Negotiation in engineering design

Group Decision and Negotiation, 3:69-91 (1994) �9 1994 Kluwer Academic Publishers

Negotiation in Engineering Design ANDREW KUSIAK Intelligent Systems Laboratory, Department of lndustrial Engineering, The University of Iowa, Iowa City, IA 52242-1527

JUITE WANG Intelligent Systems Laboratory, Department of Industrial Engineering, The University of lowa, Iowa City, IA 52242-1527

Abstract

Concurrent design may shorten the duration of a design project, reduce cost, and improve quality of the final design. However, due to the diversified problem-solving knowledge and different goal setting between design agents, it may increase the number of conflicts and make the project more difficult to manage. In this article, a goal-directed negotiation model for resolving conflicts in a cooperative design environment is presented. The proposed model generates negotiation sets, analyzes utilities derived for each design agent, and evaluates them based on three decision rules: maximization of the joint utility, minimization of individual utility differences, and minimization of individual utility differences and maximization of joint utility. A compromise solution is reached iteratively. The approach proposed in this article is concerned not just with satisfying design constraints, but attempts to maximize system objectives. An example of the poppet relief valve is used to demonstrate the negotiation concept.

Key words: engineering design, constraint analysis, negotiation, decision making, utility function

1. Introduct ion

Concurrent design attempts to incorporate various constraints related to the product life cycle, i.e., manufacturability, quality, reliability, and so on, in the early design stages. It aims at improvement of the product quality and reduction of the development time and cost. However, due to the diversified design knowledge, concurrent design implies involvement of specialists representing different disciplines (called in this article design agents) for designing a product. An individual agent tends to be narrowly focused and to have only limited knowledge about other disciplines. Furthermore, agents view problem-solving goals from a local perspective. The diversified knowledge and different goal setting among individual agents represent a common source of conflicts in the design process. For example, consider a part that satisfies functional requirements and is also easy to manufacture. A design engineer is an expert in functionality, and a manufacturing engineer is an expert in manufacturing processes and systems. However, due to the lack of knowledge in each other 's discipline, they have to collaborate in order

70 KUSIAK/WANG

to produce an acceptable design. For complex designs, no individual discipline leads too far without cooperation with other disciplines. To maintain consistency and produce an acceptable design, conflicting goals between design agents need to be negotiated. The establishment of goals and negotiation leading to an acceptable design is the focus of this article.

Negotiation involves finding a compromise solution for multiple conflicting goals. It is an ill-structured, complex, dynamic, and iterative process. The research in decision science has led to the development of quantitative models of the negotiation process (DeSanctis and Gallupe 1987; Chatterjee et al. 1991). De- pending upon the assumptions considered, it is possible to apply multi-objective decision techniques, such as game theory (Kannapan and Marshek 1993) and decision analysis (Sycara 1988). Artificial intelligence approaches use mostly logic- based deduction modeling (Rosenschein and Breese 1989; Bond 1989; ChaibDraa and Millot 1990), case-based reasoning (Sycara 1991), genetic algorithms (Matwin et al. 1991), or constraint-directed search (Sathi and Fox 1989) to resolve conflicts.

Most of the literature in engineering design is concerned with investigating ar- chitectures for communication (Lander et al. 1989; Krishnan et al. 1990) or developing negotiation protocols (Bond 1989; Klein 1991; Sycara 1991; Werkman 1991). Bond (1989) describes collaborative design as a dialogue game. He used formal logic as an interaction language for conflict resolution between agents. Bond and Ricci (1992) explain the control of the negotiation process by an orga- nizationally agreed sequence of commitment steps. Lander et al. (I989) present a framework based on the blackboard architecture that supports collaborative design among sets of knowledge-based systems. Several strategies are presented for resolution of conflicts among knowledge-based systems. Sycara (1991) discusses a negotiation model that integrates case-based reasoning with a decision-theoretic method (multi-attribute utility theory). The belief structure of the various agents and a communication protocol are introduced to support the negotiation process. Klein (1991) introduces a model that is a dialogue game approach to study the human designer's conflict resolution. A knowledge-based framework is used for selecting and executing conflict resolution strategies during the design process. Werkman (1991) introduces a knowledge-based framework for negotiation in con- struction applications. An arbitrator is used to control the negotiation process and to evaluate the solution produced. Kannapan and Marshek (1993) apply the game theory to the negotiation process for multiagent parametric design. Utility theory is used to rate the satisfaction level of design agents. They assume that conflict parameters are mutually independent and do not consider the conflict-dependent case, i.e., when more than one conflict parameters are affected by the selected decision parameters.

