The destroyer agents act on the good designs that pass through Interface 2. ... worth. Various fragmenting tactics differentiate the destroyer agent types from one ...
Module-based Multiple Product Design Venkat Allada and Rahul Rai Sustainable Design Lab Engineering Management Department University of Missouri-Rolla Rolla, MO-65401 Abstract Increasing manufacturing competition has necessitated simultaneous design of multiple products. Various design strategies such as Design for Variety (DfV) and product family design have become critical in this respect. This paper provides a new generic approach, which combines aspects of function architecting, multi-objective optimization, and multi agent systems to tackle product platform problems related to multiple product design (MPD). The approach uses functional architecting methods to determine various modules based on functional requirements. Multi-objective optimization using an adaptive multi-agent framework is then used to determine Pareto-design solutions that satisfy various constraints such as module compatibility. Post optimization analysis is applied on the Pareto-design solution set to determine the optimal product platform for the product family. The proposed method is applied to a MPD example to demonstrate its validity and effectiveness.
Keywords Multiple product design, Product Platform, Agent based optimization, Pareto-solutions
1. Introduction Due to difficulties posed by global competition and mass customization, designers are forced to seek design that can capitulate higher benefits at a sensible cost. This has led to paradigm shift in which the focus has moved from design of single products towards design of multiple products. The problem of designing multiple products is getting much attention by the research community in the recent past. The research efforts in this direction has led to a number of emergent research fields that are characterized by several strategies such as: product variety [1], product family [2], product platform [3], modular product design [4]. We can categorize the MPD methods into two groups: methods that concentrate on product architecting [4]; methods that concentrate on design optimization related to module configuration subject to various constraints [2]. Readers are referred to article by Dahmus et al. [5] for further reading in MPD. Most real world design problems are multi-objective in nature, because they consider several objectives (or alternatives) that need to be optimized. Normally, these objectives are non-commensurable (i.e., they are measured in different units) and are in conflict with each other. In this paper, we present a new generic method for addressing product platform problems.
2. The proposed approach The proposed three-level methodology for determining product platform comprises the following (refer to Figure 1): 1. Functional representation: This level generates the modules via the function architecting process and provides a rich description of the function-module mapping, modules and their relationships. A refinement in the module list provided by the heuristics (function-module mapping heuristics) is often required as some heuristics may yield incomplete product configuration. 2. Pareto-Optimization: This level generates the Pareto design solutions while satisfying all the design requirements through proper module configuration. This results in a set of Pareto optimal solutions. 3. Post-optimal techniques: Once the set of Pareto optimal solutions is obtained, a higher-level decision making can be used to solve various problems related to modular designs.
Functional Representation Pareto optimization Post optimal techniques /Refinement s Figure 1. Three levels of the proposed methodology 2.1 Functional representation The functional representation model contains function-module mapping, function/module interactions (such as material, energy and signal). In addition, it also contains information about the parameters that describe the modules instances such as cost, weight, torque, etc. We use the methodology developed by Stone et al. (1998) for the functional representation purposes. 2.2 Agent based Pareto-optimization Campbell et al. [6] developed an agent-based approach (called A-design) to help in conceptual design of electro-mechanical components. Miyashita and Yamakawa [7] used search agents to explore and find optimal solutions in the design space. We propose a new agent-based optimization architecture to deduce the Pareto-optimal solution set (refer to Figure 2a). The system uses an iterative process. During each iteration, the creator agents create new designs as well as modify existing designs. The system captures the synthesis nature of evolution and overcomes the multi-modal, non-linear, discontinuous design space problems that are typical of optimization problems associated with MPD. In this system, we have five main components, namely, Creator agents, Preserver agents, Destroyer agents, Interface 1, and Interface 2 that collaborate with each other in an iterative process. Figure 2b shows a flowchart for the iterative process. Initially, the system accepts a starting point or description of the problem to be solved. For example, the initial specification for the modular product design is a formal description of input and output behaviors. The inputs could be the module characteristics, functions associated with the different modules, module compatibility table, etc. The output behavior could be the objectives that have to be optimized. The creator agents mimic the creation process of the design evolution. The