Week 1 What is Sustainability

Identifying Sustainable Designs Using Preferences over Sustainability Attributes

Ganesh Ram Santhanam and Samik Basu and Vasant Honavar Department of Computer Science, Iowa State University, Ames, IA 50014

{gsanthan,sbasu,honavar}@iastate.edu

Abstract

We consider the problem of assessing the sustainability of alternative designs (e.g., for an urban environment) that are assembled from multiple components (e.g., water supply, transportation system, shopping centers, commercial spaces, parks). We model the sustainability of a design in terms of a set of sustainability attributes. Given the (qualitative) preferences and tradeoffs of de- cision makers over the sustainability attributes, we for- mulate the problem of identifying sustainable designs as the problem of finding the most preferred designs with respect to those preferences. We show how techniques for representing and reasoning with qualitative prefer- ences can be used to identify the most preferred designs based on the decision maker’s stated preferences and tradeoffs.

Introduction

In many applications like urban planning, the design of green buildings and space crafts, decision makers often look for designs that are more sustainable than others among all the designs that satisfy the functional requirements. Typ- ically, the sustainability of the various alternative designs are assessed with respect to a set of sustainability attributes that describe various aspects of the designs such as its ini- tial and maintenance cost, the amount of pollutants (e.g., toxic, greenhouse gases) it releases into the environment, and the amount of renewable energy used to source the en- ergy needs of the design. Identifying the most sustainable designs among a set of alternatives depends on the prefer- ences and tradeoffs of the decision maker over such sustain- ability attributes, in addition to the functional requirements of the design problem.

For example, in designing a sustainable building, a deci- sion maker might prefer to source the energy needs of the building using renewable energy sources (such as solar or wind energy) over non-renewable energy sources (such as fossil fuels). Furthermore, the decision maker may choose to trade off one sustainability attribute against another (e.g., re- newability of the energy source against cost of the building); and in other settings, the decision maker might find it use- ful to assign relative importance to sustainability attributes

Copyright c© 2011, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.

(e.g., controlling the amount of greenhouse gas emissions being more important than using renewable energy sources). A similar problem arises in the design of space crafts (Lutz et al. 2010). In order to make a space craft design more sus- tainable for a mission, the decision maker may seek a more energy efficient space craft design, i.e., one which consumes lesser electricity per unit time in comparison to various other feasible designs of the space craft. This requires more en- ergy efficient components (with lesser power ratings) to be used in the design of the space craft. Similarly, the decision maker may also want to minimize the cost of the initial de- sign of the space craft, and hence among two components with the same power ratings, the less expensive one may be part of the preferred design. In addition, the decision makers may also consider the overall cost of the design to be more important than its efficiency in terms of power consumption. Preferences such as the above may be qualitative (Brafman, Domshlak, and Shimony 2006) (e.g., binary preference re- lations over the domains) or quantitative (Fishburn 1970; Keeney and Raiffa 1993) (e.g., utility functions).

Problems in sustainable design (e.g., building design) typ- ically involve choosing and assembling multiple compo- nents (such as siding walls, flooring and heating system in the case of a building design) from a repository that sat- isfy the functional requirements of the design. Each com- ponent of the design contributes to the sustainability of the design with respect to each of the sustainability attributes, and choosing some components over others to be included in the design might make the design more sustainable based on the preferences and tradeoffs of the decision maker over the sustainability attributes. The sustainability of a design is thus a function of the sustainability of the components that make up the design and the decision maker’s stated prefer- ences and tradeoffs.

In the sustainable design of a space craft (Lutz et al. 2010) for example, an expensive component simply adds to the cost of the entire space craft as a whole. However, the power rating of a space craft may not be a simple sum of the power ratings of its components. In fact it may depend on the ar- rangement of the components in parallel or sequence in the circuitry. Furthermore, in order to determine the subset of most sustainable designs among all feasible designs, there is a need to compare two designs with respect to all the sustain- ability attributes in terms of the intra-attribute and relative

91

Artificial Intelligence and Sustainable Design — Papers from the AAAI 2011 Spring Symposium (SS-11-02)

importance preferences of the stakeholders. This is called dominance testing, i.e., does one design dominate the other with respect to the stated sustainability preferences?