In this article, a goal-directed negotiation model based on decision analysis is proposed for resolving multiple conflicts among design agents. The proposed model generates all potential solutions, analyzes them, and chooses the best satisfying solution. The evaluation is based on three decision rules: maximum joint utility, minimum individual utility differences, and minimum individual utility difference and maximum joint utility.

NEGOTIATION IN ENGINEERING DESIGN 7I

The article is organized as follows. Section 2 presents a design negotiation problem. A goal-directed negotiation model is proposed in section 3. The basic con- cepts of multi-attribute utility theory used to express the agents' preferences and three decision rules are presented. In Section 4, a design example is discussed. Section 5 concludes the article.

2. Problem statement

2.1. Design negotiation problem

Design in an engineering design environment evolves through, largely interdepen- dent, contributions of numerous multi-discipline design agents who are often required to collaborate in order to satisfy constraints. Thus, a successful design can be viewed as a compromise that incorporates trade-offs, such as cost, manufacturability, reliability, maintainability, and so on. The overall goal is to produce an acceptable design that is synthesized from contributions of different perspec- tives.

Before the design negotiation problem is defined, a basic terminology is introduced. The structure or behavior of a design can be characterized by a set of design variables. A constraint is described as a relation among several variables that can be expressed in terms of equations, tables, charts, curves, and so on. The design variables are classified into three types:

�9 Decision variable: Each design agent is allowed to make independent decisions on these variables.

�9 Intermediate variable: This variable is determined by processing decision variables and specification variables.

�9 Performance variable: The design variable that measures the performance of a system or subsystem is called a performance variable.

Design variables are classified according to the ownership relation in engineering design. The design variables that are determined or used by more than one design agent are called interaction variables. Variables that are determined by an individual agent are called private variables. If values assigned to an interaction variable by more than one agent are distinct, then we say the interaction variable is in conflict. Determining values of interaction variables is crucial, because of potential Conflicts. An outline of the design negotiation procedure is shown in Figure 1.

The design negotiation problem is defined as follows:

Definition: Design Negotiation Problem

Consider a design problem that decomposes into a set of agents A. Each agent a A, includes:

72 KUSIAK/WANG

Redefine constraints and goals for each

agent

Y No

Figure 1. The design negotiation procedure

~ Generate a design solution for each

agent

negotiation procedure

( Oon )*---

�9 a set of variables V" = (Vg, V~t, Vk), where each variable v ~ V a ranges over its own domain D a, and

V~: a set of decision variables for the design agent a V~: a set of intermediate variables for the design agent a V~: a set of performance variables for the design agent a

�9 a set of constraints C ".

The design negotiation problem is to determine a value of each interaction variable so that for each agent all of the constraints are satisfied.

Determining the value of interaction variables is critical in design, because different goals associated with agents might lead to conflicts. The purpose of this article is to focus on developing an approach to maintaining consistency of interaction variables belonging to different agents in order to obtain an acceptable design.

Depending on the kind of information dependency among design agents, two types of collaboration are defined:

Type 1: Consistency collaboration (Figure 2(a)) A solution obtained by one agent is not heavily dependent on other agents, i.e., each agent is able to determine the design variables involved in the interaction

NEGOTIATION IN ENGINEERING DESIGN 73

constraints. Agents have to collaborate in order to increase the level of confi- dence in their individual solutions and maintain the consistency of the overall solution. Type 2: Serial collaboration (Figure 2(b)) The solution obtained by one agent is heavily dependent on the other agents, i.e., an agent is unable to determine some design variables and has to rely on other agents.

2.2. The design negotiation scenario

In this section, the concept of design negotiation is illustrated with the example of a poppet-relief valve (Lyons 1982; Kannapan and Marshek 1993). Figure 3 shows the schematic of the poppet-relief valve, which includes a poppet valve, poppet valve stem, and helical compression spring enclosed in a pipe (Kannapan and Marshek 1993).

The poppet-relief valve allows flow of the fluid from the inlet to the outlet when the pressure of the fluid exceeds a certain threshold pressure called the "crack-

(a) (b)

DA1 DA2 DA1 DA2

Figure 2. Two types of collaboration based on information dependency (a) Consistent collaboration (b) Serial collaboration

Pipe

Inlet v Outlet

Figure 3. Schematic of a poppet-relief valve

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ing" pressure. If a pressure is greater than the cracking pressure, the fluid opens the poppet valve and holds it in equilibrium against a helical compression spring. At a pressure below the cracking pressure, the poppet valve is held against a seal due to the helical spring, and thereby cuts off fluid flow from the inlet to outlet.

