Calculating Valid Domains for BDD-Based Interactive Configuration

In these notes we formally describe the functionality of Calculating Valid Domains from the BDD representing the solution space of valid configurations. The formalization is largely based on the CLab configuration framework

Further empowering variant tables for mass customization

Tables are a standard form of data representation in business. A variant table lists valid or excluded combi-nations of product features where each table column refers to a product property and each table row denotes a combination of product features. A table cell defines a feature, e.g. Color = Red, as an assignment of its value to the column's property. As technology and consumer demand drive ever increasing product choices, the number of feature combinations that can be offered for a product increases exponentially and can easily exceed the limits of a traditional table. However, variant tables can often be compressed in a way that scales both in size and query performance while retaining the tabular paradigm in a manner useful for a business. The basic idea is to partition the table rows into unconstrained slices, where each slice consists of all possible combinations of the product features it references. Such a slice can be represented as a c-tuple and readily stored in a spreadsheet. C-tuple representation is already supported in some product configurators. We give examples of products where it is feasible to efficiently represent all valid variants in one overall table using c-tuple compression. For cases where c-tuples do not suffice, the stronger compression to a variant decom-position diagram (VDD), a form of decision diagram, can be used. We propose complexity measures for a product based on the compressibility of its variants and discuss their usefulness to the business. We illustrate these ideas with examples and present some results on dealing with variant tables from real-world product models. We show that compression empowers variant tables by enabling enormous tables to be functionally used in a way like regular tables

Enriching Solutions to Combinatorial Problems via Solution Engineering

International audienceExisting approaches to identify multiple solutions to combinatorial problems in practice are at best limited in their ability to simultaneously incorporate both diversity among generated solutions, as well as problem-specific desires that may only be discovered or articulated by the user after further analysis of solver output. We propose a general framework for problems of a combinatorial nature that can generate a set of of multiple (near-)optimal, diverse solutions, that are further infused with desirable features. We call our approach solution engineering. A key novelty is that desirable solution properties need not be explicitly modeled in advance. We customize the framework to both the mathematical programming and constraint programming technologies, and subsequently demonstrate its prac-ticality by implementing and then conducting computational experiments on existing test instances from the literature. Our computational results confirm the very real possibility of generating sets of solutions infused with features that might otherwise remain undiscovered

Interactive Cost Configuration Over Decision Diagrams

Abstract In many AI domains such as product configuration, a user should interactively specify a solution that must satisfy a set of constraints. In such scenarios, offline compilation of feasible solutions into a tractable representation is an important approach to delivering efficient backtrack-free user interaction online. In particular, binary decision diagrams (BDDs) have been successfully used as a compilation target for product and service configuration. In this paper we discuss how to extend BDD-based configuration to scenarios involving cost functions which express user preferences. We first show that an efficient, robust and easy to implement extension is possible if the cost function is additive, and feasible solutions are represented using multi-valued decision diagrams (MDDs). We also discuss the effect on MDD size if the cost function is non-additive or if it is encoded explicitly into MDD. We then discuss interactive configuration in the presence of multiple cost functions. We prove that even in its simplest form, multiple-cost configuration is NP-hard in the input MDD. However, for solving two-cost configuration we develop a pseudo-polynomial scheme and a fully polynomial approximation scheme. The applicability of our approach is demonstrated through experiments over real-world configuration models and product-catalogue datasets. Response times are generally within a fraction of a second even for very large instances