Hence, in order to identify sustainable designs from a set of alternatives, there is a need for principled methods that assess and compare alternative designs based on (a) the pref- erences and tradeoffs of the decision maker with respect to the sustainability attributes, and (b) the impact of various components and materials that are included in the design.

Our approach to the problem of identifying the most sus- tainable design(s) involves representing sustainability re- quirements (in addition to the functional requirements) of the decision makers in terms of qualitative preferences over a set of application specific sustainability attributes of the design alternatives. We propose to leverage the existing body of work in the AI literature for representing and reasoning with qualitative preferences over multiple attributes. Follow- ing the representation language given in (Santhanam, Basu, and Honavar 2010b), we represent sustainability preferences of the decision makers in the form of: (a) intra-attribute pref- erences, i.e., preferences over the various possible values that can be taken by each attribute; and (b) relative impor- tance among the attributes, i.e., which of the sustainabil- ity attributes the stakeholders care more about. While intra- attribute preferences make one design preferred over another in terms of a particular attribute, relative importance prefer- ences allow one attribute to be traded off against others.

In this paper we restrict our scope to preferences over an attributes that do not depend on specific values assigned to other attributes (i.e., unconditional preferences). However, our approach can be extended to use other more expressive languages, particularly CP-nets (Boutilier et al. 2004), TCP- nets (Brafman, Domshlak, and Shimony 2006), and UCP- nets (Boutilier, Bacchus, and Brafman 2001) that can rep- resent and reason with conditional preferences. We leverage on existing dominance testing strategies that are well studied in the AI literature (Santhanam, Basu, and Honavar 2010b; 2010a; Boutilier et al. 2004; Brafman, Domshlak, and Shi- mony 2006) that have been successfully used in other design applications such as Web services composition (Santhanam, Basu, and Honavar 2008). We provide a generic model and a practical approach that can be used along with existing design tools for identifying sustainable designs in various application domains.

Illustrative Example

In order to explain our approach to sustainable design, we consider the problem of building design, where the deci- sion maker is tasked with identifying sustainable building designs from a set of candidate designs that meet some pre- specified functional requirements of the building.

Sustainability attributes The sustainability of a building depends on how cost-effective, environmentally preferable and safe are the components and materials used in the de- sign. Key factors in determining the sustainability of a com- ponent used in the design of a building include its energy costs, potential global warming effects in terms of green-

house gas emissions, and environmental, health, and safety concerns related to the potential release of toxic chemicals and pollutants from the components and materials (Lippiatt 2007).

The Building for Environmental and Economic Sustain- ability (BEES 4.0) tool (Lippiatt 2007) released by the Na- tional Institute of Standards and Technology (NIST1) con- siders several attributes for measuring sustainability of com- ponents and materials used in building design. This decision support tool is intended towards aiding building decision makers to choose components and materials in their design that increase the sustainability of the building as a whole. The tool includes actual environmental and economic per- formance data for 230 building products over these sustain- ability attributes. In our example we consider the following four attributes (included in the BEES tool) as indicators of sustainability of components for the purpose of this discus- sion.

• Initial Cost (IC): This determines the cost of constructing the building as per the design.

• Future Cost (FC): This determines the cost of maintaining and operating the building for its intended purpose.

• Renewability (RE): This measures how much renewable (and non-renewable) energy is embodied in the materials used to construct the building. For example, the use of components that are made of renewable materials (such as wood) for components such as doors, windows, siding walls, etc. in the construction of the building, and the use of renewable energy sources (such as solar power) to meet the energy needs of the building makes a design more sus- tainable in terms of this attribute.

• Toxicity/Greenhouse Gas Emission (TG): During the con- struction and operation of a building, several chemicals are released into the environment. Ecological toxicity refers to the potential of a pollutant that is released into the environment to harm ecosystems. Similarly, green- house gases such as carbon dioxide (CO2) are believed to contribute to global warming, so a sustainable building will minimize the emissions of greenhouse gases during construction and operation.