Assume that design of the poppet relief valve is performed by the three design agents (DAs) shown in Figure 4, namely, valve DA, spring DA, and enclosure DA. The negotiation environment is based on the blackboard architecture (Morse and Hendrickson 1990). The valve DA is responsible for determining the configuration of valve for optimal value of the flow based on the valve requirements. After completing the configuration design, valve DA passes some parameters to the spring DA and the enclosure DA. The spring DA designs a spring, i.e., determines the cracking pressure, the distance the poppet will move, and the stability of the seal in the closed position. The size and the thickness of the stem and enclosure are determined by the enclosure DA. Note that the valve DA dominates the entire design process, because he/she makes design decisions and then trans- fers the required information to the agents in downstream design process (Figure 5). The collaboration between valve DA, enclosure DA, and spring DA is serial, because the spring DA and the enclosure DA are heavily dependent on the valve DA. Nevertheless, the relationship between spring DA and enclosure DA is consistent. A design coordinator is responsible for detection of conflicts and suggests a compromise solution and sends it back to the agents. In Figure 5, the values of variables Do and D; have to be consistent for the spring DA and enclosure DA. The design variables are defined in Appendix A and B.

Figure 4. Three design agents and their relationship in design of a poppet-relief valve


Valve DA

Di Do Spr ing ~ ~., ( ~ , , ~ , ~ ,

D A J ~ ~ ~ . . D A

Figure 5. Information flow among agents

3. Analytical model of design negotiation

To model the negotiation process in engineering design, two issues must be ad- dressed:

1. Representat ion of the preference structure of each agent. 2. The rational behavior of each agent; i.e., a possible behavior of each agent

under a conflict situation has to be determined.

3.1. Multi-attribute utility theory

Modeling of human preferences with utility functions is a major concern of decision analysis. The concept of utility is the basis for selection among several alternatives, as well as for evaluating past actions. Each alternative is evaluated in terms of the number of attributes that a decision maker considers important in order to select the one with the maximum overall utility. Multi-attribute utility theory (MAUT) (Keeney and Raiffa 1976) is widely used for modeling human preferences.

In order to evaluate decisions, an objective function that aggregates all the individual objectives and an attitude towards a risk is needed. The risk attitude is not considered in this article. Such an objective function is referred to as utility function and is denoted by Ix. Then Ix(x), the utility of the at tr ibute x, indicates the desirability of x relative to all other attributes. The decision with a higher expected value of the utility function is preferred to the one with a lower expected value of the utility function:

Ix(x) -> Ix(y), if and only if x > y,

where the symbol > reads "preferred or indifferent to ."

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The utility function mentioned above is a single-attribute utility function. In general, there is more than one objective involved in the design negotiation process. The need to utilize the multi-attribute utility function Ix(x, x2 . . . . . xn) (Kee- ney and Raiffa 1976) is apparent. To determine the multi-attribute utility function, the value independence concept, which is identical to probabilistic independence, is employed. The independence concept is used to derive a simple func t i on f such a s :

~(x~, x2 . . . . . x . ) = A ~ l ( x l ) , ~2(x2) . . . . . ~ . (x . ) , kl, k: . . . . . 1~ (1)

where the P~i, i = 1 . . . . . n is a single-attribute utility function, and the km, m = 1 . . . . . n is a scaling constant.

The scaling constant of an attribute is related to the relative desirability of different values of the attribute. The additive utility function that will be used later is as follows:

n //

~x(xl, x2 . . . . . xn) = ~k i~x i ( x l ) , where ~ k i = 1. i = 1 i = l

(2)

3 . 2 . D e c i s i o n r u l e s in d e s i g n n e g o t i a t i o n

In engineering design, design agents suggest, critique, and implement changes in the product design and contribute their knowledge for problem solving. However, an alternative that is the most preferable to one agent may be the least preferable to another one, since their goals may conflict. Hence, the selection of a solution that is potentially acceptable to all design agents becomes important.

To reach a satisfying solution, the rational behavior of an agent has to be determined under the conflict situation. A design agent should make a rational choice among alternatives according to his/her preference structure (Doyle 1992). Espe- cially in an engineering design environment, each agent may sacrifice his/her individual interest in order to optimize the global objective. The latter is the major difference between the process of negotiation in the engineering design environment and that in other areas, such as labor-management negotiation (Sycara 1991) or house-purchasing negotiation (Kersten et al. 1991), which belong to noncoop- erative negotiation.

Three decision rules are considered for the selection of the best compromise solution from the negotiation set, i.e. set of possible solutions.

Notation:

rn = number of agents n = number of alternatives ~x~j(x~, x2 . . . . . xk) = utility function of agent i for alternative j based on

attributes xl, x2 . . . . . xk; for i = 1 . . . . . m ; j = 1 . . . . . n


tXmi = mean utility of alternative j , which is defined as

IXm i = -- IX0.(Xl, X z, . . . , Xk); for j = 1 . . . . . n m i = l

Uj. = joint utility for alternative j ; f o r j = 1 , . . . , n Ud. = deviation of utility for alternative j ; f o r j = 1 . . . . . n U,~ . . = compromise utility for alternative j ; for j = 1, . , n.