number of creator agents equals the number of modules available for design purposes. The creator agents work directly with the input specifications to produce a set of design solutions. These design solutions are then evaluated on the various objectives specified by the user and then sent to the preserver agents that modify them based upon the objectives allocated to them. There are two types of preserver agents: innovator agents and random agents. The innovator agents act on a good des ign and improve the design solution by making suitable modification along at least one of the objective functions. The random agents randomly (without motive) change the design solutions allocated to them. The destroyer agents act on the good designs that pass through Interface 2. The destroyer agents fragment the design solution in order to improve the current design states. The destroyer agent individually selects a design to be modified, and removes modules from the design that are believed to be reducing the design’s worth. Various fragmenting tactics differentiate the destroyer agent types from one another. Predominantly, these agents differ in their choice of their objectives. For example, some destroyer agents have an objective of removing expensive modules while others may remove only the heavy weight modules. The incomplete designs generated by the destroyer agents are sent to the creator agents to be completed. The Interface 1 helps to maintain a priori number of design solutions by checking the total number of design solutions passing on to the next phase. They also eliminate any redundant copies of the same design solution. Finally, the Interface 1 sorts design solutions into Pareto optimal solutions and non-Pareto solutions. The Interface 2 classifies the non-Pareto solutions (modified by the preserver agents) into good and poor solutions and then eliminates the poor solutions from the system. The destroyer agents process the good solutions. Finally, the Interface 2 creates the Pareto optimal surface (from the Pareto-optimal solutions provided by Interface 1) for the given iteration. The overall iterative process continues until the system converges or the resource and time constraints require the acceptance of the current best design. For a problem having more than one objective function (say fi , i=1, 2…., N and N>1), any two solutions x1 and x2 (having M decision variable each) can have one of the two possibilities: one dominates the other or none dominates the other. The condition for determination of Pareto and non-Pareto solutions is discussed below [8]. A solution x1 is said to dominate the other solution x2 , if both the following condition are true: 1. The solution x1 is no worse (say the operator ⊂ denotes worse and ⊃ denotes better) than x2 in all objectives or fi (x1 ) ⊄ fi (x2 ) for all i =1,2,…, N objectives. 2. The solution is x1 strictly better than x2 in at least one objective or fj (x1 ) ⊃ fj (x2 ) for at least one i 5 {1,2,…, N}.
There are two types of Pareto-optimal set: non-dominated set and a Pareto-optimal set. A non-dominated set is defined with respect to a portion of the search space, whereas, a Pareto-optimal set is a nondominated set with respect to the entire search space. There are two goals that a multi-criteria optimization algorithm must try to achieve [8]: 1. Guide the search towards the global Pareto-optimal region, and 2. Maintain solution population diversity in the Pareto-optimal front. Input specification Module attributes, Module compatibility Etc.
Creator agents
Creator agent create alternative design solutions
Interface 1
Interface1 screens and classify the design solutions Paretodesign
Non-pareto -design
Preserver agents
Preserver agent modifies the design solution
Interface 2
Destroyer agent eliminates “faulty”modules
Interface2 further classify the modified design solutions Poor design
Remove
Destroyer agents
Good design
b
a
Objective 2
Ite ra tio ns
Figure 2. a) Agent based optimization architecture b) flowchart for the optimization process.
Non-dominated front Pareto-optimal front
Objective 1 Figure 3. Propagation of non-dominated front towards the Pareto-optimal front
The search for global Pareto-optimal region is carried out through the iterative process described previously. The essence of the proposed agent-based algorithm proposed is to propagate the non-dominated solution front towards the Pareto-optimal front through an iterative process while maintaining diversity in the solution population (refer to Figure 3.).
3. Modular design example We use the example of designing a power screwdriver from its modules (adapted from Stone et al. (1998)) to illustrate the working of our proposed methodology. In order to pose the design problem, the user supplies the desired objectives: minimize cost, and minimize weight. The input to design problem is generated from the heuristics for determining the modules (developed originally by Stone et al. (1998)).
The catalog of modules generated from heuristics for this test example consists of various embodiments shown in Table 1a. For each of these 12 embodiments listed, there exists actual modules drawn from SKIL, BLACK AND DECKER, and PANASONIC supply catalogs that are available online. This table also consists of the corresponding components that are present in each of these modules. The data for each of these attributes for each modules were generated from various catalogs available online and is presented in Table1b. It is assumed that two instances of same module (a and b) are available and data for both the instances is presented in Table 1b.