Preferences For each of the above attributes, we allow the following values: Excellent (E), Good (G), Average (A), Bad (B) and Poor (P). These levels indicate the sustainability of the component2, and the intra-attribute preferences for all the attributes correspond to E > G > A > B > P. For exam- ple, a component that has ‘P’ as the value of the attribute Re- newability (RE), it indicates that the component consumes a lot of non-renewable energy sources, and is not preferable to another component valued at ‘B’ for RE. Similarly, a com- ponent that has ‘A’ for the attribute initial cost (IC) is con-

1http://www.nist.gov 2The BEES 4.0 (Lippiatt 2007) tool provides values on a nu-

meric scale for each of the attributes for the components, but we use qualitative levels that roughly correspond to those numerical values in order to simplify our discussion in our paper.

92

Function Component IC FC RE TG

Heating Electric G B B B Heating Gas A G B B Heating Solar P E E E Flooring Ceramic Tile A E B B Flooring Vinyl Tile E G A G Flooring Natural Cork P E G E Siding Brick&Mortar P E P B Siding Aluminum G G G A Siding Cedar A A G G

Table 1: Available Building Components in the Repository

Design Heating Flooring Siding

D1 Electric Vinyl Tile Aluminum D2 Gas Ceramic Tile Brick&Mortar D3 Gas Vinyl Tile Aluminum D4 Solar Ceramic Tile Brick&Mortar D5 Solar Natural Cork Aluminum

Table 2: Candidate Building Designs

sidered more economically sustainable (less expensive) than another with a level of ‘P’.

Furthermore, suppose that the the decision maker has some preferences in terms of the relative importance of the sustainability attributes, such that:

• Future Cost is more important than Initial Cost and Re- newability

• Toxicity/Greenhouse gas emission is more important than Initial Cost

Functional Requirements In order to simplify the discus- sion, we consider only three aspects of the functional re- quirements of a building design: (a) the heating mechanism; (b) the type of flooring; and (c) the type of external wall sid- ing used in the design. Suppose that the only choices avail- able (for each of the components in the repository) are as given in Table 1. The table also shows the valuations3 of the components with respect to the sustainability attributes.

A candidate design constitutes a combination of the heat- ing mechanism (Electric/Gas/Solar), type of flooring (Ce- ramic Tile/Vinyl Tile/Natural Cork), and external wall sid- ing (Brick&Mortar/Aluminum/Cedar), thus satisfying the functional requirements. Suppose that the decision maker is tasked with choosing the most sustainable design(s) from five candidate building designs as given in Table 2.

In this example, the problem we address corresponds to identifying the most sustainable design(s) from those given in Table 2, i.e., designs with preferred values (closer to E)

3The valuations for the flooring and external siding wall com- ponents are roughly based on data for the respective materials from the BEES 4.0 (Lippiatt 2007) tool.

for the sustainability attributes, while at the same time re- specting the relative importance among the attributes.

Model

Designs and Feasible Designs

A design problem consists of a repository of available com- ponents from which we are interested in assembling designs that satisfy some given functionality ϕ. Formally, we repre- sent a design problem as a tuple 〈R, ⊕, |=, ϕ〉 where • R = {C1, C2 . . . Cr} is a set of available components • ⊕ denotes a design operator that functionally aggregates

components and encodes how the components interact when included within the same design. ⊕ is a binary op- eration on components Ci, Cj in the repository that pro- duces a design Ci ⊕ Cj

• |= is a satisfaction relation that evaluates to true when a design satisfies the given functional requirements ϕ

• ϕ is a set of functional requirements that each candidate solution to the design problem is required to satisfy

Definition 1 (Candidate or Feasible Design). Given a design problem 〈R, ⊕, |=, ϕ〉, a design D = Ci1 ⊕ Ci2 ⊕ . . . Cin is an arbitrary collection of components Ci1, Ci2, . . . , Cin s.t. ∀j ∈ [1, n] : Cij ∈ R.

A feasible design or a candidate design is a design D that satisfies the functional requirements ϕ, denoted by D |= ϕ.

The repository of available components R in our example problem of building design is given in Table 1. The func- tional requirements ϕ in our problem state that a building design is feasible if it includes exactly one heating compo- nent (electric, gas, or solar heating), one flooring component (ceramic, vinyl tile, or natural cork) and one siding compo- nent (brick&mortar, aluminum or cedar siding). The set of candidate or feasible designs considered in the example is given Table 2.