(1) The Maximum Joint Utility Rule A group evaluation of an alternative has an additive form which consists of all group members. Due to its simplicity, the maximum joint utility rule is one of the most frequently used techniques for aggregation of preferences. The rule maximizes:

Uj = ~ txi j (xl , x 2 . . . . , x k ) . (3) i = 1

(2) The Minimum Deviation Rule The minimum deviation rule minimizes individual utility differences. The purpose of this rule is to estimate the "mean utility" of alternative j, ~x m ( j = 1 . . . . , n). The difference between agent utility and the mean utlhty J is calculated as follows:

= I 0(x,, x2 . . . . . x k ) - ( 4 ) i = 1

(3) The alternative that minimizes the expression Udj is selected. The Compromise Utility Rule The rule minimizes the deviation and maximizes the joint utility, i.e., maximizes Uc; where:

4 - ud . (5)

The expression (5) which conbines the previous two decision rules selects an alternative that maximizes the joint utility and minimizes individual utility derivations. Once the difference Ucj for each alternative is calculated, the alternative that maximizes Ucj is selected.

The selection of decision rules depends on the design criteria.

3 . 3 . G o a l - d i r e c t e d n e g o t i a t i o n m o d e l

Negotiation can be represented as a process of achieving certain goals (Kersten 1991). The most general goal, i.e., the overall goal is further decomposed into several subgoals. The relationship between the overall goal and its subgoals can

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Overall goal

Optimum flow

Minimum flow area

Minimum weight Maximum spring of helical spring stability

Minimum volume of valve enclosure

Valve Spring Enclosure DA DA DA

Figur~, 6, The goal tree for poppet-relief design

be viewed as a hierarchy. High-level goals are expressed in terms of more detailed subgoals. For example, the overall goal of valve design is to design a relief valve with optimal flow. This overall goal can be decomposed into three subgoals, namely, to minimize the flow area (dL), to minimize valve size (lie), and to minimize the volume of spring (Dr) and maximize spring stability (r,). These subgoals are assigned to three agents: valve DA, enclosure DA, and spring DA, respec- tively (see Figure 6). Since each subgoal is a component of the overall goal, the effort of each agent indirectly contributes to the overall goal.

The negotiation model begins by determining the best solution for each design agent according to the design specifications. A coordinator detects conflicts and determines design agents who should be involved in the negotiation process. Each agent has to construct his/her utility function. In contrast to the literature (Kan- napan and Marshek 1993), the performance variables that characterize the goal of an agent are used as attributes of the utility function of that agent. The negotiation set (a, b) of a conflict variable, i.e., a set of possible compromise values should lie in the range of the best solutions generated by an agent. Next, the linear search approach (Luenberger 1984) is applied to determine a compromise solution within the range (a, b). The compromise values of conflict variables are propa- gated back to the decision variables. Two heuristic rules are used for selecting decision variables for propagation. The utility values for all potential solutions are calculated and evaluated based on the three decision rules discussed in section 3.2. If a solution is acceptable to the agents involved in the negotiation process, then stop. Otherwise, agents have to modify their goals, utility functions, or specifications, and then renegotiate. The negotiation process terminates when a compromise solution is reached or no agent intends to modify his/her goal and utility function.

The design negotiation procedure is presented next.

N E G O T I A T I O N I N E N G I N E E R I N G D E S I G N 79

Design Negotiation Procedure Step 1: Detect interaction variables in conflict and determine the agents in-

volved in conflict. Step 2: For each design agent, set a satisfying goal. Step 3: For each design agent, identify scaling constants of design variables

involved in the negotiation process. Step 4: For each design agent, construct a multi-attribute utility function ac-

cording to equation (2). Step 5: Identify the negotiation set for each conflict variable. The negotiation

set is defined as follows: Si = [a~, bl] , where:

m = the number of conflict variables n = the number of design agents S~ = the negotiation set for conflict variable G, for i

= 1 , . . . , m n

ai = Min{G}, for i = 1 . . . . , m j = l

n

b i = Max{c/}, for i = 1 . . . . . m. j = l

Step 6: Generate all potential solutions for the set of conflict variables and propagate the changes back to the decision variables. The potential solutions are produced by dividing the range of each conflict variable into intervals and generating all possible combinations of the endpoint values derived from the division. The size of an interval is:

d = [b~ - all, where n is the number of intervals within Si. /7

Si = [a~, ai + d] U [ai + d, ai + 2d] U . . . U [a~ + (n - 2)d,

ai + (n - l)d] U [ai + (n - 1)d, bi]. The potential solutions that do not satisfy design constraints are ig- nored. Two heuristic rules are used to determine decision variables for propagation: (1) Select dependent decision variables that do not affect other conflict

variables. (2) Select a dependent decision variable with the minimum number of

paths for propagation. Step 7: Calculate the utility value for each possible solution according to the

utility function built in Step 4. Evaluate all possible solutions based on the three decision rules and select the best alternative. Denote the compromise solution suggested by y.

