3.5), the afected variables will be given priority for selection. • Value-order Selector: this selector considers the current preference metric of the corresponding variable (see Section 3.1). It assigns either the IntDomainClosest or IntDomainMedian value-order heuristic from the Choco [10] constraint solver to each variable. These selectors choose the value from the variable domain that is closest to the specified target value or the median value, respectively. If the preference metric is nearer-is-better or equal-is-better, the IntDomainClosest heuristic is used, with the target value set to the current recommendation’s variable value or the new critique, respectively. Conversely, if the metric is more-is-better, less-is-better, or in-range-isbetter, the IntDomainMedian heuristic is employed.
When multiple solutions are possible, ranking the items becomes necessary. The method presented in [8] determines the degree of similarity between user requirements and recommendations. We adapt these metrics to meet our needs (see Formulae 4–8). The utility of a recommendation is calculated as a weighted sum over the variables describing racket properties , based on user preferences (see Formula 3). Specifically, (, ) denotes the utility of recommendation with respect to variable , () is the preferred value for stored in the user’s preference model, and () corresponds to the constrained range of variable . For example, if a critique indicates that the optimal racket’s stifness is mid-stif, then the constrained range for stifness is from 64 to 67. The terms and represent the minimum and maximum values for variable according to the KB definitions. Additionally, the metrics are categorized as follows: more-is-better (MIB; e.g., a heavier racket is better), less-is-better (LIB; e.g., lower stifness is better), nearer-is-better (NIB; e.g., stifness closer to 65 is better), equal-is-better (EIB; e.g., a grip size of 2 is optimal), and in-range-is-better (IRIB; e.g., medium stifness is preferable). The choice of metric for each variable depends on its assigned metric (see Section 3.1).
In our working example, calculating utility is crucial for ranking attribute-oriented critiques (see Section 3.2) and valid configurations. In the latter case, the item with the highest utility is recommended, and the preferred values of variables in the user’s preference model are updated to match this item. () = ∑︁ (, ) * () ∈
− () : (, ) = () − ()
() − : (, ) = () − ()
| () − | : (, ) = 1 − () − () : (, ) = {︃1, = () {︃1, ∈ ()
(8)
(9)
In scenarios where no item satisfies the critiques (constraints), displaying a message such as “no product
found” is highly undesirable [
To address this issue, we employ a linear-time constraint relaxation technique based on the data
structure described in [
1 _() = ∑︀∈ () If the top-ranked relaxation includes only prior constraints, it is automatically applied by removing the diagnosed user critiques (constraints). This method is known as hard relaxation (see [8]). Conversely, if the top-ranked relaxation includes at least one new constraint, the user is presented with a relaxation proposal that includes only the new constraints and omits prior ones. This approach helps prevent the user from being overwhelmed by potentially irrelevant information due to changes in preferences. Additionally, relaxation proposals are suggested based on the ranking. If the user does not accept any proposal, no constraints will be removed from the model. Conversely, accepting a proposal implies the application of hard relaxation to the constraints within the corresponding constraint set.
After performing the relaxation, the preference metric for variables afected by the relaxation (i.e., those involved in relaxing constraints) is set to nearer-is-better. These variables are then prioritized by the Variable-order Selector when identifying the next solution (see Section 3.3). Once this process is complete, the prioritization of these variables is removed.
The prototype follows the typical interaction model between users and a critiquing-based recommender
system, as described in [
After specifying their profile information, users can enter preferred values for known racket features (or all features, in the case of advanced knowledge), along with their importance on a scale from 0 to 5, where 0 indicates the lowest importance and 5 the highest. The system stores these preferences and calculates the importance as follows: () = 1 + _ * , where represents the number of racket variables, _ is the chosen importance value, and is a constant factor, set to 0.2. If users do not specify a preference for a particular variable, its default value and importance are assigned based on their profile.