Sustainability Attributes

Let X = {X1, X2, ..Xn} be the set of sustainability at- tributes in a design problem, each Xi having a domain of possible values Domi. We define the valuation of a compo- nent in terms of the sustainability attributes as follows, simi- lar to the definition of the valuation of Web services with re- spect to their non-functional properties in (Santhanam, Basu, and Honavar 2008). Definition 2 (Valuation of a Design Component). The val- uation of a component Cj ∈ R with respect to the at- tribute Xi ∈ X is denoted by VCj (Xi). The overall valu- ation of the component Cj is described by the tuple VCj = 〈VCj (X1), VCj (X2), . . . VCj (Xn)〉 of valuations.

In our running example, the sustainability attributes are X = {IC, FC, RE, TG}, and all the attributes have the same domain, namely {E, G, A, B, P}. According to the above definition, the overall val- uation of the heating component Gas with re- spect to the above sustainability attributes is: VGas = 〈VGas(IC), VGas(FC), VGas(RE), VGas(TG)〉 = 〈G, B, B, B〉.

93

Preferences over Sustainability Attributes

Our goal is to find the most preferred designs among those that are feasible, with respect to a set of sustainability at- tributes X. In order to identify the most preferred designs, it is necessary that the decision maker specifies his/her pref- erences over the attributes. We propose to represent prefer- ences over the values of the sustainability attributes X as follows. • Intra-attribute preferences (�i): For each attribute Xi, �i

is a binary preference relation on Domi such that if u, v ∈ Domi then u �i v if and only if u is preferred to v in terms of the sustainability attribute Xi.

• Relative importance preferences (�): Given a set of sus- tainability attributes X, � is a binary preference relation on X such that Xi � Xj if and only if Xi is relatively more important than Xj . In our example of building design, the intra-attribute pref-

erences can be represented as E �i G �i A �i B �i P , i = {IC, FC, RE, TG} and the relative importance pref- erences can be represented as FC � IC, FC � RE and TG � IC.

Solution Approach Our goal is to identify most sustainable designs from a set of candidate designs based on their sustainability attributes. Because the sustainability of a design is a function of the sustainability attributes of its components, we hereby pro- pose to measure the sustainability of a design in terms of the same attributes that describe the sustainability of its com- ponents. Before we proceed to identify the most sustainable designs in our approach, the following non-trivial questions need to be addressed.

a) Aggregation: Given a sustainability attribute Xi ∈ X and a design D = C1 ⊕ C2 ⊕ . . . Cn, each Cj having its own valuation VCj (Xi) with respect to Xi, how do we define the aggregated valuation of the D with respect to Xi? Fur- ther, given two designs D1 and D2, how do we determine whether D1 is more sustainable in comparison to D2 with respect to Xi?

b) Dominance: Given two designs, how do we compare them in terms of their sustainability attributes with respect to the stated sustainability preferences? Note that compar- ing designs is more complicated than simply comparing components, because the sustainability of a given design depends on the sustainability of the components that make up the design. In our running example, consider the designs D1 =

Electric ⊕ V inylTile ⊕ Aluminum and D2 = Gas ⊕ CeramicTile⊕Brick&Mortar (see Table 2). The follow- ing examples correspond to the above questions.

a) Aggregation: How do we compute D1(IC), D1(FC), etc.? How do we determine if D1 is more sustainable than D2 with respect to RE, i.e., is D1(RE) �RE D2(RE)?

c) Dominance: Is D1 more sustainable than D2 overall? We now proceed to describe our approach to addressing

the above questions.

Design Valuation

D1 〈G, B, B, B〉 D2 〈P, G, P, B〉 D3 〈A, G, B, A〉 D4 〈P, E, P, B〉 D5 〈P, G, G, A〉

Table 3: Valuations of the Candidate Building Designs

Aggregation

Let D = C1 ⊕ C2 ⊕ . . . Cn be a design. For each sustainability attribute Xi, we define an appropriate ag- gregation function Φi that computes the valuation of D with respect to Xi, denoted D(Xi), based on the set {C1(Xi), C2(Xi), . . . Cn(Xi)} of valuations. Therefore, we have

Φi : P(Domi) −→ F (Xi) where F (Xi) denotes the range of the aggregation function. The range F (Xi) of Φi depends on the choice of aggrega- tion function and the domain of the attribute Xi.