Step 8: Check the satisfying goal for each design agent involved in the negotiation process. (1) If individual utility of each design agent is greater than his/her sat-

isfying goal, then stop.

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(2) I f t h e s a t i s f y i n g g o a l s o f s o m e d e s i g n a g e n t s a re no t m e t a n d the

a g e n t s a r e wi l l ing to a d j u s t t he i r g o a l s to r e a c h a c o n s e n s u s , t h e n

m o d i f y t h o s e g o a l s a n d s top .

(3) I f t h e u t i l i ty o f t h e a g e n t i is l e ss t h a n h i s / h e r goa l , t h e n r e d u c e t h e

n e g o t i a t i o n se t Si to SI w h e r e SI = [a~, y] a n d go to S t e p 6.

(4) O t h e r w i s e , u s e o n e o f t h e t w o r e n e g o t i a t i o n s t r a t eg i e s :

�9 G o to S t e p 3 a n d m o d i f y the u t i l i ty f u n c t i o n f o r e a c h a g e n t .

�9 M o d i f y s o m e o f t h e d e s i g n s p e c i f i c a t i o n s a n d go to S t e p 2.

4. Application of the design negotiation model: design of a poppet-relief valve

In t he d e s i g n n e g o t i a t i o n m o d e l , an in i t ia l d e s i g n is r e q u i r e d as inpu t . T h e ini t ia l

d e s i g n s p e c i f i c a t i o n s a r e as f o l l o w s :

Ap = 2 psi Q = 150 GPM water P = 100 psi S = 1.0 Pc = 1.0-1.5 psi (mean 1.25 psi), L~ = 1.5

Decision variables for valve DA: C, = 1.45 C s = 0.6 d L = 1.65

Decision variables for spring DA: D = 1.8 r~l = 0.1 d = 0.14

S~,,~ = Monel-400 (G = 9500000), , r s = V . I

Decision variables for enclosure DA: At = 0.01 A2 = 0.01 D v = 2.0

rc2 = 0.1

Pm~,l = AP15L (Sp = 18000)

The following values of all design variables are computed: Design variables for valve DA:

F, = 2.673 Fd = 13.686 Design variables for spring DA:

k,,,j = 29.860 D~ = 1.550 N = 2.620 L I = 1.590

Design variables for enclosure DA: D~ = 1.679 Do = 1.969

k s = 33.180 ~ = 0 . 4 1 3 , . . . ,e tc .

Do = 2.050 L~ = 0.647 . . . . . etc.

t~ = 0.016 tp = 0.016 . . . . . etc.

T h e s t eps o f t h e n e g o t i a t i o n a r e p r e s e n t e d nex t .

Step 1. D e t e r m i n e t h e c o n f l i c t v a r i a b l e s a n d t h e d e s i g n a g e n t s in c o n f l i c t ( see

F i g u r e 7).

T w o c o n f l i c t v a r i a b l e s Do a n d Di, w h i c h b e l o n g to e n c l o s u r e D A a n d s p r i n g D A ,

a re d e t e r m i n e d . T h e e n c l o s u r e D A s u g g e s t s t h e v a l u e 1.969 fo r t h e o u t e r d i a m e t e r

o f t h e s p r i n g e n c l o s u r e (Do); h o w e v e r , t h e v a l u e o f 2.050 is m o r e f a v o r a b l e to t h e s p r i n g D A . F o r t he i n n e r d i a m e t e r o f s p r i n g e n c l o s u r e (Di), t he l a r g e r d i a m e t e r is

p r e f e r a b l e to t h e e n c l o s u r e D A (1.679 > 1.550).


~des ign agent ~ - ~ . ~ ~ ~ d e s i g n agent ~}

Figure 7. Conflict variables D,, and D~

Step 2. Set a satisfying goal for spring DA and enclosure DA.

In this case, it is assumed that the satisfying goals for both agents are 80% of the maximum utility.

Step 3. Identify the scaling constants of the performance variables for the spring DA and enclosure DA.