The system then identifies and presents the best-fitting recommendation to the user (see Figure 1). The user can either accept this recommendation or provide critiques. Each profile-based and attribute-oriented critique can be selected to apply the corresponding critique. For users with advanced knowledge of tennis rackets, the suggestion of profile-based critiques is omitted. Additionally, attribute-oriented critiques follow a simple presentation pattern [15] and include an "Explain" option for a detailed explanation of the critique’s impact on the search space. Conversely, the navigation panel for user-initiated critiquing allows users to manually specify critiques using the options from "Keep" and "Improve" components. The "Improve" component for a specific racket attribute includes possible critiques to modify the recommended product, such as "decrease", "increase", "Flexible", "Medium", and "Stif" for racket stifness. For example, the user can choose to retain the current recommendation’s brand by selecting the "Keep" option for the brand, while simultaneously constraining the stifness by selecting the " Medium" option (see Figure 1). For users with advanced knowledge, this panel includes all racket features, while for basic users, it displays only features they identified as familiar, which can be modified using the "Change shown features" option. By clicking on the "Find" option, the system applies the selected critiques from the navigation panel. If no solutions meeting the new user criteria exist, the system presents relaxation proposals (see Figure 2). The "Previous Proposal" and "Next Proposal" options allow the user to navigate through a maximum of three proposals. The user can then either accept the proposal via the "Apply Relaxation" option, or select "Continue Without Relaxation".
Additionally, users can access explanations of their profile through the "Explain My Profile" option and receive details about racket features via the "Explain Features" option. These explanations facilitate a deeper exploration of the item space. Furthermore, the system incorporates explanations for the rationale behind the given recommendation or relaxation (see Figures 1 and 2), adhering to the criterion of satisfaction described in [16]. Finally, the "History of Shown Rackets" option displays the last three recommendations, their specifications, and an option to set them as the current recommendation again.
In this evaluation, we compared our approach with the conventional CBR approach by examining the
performance of unit critiquing. For the evaluation, we used a custom dataset of 523 real-world rackets
obtained from online selling platforms. Each racket is described by 9 variables (see Section 2), and
all of these variables, except for the racket’s name, were subject to critique. We conducted an ofline
experiment employing the leave-one-out approach described in [
For generating recommendations, our approach follows the principles mentioned in previous sections.
Conversely, in the conventional CBR approach, all items in the product catalog CB are modeled as
product cases [6], which capture product details through predefined variables. When a user applies
a critique c to a recommended item r, the goal is to find an item that satisfies c and is maximally
similar to r [
The evaluation results show that the conventional approach needed an average of 8.04 critiquing cycles to recommend the target item, whereas our approach required 5.18 cycles. These results highlight the potential eficiency and flexibility of our approach.
In summary, conceptualizing the recommendation task within a critiquing-based recommender system
as a CSP enables the efective utilization of constraint solving technology. Unlike conventional methods
that typically require exhaustive scanning of the entire case-base to identify optimal products, a
CSPbased approach narrows the solution space and employs a targeted search heuristic. This not only
mitigates issues related to poor runtime performance but also has the potential to enhance the system’s
ability to identify highly preferred configurations, as indicated by the preliminary evaluation conducted
in Section 5. This aligns well with the objective of aiding users in efective product configuration [
This paper introduced a new approach to designing critiquing-based recommender systems by combining
the strengths of critiquing with constraint solving technologies, particularly relevant for assisting
users in configuring products. We demonstrated this approach within the context of a tennis racket
recommender system by representing the recommendation task as a constraint satisfaction problem
and detailing its key components for user support and recommendation generation. Additionally,
we conducted a preliminary ofline experiment to evaluate the performance of unit-critiquing within
the prototype system. The results indicate that this approach is promising in terms of eficiency and
lfexibility. However, a limitation of our evaluation strategy is the reliance on simulated users, which may
not fully reflect real-world scenarios. To address this, we plan to validate the approach in a real-world
study to obtain practical insights. Future work will also focus on integrating additional concepts, such
as optimizing performance. Finally, we plan to extend our approach by incorporating information from
successfully completed critiquing sessions to enhance the eficiency of the critiquing process [
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