In our running example, all the attributes in X have the domain {E, G, A, B, P}; E is the most preferred and P is the least preferred value in terms of sustainability. We choose an aggregation function that computes the worst value (low- est or minimum) among all the components in the design. This choice is based on the rationale that the sustainability of a design is only as good as its least sustainable compo- nent. For example, even if one of the components, say C in a design D is known to release high amounts of toxic gases, i.e., C(TG) = P , then the entire design suffers, i.e., D(TG) = P , regardless of the levels of toxicity of all other components in the design. Others choices for ag- gregation functions can be also used, and some of them are mentioned later in the section. We use the following aggre- gation function which was introduced in (Santhanam, Basu, and Honavar 2008) to compute the aggregated valuations of composite Web services with respect to their non-functional attributes.

Definition 3 (Aggregation: Choosing the Minimum Val- uation). Given a set S of valuations of an attribute Xi, the aggregation function Φi is defined by

Φi(S) := {mins∈Ss} Assuming the above aggregation function for all the four

sustainability attributes, namely IC, FC, RE and TG, the valuations of the sustainability attributes of the candidate de- sign S2 given in Table 2 is computed as follows.

VS2(IC) = ΦIC({VGas(IC), VCeramicT ile(IC), VBrick&Mortar(IC)})

= ΦIC({A, A, P}) = ΦIC({A, P} = P

Definition 4 (Overall Valuation of a Design (Santhanam, Basu, and Honavar 2008)). The valuation of a design D = C1 ⊕ C2 . . . Cn with respect to the attribute Xi ∈ X is

94

defined as VD(Xi) = Φi(VC1(Xi), VC2(Xi), . . . VCn(Xi)), where Φi is the aggregation function with respect to Xi.

The overall valuation of the design D over all m attributes in X is described by the tuple VD = 〈VD(X1), VD(X2), . . . VD(Xm)〉 of valuations.

The overall sustainability of the candidate designs with respect to the four sustainability attributes for our running example are given in Table 3.

The next step is to compare two designs with re- spect to a given attribute Xi. Because of the na- ture of the aggregation of function we have chosen, the ranges F (IC), F (FC), F (RE), F (TG) of the ag- gregation function is same as their domains, namely {E, G, A, B, P}. Hence, in this case it is easy to com- pare the aggregated valuations in any two designs, using the corresponding intra-attribute preference relations. In this case, it amounts to �IC, �F C, �RE, �T G. For example, D3(TG) = A and D4(TG) = B, which means that D3 is more sustainable in terms of the attribute TG in comparison with D4.

However, in general the aggregation function Φi may have a range F (Xi) that is different from the domain Domi of the attribute, in which case the originally specified intra- attribute preference relation �i cannot be used to compare two designs with respect to Xi. In such settings, a new pref- erence relation �′i can be defined on F (Xi) in order to compare two designs with respect to the aggregated valu- ations for Xi.

Other Types of Aggregation Some examples of aggrega- tion functions are given below.

1. Summation. This is applicable in cases where an attribute is real-valued and represents some kind of additive cost. For example, the cost of a space craft is the sum of the costs of its constituent components. If S is the set of val- uations of the individual components with respect to at- tribute Xi , then

Φi(S) := {Σs∈Ss} 2. Best/Maximum. Here, the valuation of a design with re-

spect to an attribute is the best (as opposed to worst in our example), i.e., the maximum among the valuations of its components. This type of aggregation is a natural one to consider while designing systems with low risk such as job scheduling, where it does not hurt to have some com- ponents that are bad, but it is important to have at least a few that have good values for the attribute Xi.

Φi(S) := {mins∈Ss} 3. Best/Worst Frontier. In some settings, it is possible that

the intra-attribute preference over the values of an at- tribute is a partial order (not necessarily a ranking or a total order). Hence, it may not be possible to compute the valuation of a design as the best or worst among the val- uations of its components because a unique maximum or minimum may not exist. For example, it may be useful to compute the valuation of a design as the minimal set of

valuations among the valuations of its components, which we call the worst frontier. The worst frontier represents the worst possible valuations of an attribute Xi with re- spect to �i, i.e., the minimal set4 among the set of valua- tions of the components in a design.

Dominance

We have so far only considered the intra-attribute prefer- ences (�i and �′i) of the decision maker in comparing de- signs, with respect to one sustainability attribute at a time. We now proceed to show how designs can be compared by factoring in all the attributes and the preferences of the decision maker, leveraging existing work in the area of qualitative decision theory (Doyle and Thomason 1999; Brafman and Domshlak 2009).