The performance variables for the spring DA are the volume of the spring material (Vn) and the stability ratio (rs). The performance variable for the enclosure DA is the valve outer diameter (Dr). In addition to the performance variables, some design variables, such as clearance ratios (r,,~ and re2) and corrosion resistance allowances (A1 and Az), which are also important to the individual agents, have to be considered. The scaling constants of the performance variables are determined by a designer according to design criteria. Assume that for both agents the scaling constants of the performance variables are:

Spring DA: kvH = 0.2, krs = 0.4, krc I = 0.2, krc2 = 0.2

Enclosure DA: kov = 0.6, ka~ = 0.2, kz2 = 0.2.

Step 4. Construct a multi-attribute utility function for the spring DA and the enclosure DA.

The additive form of the utility function is used for each design agent. The multi-attribute utility functions for the enclosure DA and the spring DA are as follows:

tx s = 0.2 iXv~ + 0.4 Ix,~ + 0.2 ~rcl + 0.2 ~Lrc 2 Ix e = 0.6 tXOv + 0.2 ~LAI + 0.2 ~LA2 where:

tXs: utility of spring DA iXvH: utility of the volume of spring for spring DA Ix~: utility of the stability ratio of spring for spring DA Ixrc1, Ix, c2: utility of the outer and inner diametric clearance ratios for spring

DA txe: utility of enclosure DA

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P~Dv: utility of the valve outer diameter for enclosure DA tXAI, ~a2: utility of outer and inner corrosion resistance allowances for en-

closure DA. The utility functions of performance variables and decision variables for the two agents are shown in Appendix C. The maximum utility value of each variable is 1.0, which is the best solution determined by an individual agent.

Step 5. Identify the negotiation set for each conflict variable.

The negotiation sets for both conflict variables are:

SDo = [1.969, 2.050], See = [1.550, 1.679].

Step 6. Generate all potential solutions for conflict variables Do, Di and propagate back the results to the dependent decision variables.

Subdividing the range [1.969, 2.050] of Do and the range [1.550, 1.679] of Di into four intervals and generating the combination of endpoints result in 25 possible solutions (see Table 1). Applying rules (1) and (2), decision variables rc~ and rc2 are selected for adjustment of their values for the spring DA, and decision variables AI and A2 are selected for the enclosure DA. However , the only feasible solution is D; = 1.679 and Do = 1.969, when re1 = 0.055, rc2 =- 0.028, A~ = 0.01, and A 2 = 0.01 (see Table 1).

Step 7. Calculate the utility value of the feasible solution.

For Vn -- 0.228, rs = 0.1, rcl = 0.055, and re2 = 0.028, according to the utility functions listed in Appendix C, the individual utility of spring DA is:

~Xs = 0.2 iXv, + 0.4 ~Lrs "~- 0.2 IXr~ , + 0.2 ~Xrc 2

= 0.2(1.0) + 0.4(1.0) + 0.2(0.28) + 0.2(0)

= 0.656.

Similarly, for D~ = 2.0, Al = 0.01, and A2 = 0.01, the individual utility of enclosure DA is:

~L E = 0.6 ~JLD~, -[- 0 . 2 ~lbAi + 0.2 ~LAz

= 0.6(1.0) + 0.2(1.0) + 0.2(1.0)

= 1.0.


Table 1. Possible settings of conflict variables Do and Di

Do

Design D i variable 1.550 1.582 1.615 1.647 1.679

rcl 0.055 0.055 0.055 0.055 0.055

1.969 rc2 0.100 0.082 0.064 0.046 0.028

A1 0.010 0.010 0.010 0.010 0.010

A2 N/A N/A N/A N/A 0.010

rcl 0.066 0.066 0.066 0.066 0.066

1.989 rc2 0.100 0.082 0.064 0.046 0.028

A 1 N/A N/A N/A N/A N/A

A2 N/A N/A N/A N/A 0.010

rcl 0.078 0.078 0:078 0.078 0.078

2.009 rc2 0.100 0.082 0.064 0.046 0.028


A2 N/A N/A N/A N/A 0.010

rcl 0.089 0.089 0.089 0.089 0.089

2.023 rc2 0.100 0.082 0.064 0.046 0.028


A2 N/A N/A N/A N/A 0.010

rcl 0.100 0.100 0.100 0.100 0.100

2.050 rc2 0.100 0.082 0.064 0.046 0.028


A 2 N/A N/A N/A N/A 0.010

The utility value of a design variable is derived from its utility function, listed in Appendix C.

(1) The Maximum Joint Utility Rule Using equation (3), the max imum joint utility is:

Umax = tXs + txe = 1.656.

(2) The Minimum Deviation Rule Using equation (4), the minimum utility difference is:

= 10.656 - 0.828[ + [1.0 - 0.828 I = 0.344.

84 KUSIAK/WANG

(3) The Compromise Utility Rule Using equation (5), the compromise utility is:

Ucmax = Umax- Udmi,, = 1.312.

Step 8. Check the compromise solution suggested by the spring DA and the enclosure DA.

