Keywords: case based reasoning, derivational analogy, cost estimation, probability distribution.

Most case based reasoning (CBR) systems that have been developed in the last couple of decades follow the transformational analogy approach. In transformational analogy, similar past solutions are retrieved and adapted in order to propose new solutions. In contrast, derivational analogy involves applying the reasoning steps that were used to perform tasks in the past. There are only a few engineering applications of derivational analogy in the published literature. This paper describes a new CBR system called KnowPrice that uses derivational analogy. The software was developed in collaboration with a Swiss construction management company. KnowPrice estimates probability distributions of project costs using cases containing details of past projects.

In KnowPrice, cases are represented using a data structure called MREM (Memory Reconstruction Method) which was first proposed in another CBR system called CADREM. CADREM is a case based design system that uses derivational analogy for the conceptual structural design of buildings. MREMs store case-specific methods in forms that enable reuse in new situations. This representation permits reasoning about methods, retrieving relevant methods in a given situation and automatically adapting them to suit the requirements. CADREM contains several classes of MREMs for representing complex design methods. In KnowPrice, mainly three simple MREM classes are used. They are, 1) Instantiation of a variable with a constant 2) Instantiation of a variable with a mathematical expression and 3) Compound MREM (that contains other MREMs). Compound MREMs permit hierarchical representation of methods and are of particular importance in engineering applications, since most tasks have a hierarchical decomposition.

A two-stage retrieval procedure is followed. In the first stage, context elaboration is performed using rules defined by users. Simple forward chaining is used to make inferences from data provided by users, during which secondary variables are created. In the second stage, relevant MREMs are retrieved for each task in a recursive manner. Relevance of an MREM is determined by two criteria, A) the set of variables that are required for the application of the MREM (dependencies of the MREM) B) similarity of the case containing the MREM to the current context.

Adaptation happens automatically due to re-instantiation of an MREM in a new context. The structure of the resulting solution might be fundamentally different from that stored in the case base, especially when MREMs that are retrieved for subtasks are different from those of the parent MREM. Case-specific methods are easily adapted to a new situation by substituting nodes in the MREM decomposition with more relevant ones selected from other cases.

In order to estimate the cost of a new project, users input available information that are known about the project. Appropriate methods (MREMs) are retrieved from the case base using the criteria of relevance and similarity. These methods are used to compute the probability distributions of total cost and other variables using monte-carlo simulation.

Eleven cases consisting of real projects completed by the industrial partner have been stored in the case base. Each case contains more than a thousand attributes. Attributes belong to three groups. The first group contains descriptive attributes that represent project characteristics. These attributes are not directly involved in cost calculations. Nevertheless, they influence probability distributions since they determine similarity of cases. The second group of attributes contain quantities that might be used in cost calculations. The third group contains attributes that represent the cost of building components. Cost attributes are structured into a hierarchical form following the CFC ("Code des frais de construction") scheme, which is currently being used by the enterprise for building projects. Attributes belonging to the first two groups are represented using the MREM class, variable instantiation with a constant. Cost attributes are mostly represented using the MREM class variable instantiation with an expression. Most CFC attributes are computed by summing up values of lower-level CFC attributes. fewer generic, case-specific methods are also used. For example, a crude estimate for the cost of super-structure is obtained by multiplying plan area by the unit cost.

KnowPrice is an application of the CADREM methodology to a domain other than structural design and thus demonstrates the generic nature of the representation and the algorithm. The MREM representation is natural and intuitive for this task. Cost estimates are obtained using available data and users are not forced to input values of variables that are not known precisely. Appropriate methods are automatically selected and applied. KnowPrice is being used to estimate project costs using real data and is an example of successful partnership between researchers and industry.

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