The previous section showed how to evaluate a design with respect to a single attribute as a function of its com- ponents using an aggregation function, and compare two de- signs based on their aggregation function with respect to that attribute. However, to find sustainable designs with respect to both the intra-attribute and the relative importance prefer- ences, we need to compare designs with respect to their ag- gregated valuations over all attributes. We call this compar- ison as dominance testing, and we present a specific domi- nance relation introduced in (Santhanam, Basu, and Honavar 2010b) for performing such a comparison.

Definition 5 (Witness based Dominance (Santhanam, Basu, and Honavar 2010b)). Dominance �d is a binary relation defined as follows. Let U, V be two designs, and X the set of sustainability attributes describing the valuations of their components.

U �d V ⇔ ∃Xi : U(Xi) �′iV (Xi) ∧ ∀Xk : (Xk � Xi ∨ Xk ∼� Xi) ⇒ (U(Xk) �′kV (Xk) ∨ U(Xk) = V (Xk))

In the above, we call the attribute Xi as the witness of the relation. The dominance relation �d is derived from and re- spects both the intra-attribute preferences (�i) as well as the relative importance preferences (�) of the decision maker. The definition states that a design U dominates V if and only if we can find a witness attribute Xi such that with respect to the intra-attribute preference �i, the aggregated valuation of U dominates V when compared using �′i, and for all attributes Xk which the decision maker considers more im- portant than (�) or indifferent to (∼�) the witness Xi, the valuation of Xk in U is at least as preferred as ( �′i or equals) the valuation of Xk in V .

When the above dominance relation is applied to our run- ning example, we have FC �IC, FC �RE and TG�IC, resulting in the following comparisons.

• D5 �d D1 with FC as witness • D5 �d D2 with RE as witness • D5 �d D3 with RE as witness • D4 �d D1 with FC as witness

4Note that if �i is a total order, then worst frontier represents the minimum or lowest element in the set with respect to the total order.

95

• D4 �d D2 with FC as witness • D3 �d D2 with IC as witness

Other dominance relations such as pareto dominance (de- noted �p) can be used to compare designs based on their ag- gregated valuations for the sustainability attributes. In pareto dominance, a design is preferred to another if it is preferred to ( �′i) or equals the other with respect to every attribute, and in addition it is preferred ( �′i) to the other with respect to at least one attribute. However, pareto dominance consid- ers all attributes equally important, i.e., it ignores the relative importance over the sustainability attributes specified by the decision maker. The following comparisons result from ap- plying pareto dominance to our running example.

• D5 �p D2 • D4 �p D2 • D3 �p D2 As expected, pareto dominance is unable to ascertain that D5 and D4 are more sustainable than D1, and that D5 is more sustainable than D3 due to ignoring the relative importance preferences.

Identifying Sustainable Designs

We can observe that because of considering multiple at- tributes at a time, and due to the influence of the decision maker’s preferences, the dominance relation may not pro- vide us a ranking over the set of candidate designs. In other words, there may be pairs of designs that are incompara- ble with respect to the decision maker’s preferences, or the dominance relation is a partial order (as opposed to a total order). In such a case, the set of most sustainable designs can be computed as the set of candidate designs that are not dominated by any other other candidate designs. Definition 6 (Non-dominated Set). The non-dominated set of designs with respect to a set S of designs and a (partially ordered) dominance relation �, denoted Ψ�(S), is a subset of S such that none of the elements in S are preferred to any element in Ψ�(S).

Ψ�(S) = {Si ∈ S|�Sj ∈ S : Sj � Si} Note that as per this definition, Ψ�(S) is the maximal

set of elements in S with respect to the relation �. It is also easy to observe that this set is non-empty as long as S is non-empty, i.e., at least one most sustainable de- sign can be identified if it exists. In our running exam- ple, we find that Ψ �d ({D1, . . . , D5} = {D4, D5} and Ψ�p({D1, . . . , D5} = {D1, D3, D4, D5}

Conclusion

In summary, we show how to use reasoning about qualita- tive preferences to solve the problem of identifying sustain- able designs, given a set of preferences of the decision maker over a set of sustainability attributes of the components that make up a design. We use existing methods in qualitative de- cision theory to compare design alternatives and choose the most sustainable ones with respect to the decision maker’s stated preferences and tradeoffs. Our solution constitutes (a)

evaluating each design in terms of each sustainability at- tribute by aggregating the values taken by the components that make up the design (using an aggregation function that can be attribute specific); and (b) comparing two designs and determining the more sustainable design using a dominance testing strategy that respects the decision makers’ prefer- ences and tradeoffs.