The compromise solution is not acceptable to the spring DA, because:

ix s = 0.656 < 0.8 (satisfying goal).

Assume that both agents want to modify their design specifications. The enclosure DA wants to change variable D~ from 2.0 to 2.1, and the spring DA changes variable D from 1.8 to 1.84 and variable re2 from 0.1 to 0.05. Suppose that the satisfying goals and utility functions of both agents are not modified. Go to Step 5.

Step 5. Identify the negotiation set for each conflict variable.

Due to the modification of design specifications, the negotiation sets also change:

Soo = [2.068, 2.094], SD~ = [1.586, 1.679].

Step 6. Generate all potential solutions for conflict variables D o, Di, and propagate back the results to the dependent design variables.

Subdividing the range [1.969, 2.094] of Do and the range [1.586, 1.679] of D~ into four intervals and generating the combination of endpoints result in 25 possible solutions (see Table 2). Similarly, decision variables re1, re2, A1 and A 2 are selected for adjustment. Three feasible solutions are determined: Do = 2.068, D~, = 1.679, Do = 2.075, Di = 1.679, and Do = 2.081, D i = 1.679.

Step 7. Calculate the utility value of the feasible solutions shown in Table 3.

Applying the compromise utility rule, the setting Do = 2.068, Di = 1.679 is chosen.


Table 2. Possible settings of conflict variables Do and Di

Do

Possible Di setting 1.586 1 .609 1 .633 1 .656 1.679

rcl 0.086 0.086 0.086 0,086 0.086

2.068 rc2 0.100 0,087 0.075 0.062 0.050

A1 01010 0.010 0.010 0.010 0.010

A2 N/A N/A N/A N/A 0.010

rcl 0.090 0,090 0.090 0.090 0.090 2,075 rc2 0,i00 0.087 0.075 0.062 0.05

A1 0.007 0.007 0.007 0.007 0.007

A2 N/A N/A N/A N/A 0.01 II

rcl 0.093 0.093 0 ,093 0.093 0.093

2.081 rc2 0.100 0,087 0.075 0,062 0.050 A 1 0,004 0.004 0,004 0,004 0,004

A2 N/A N/A N/A N/A 0.010

rcl 0.097 0.097 0,097 0,097 0.097

2,088 rc2 0,100 0,087 0,075 0,062 0,050


A2 N/A N/A N/A N/A 0.01

rcl 0.100 0.100 0.100 0.100 0.100

2.094 rc2 0,100 0.087 0.075 0.062 0.050

a l N/A N/A N/A N/A N/A

A2 N/A N/A N/A N/A 0.010

Table 3. The individual utilities and group utilities of the three feasible solutions

Feasible setting

D O = 2.068 D i --- 1,679 D O = 2,075 D i = 1,679

I .Do = 2.081 D i = 1,679

Individual utility Group utility

~lS ~E Umax Udmin Ucmax 0.796 0,800 1.596 0,005 1.591 0.806 0.672 1.478 0.134 1,344 0.818 0,600 1.418 0.218 1,200

86 KUSIAK/WANG

Step 8. Check the satisfying goal for both agents.

The spring DA is not satisfied, because the individual utility of the compromise solution suggested is 0.796, which is less than the satisfying goal, i.e., 0.8. How- ever, the spring DA prefers to adjust his goal to 0.79 in order to reach a compromise solution. Thus, the final compromise solution is:

D o = 2.068, Di = 1.679, rcl = 0.086, re2 = 0.050, r s = 0.1, VH = 0.218 Dv = 2.1, Aj = 0.01, A 2 = 0.01.

The compromise solution is reached in two iterations, because the differences between the variables in conflict are rather small, and the spring DA and the enclosure DA are willing to compromise. As compared to the solution obtained by individual agents, the volume of the spring (V/~) is decreased from 0.228 to 0.218, but the volume of the valve (D~) is increased from 2.0 to 2.1. The joint utility is decreased by 0.404.

It is observed that the solution chosen by the maximum joint utility rule may not be acceptable to all agents. For example, the joint utility of the solution derived in iteration 1 is greater than the solution obtained in iteration 2. However, the difference between individual utilities is quite large. Thus, the compromise utility rule may be a better rule for the selection.

In Step 8 of the last iteration, if the compromise solution suggested were: Do = 2.075 and Di = 1.679, then the enclosure DA would not be satisfied, because the individual utility 0.672 would be less than the goal 0.8. If the enclosure DA were unwilling to adjust his/her goal, then Step 8(3) would be fired. The new negotiation sets would be S'Vo = [2.068, 2.075] and S~i = [1.679, 1.679]. Return to Step 6,

and the procedure would continue.