In this paper we have shown the use of our approach to identify the most sustainable designs for a building with respect to functional requirements and sustainability pref- erences of the decision maker. We have illustrated the use of qualitative intra-attribute and relative importance prefer- ences using a specific aggregation function and dominance relation. However, other choices of aggregation functions and dominance relations can also be used in our model such as those mentioned in (Brafman, Domshlak, and Shi- mony 2006; Wilson 2004). In addition, qualitative prefer- ences can be combined with or replaced by quantitative preferences, which have been well studied in the context of multi-attribute utility theory (Fishburn 1970; Keeney and Raiffa 1993).

Acknowledgments

The work of Ganesh Ram Santhanam and Samik Basu was supported in part by the grant CCF0702758 from the Na- tional Science Foundation. The work of Vasant Honavar was supported by the National Science Foundation, while work- ing at the Foundation. Any opinions, findings, and conclu- sions contained in this article are those of the authors and do not necessarily reflect the views of the National Science Foundation.

References

Boutilier, C.; Bacchus, F.; and Brafman, R. I. 2001. UCP- networks: A directed graphical representation of conditional utilities. In Proceedings of the 17th Conference in Uncer- tainty in Artificial Intelligence (UAI-2001), 56–64. Boutilier, C.; Brafman, R. I.; Domshlak, C.; Hoos, H. H.; and Poole, D. 2004. Cp-nets: A tool for representing and reasoning with conditional ceteris paribus preference state- ments. J. Artif. Intell. Res. (JAIR) 21:135–191. Brafman, R., and Domshlak, C. 2009. Preference handling - an introductory tutorial. AI magazine 30(1). Brafman, R. I.; Domshlak, C.; and Shimony, S. E. 2006. On graphical modeling of preference and importance. J. Artif. Intell. Res. (JAIR) 25:389424. Doyle, J., and Thomason, R. H. 1999. Background to qual- itative decision theory. AI magazine 20:55–68. Fishburn, P. 1970. Utility Theory for Decision Making. John Wiley and Sons. Keeney, R. L., and Raiffa, H. 1993. Decisions with multiple objectives: Preferences and value trade-offs. Lippiatt, B. C. 2007. Bees 4.0: Building for environmen- tal and economic sustainability. technical manual and user guide. Technical Report NIST Interagency/Internal Report (NISTIR) - 7423, National Institute of Standards and Tech- nology (NIST).

96

Lutz, R.; Weiss, D.; Krishnan, S.; and Yang, J. 2010. Soft- ware product line engineering for long-lived, sustainable systems. In Proceedings of the 14th international confer- ence on Software product lines: going beyond, SPLC’10, 430–434. Berlin, Heidelberg: Springer-Verlag. Santhanam, G. R.; Basu, S.; and Honavar, V. 2008. Tcp- compose� - a tcp-net based algorithm for efficient com- position of web services using qualitative preferences. In Bouguettaya, A.; Krger, I.; and Margaria, T., eds., Proc- ceedings of the Sixth International Conference on Service- Oriented Computing, volume 5364 of Lecture Notes in Com- puter Science, 453–467. Santhanam, G. R.; Basu, S.; and Honavar, V. 2010a. Dom- inance testing via model checking. In Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence (AAAI), 357–362. AAAI Press. Santhanam, G. R.; Basu, S.; and Honavar, V. 2010b. Effi- cient dominance testing for unconditional preferences. In Proceedings of the Twelfth International Conference on the Principles of Knowledge Representation and Reasoning (KR), 590–592. AAAI Press. Wilson, N. 2004. Consistency and constrained optimisation for conditional preferences. In ECAI, 888–894.

97

The author has requested enhancement of the downloaded file. All in-text references underlined in blue are linked to publications on ResearchGate.The author has requested enhancement of the downloaded file. All in-text references underlined in blue are linked to publications on ResearchGate.