5. Conclusion

In this article, a design methodology for resolving multiple conflicts in a multiagent environment was presented. The methodology generated negotiation sets, analyzed utilities derived for each design agent, and evaluated them based on the three decision rules. The compromise solution was reached iteratively. The valve design problem was not just concerned with satisfying design constraints, but attempts were made to maximize the system objectives. The goal-directed negotiation decreased the degree of interaction among agents so that the complexity of the system was reduced.

Since agents' goals are generally non-numerical, it is difficult to derive a utility function for each design agent. To improve the effectiveness of the negotiation process, one should characterize the relationship among decision variables, goals, and conflict variables. The agents have to adjust the value of decision variables to reach a consensus. It is critical to design a negotiation support system to main-


tain the solution consistency during the synthesis stage in a cooperative design environment. The limitations stated above have become our future research issues.

Acknowledgment

This research has been partially supported by grant DDM-9215259 from the Na- tional Science Foundation and research contracts from the Rockwell International Corporation and John Deere and Company.

Appendix A: List of parameters and variables of the poppet-relief valve

A (in 2) Al (in) A2 (in) C q Cc C~ Cjl (in) CI2 (in) d (in) deo (in) do (in) dL (in) D (in) Di (in) Do (in) D~ (in) Fc (in) Fa (in) Ft (in) g (ft/s 2) G (psi) koc/ (lbs/in) ks (Ibs/in) K L f (in) L i (in) Ls (in) N P (psi)

pipeline cross-sectional area corrosion resistance allowance for valve enclosure corrosion resistance allowance for poppet-valve stem helical spring index orifice coefficient valve configuration factor coefficient valve flow coefficient radial clearance between helical spring and enclosure radial clearance between helical spring and poppet stem helical spring wire diameter equivalent orifice diameter orifice diameter flow-line diameter mean helical spring diameter inner diameter of spring enclosure outer diameter of spring enclosure valve outer diameter cracking force on helical spring dynamic fluid force total force on helical spring acceleration due to gravity (32.2) share modulus of spring material actual spring rate computed spring rate Wahl spring factor helical spring free length helical spring installed length helical spring solid length number of helical spring coils maximum fluid pressure in pipeline

88 KUSIAK/WANG

Pmatl P~, (psi) AP (psi) Q (GPM) r~.j rc2 G S Sp (psi) Smatl tp (in) ts (in) VE (in 3) VN (in 3) 8 (in) p,, (lbs/in 3)

valve-enclosure material cracking pressure pressure drop from valve inlet to outlet fluid flow rate helical spring outer diametric clearance ratio helical spring inner diametric clearance ratio spring stability ratio fluid specific gravity allowable stress for pipe material spring material pipe thickness valve cylinder thickness volume of valve enclosure volume of helical spring maximum deflection of valve and spring due to fluid force density of water (62.4)

Appendix B: Relationship between parameters and variables for design agents

Valve Design Agent. The relationships between parameters and variables for the valve DA are:

d~o = do

C/co = c~ (dO '.~

ts = d s - d L

~d~ Fc =P,.~

O.O007056QZpw 110 ~ Fd = vd 2 x sin 2

g 4

&

4

F, = C + F ~

Spring Design Agent. The relationships between parameters and variables for the spring DA are:

N E G O T I A T I O N I N E N G I N E E R I N G D E S I G N 89

F~ k s ~ - -

Kad = (1 - - rs)ks

4 C - 1 0.615 K - + - -

4C - 4 C

S - 2"55FtDK d 3

D C ~ - -

d

G d 4 N -

8D3ks

C11 z Drcl

CI2 ~ - Drc2

L~ = d ( N + 2)

L f = L i + Fc k~

d D i = D - - - C12

2

d Do = D + ~ + C .

7r2dZDN

V . - 4

Enclosure Design Agent. The relationships between parameters and variables for the enclosure DA are:

P D v t r = A~ + - -

2Sp

P D i t s = A 2 q- - -

2Sp

Do = Dv - 2tp

d L = D i - 2ts

90 KUSIAK/WANG

Appendix C: Utility functions

~tvi_u

1.0 1.0

0.18 0.228 0.35 VH 0.01 0.1 0.2 0.5 r s

~1. rc 2

1.(

0.2.

1s

._ 0.2 - ~ _ r

0.05 0.1 0.3 rcl 0.05 0.1 0.3 rc 2

Figure C-1. Utility functions of performance variables (VM and rs) and decision variables (rr and rc2 ) for spring design agent

1.0

1.8 2.0 2.5 , - ,

~J'All

1.0

0.2

t-thzl 1.0

v

0.005 0.01 0.1 A1 0.005 0.01 0.1 A2

Figure C-2. Utility functions of performance variables (D.) and decision variables (A~ and A2) for valve-enclosure design agent


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