Module names
Actual component
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
Electrical supply module Coupling module Torque transmission module Coupling/decoupling module Rotational lock module Positioning module Actuating module Bit torque module Manual use module Electricity to torque module Switch module Decoupling mechanism
Rechargeable battery + Switch Transmission coupling only Motor Transmission (coupling+decoupling) Rotational lock Plastic casing Rechargeable battery (no switch) Bit Rotational Lock+manual locking mech Motor+drivertrain+transmission Switch Decoupling mechanism
Module number 1 2 3 4 5 6 7 8 9 10 11 12
Instance a Weight(gm) Cost($) 130 35 100 45 35 50 115 30 50 115 10 7
Motor torque(in/lbs)
a
30 7 15 6 7 10 25 15 6 20 1 2
Instance b Weight(gm) Cost($) 140 39 85 50 40 57 100 20 37 105 15 5
a= 26
25 9 18 5 8 8 22 17 10 23 2 3
b= 32
b
Table 1. a ) Modules and corresponding actual components after architecting and refinement process b) Module attributes (for the two types of instances) 3.1 Functional representation The application of heuristics proposed by Stone et al. (1998) on the functional representation of power screwdriver resulted in ten unique modules. Apart from these ten modules, two other modules namely switch and decoupling mechanism were added to refine the module list as shown in Table 1a. This was done to provide supporting modules to complete entire functionality required for power screwdriver (which would otherwise have been incomplete for some possible combination of modules). For example, the electrical supply module essentially comprises the battery and switch, whereas the actuating module comprises only the battery. In order to generate feasible solutions that satisfy all the functionalities with the actuating module, we must have switch module as an independent module. The addition of these two modules is an example of refinement required to complete the functional requirement of the overall product for some module configurations. 3.2. Agent based Pareto optimization The numbers of creator agents were set at 12 agents with each agent corresponding to one module. Each agent is capable of producing different instances of the modules, which differ from one another only in the value of attribute they encapsulate. The number of instances of each module was restricted to two. However, increasing or decreasing the number of instances associated with each module does not affect the overall methodology. In order to generate feasible designs from the modules mentioned in Table 1, the sequence in which creator agents collaborated was based on the AND/OR logic. The example of OR collaboration can be seen between agent 1 (corresponding to module 1) and agent 7 (corresponding to module 7). This type of collaboration means that only one of two agents can contribute towards the design solution. The AND/OR collaboration between the agent enables us to generate feasible design solutions in a simple and effective way while checking the feasibility of the overall design produced by the agents. The number of design solutions processed at each iteration was limited to 20. The percentage of design solutions that is altered by the innovator agent was kept 80% while the random agents alter the remaining 20% of the design solutions. The number of destroyer agents for the problem equaled two corresponding to the two objective functions. The output of the Pareto-optimization process is presented in the Figure 4. The Pareto surface is indicated by dotted lines. Figure 4 essentially plots the Pareto surface when we consider only two objectives i.e., weight and cost, in order to illustrate the propagation of Pareto surface during iterations. This methodology could be easily extended to accommodate multiple objectives.
3.3 Post optimal technique Once the set of Pareto optimal solutions is obtained, usually some higher-level decision-making consideration (often based on the goal of the designer) is used to pick a solution or a set of solutions. The use of post-optimal techniques is illustrated through example problems related to MPD. If the goal is to select the appropriate Pareto designs for a given number of identified market segments, then the weight method can be used to pick the appropriate Pareto designs to suit each of the identified market segment. Figure 5 shows the chosen solution with a weighted scheme of (w1, w2) = (0.85, 0.15), where w1 is the weight for cost objective function and w2 is the weight for weight objective function. This procedure is different from classical weighted average scheme in that here a solution is chosen after many Pareto optimal solutions have been found. In the classical weighted average scheme, only one solution optimi zing the weighted average of the objectives would be found. The market segmentation can be viewed as identification of product configurations to suit different markets (which are assumed to differ from one another only due to different weight vectors of objective functions). Four different market segments were hypothetically created and weights vectors associated with them is presented in Table 3. We then use the weighted method to identify the Pareto design solution with each of the market segments. The results are presented in Table 3. Table 2 presents the range of weights for both the objectives for which a particular design solution from the Pareto set will be selected. If the goal is to decide a product platform for the product family shown in Table 3, then one can compile the common modules for each of the market segments. The product platform for the example problem consists of modules listed in Table 4. It is to be noted that though initially we had 24 (12x2) modules from which we could construct the family, only 12 modules were required to construct the entire set of Pareto designs.
4. Concluding remarks This paper proposed a new approach that has ability to address problems pertinent to related concepts of Multiple Product Development (MPD). The paper discusses a new agent based optimization techniques for determining pareto-spaces. The overall methodology proposed is elaborated through a real design problem of power screwdriver. The demonstrated examples ascertain the validity and effectiveness of the proposed methodology. Further investigations are needed to address the performance issues of the agent based pareto-optimization technique proposed in this study. 90
85
85
85
cost 80
75 350
cost
90
cost
90
80
355
360
365
370
a
375
380
385
390
395
75 350
400
80
355
weight
360
365
370
375 weight
b
380
385
390
395
400
75 350
360
370
380
c
390 weight
400
410
420
Figure 4. Results of the agent based optimization process, for varying initial number of design solution a) 25 b) 50 c) 100
Pareto designs
Module combination
1
7b
11
2
12
5
3b
2
7b
11
4
5
3
8
3
7b
11
4
5
3
8b
4
7b
11
4
5
3b
8
5
7b
11
4
9
3
8
Objective function values Weight Cost 8
Weight vector range W1 W2
6
352
82
6
0
370
76
[0.91 - 0.68] [0.08 - 0.33]
6
0
360
78
[0.67 - 0.37] [0.34 - 0.62]
6
0
355
79
[0.36 - 0.13] [0.63 - 0.87]
6
0
385
75
[0.12 – 0.0]
Table 2. Pareto optimal solution for example problem
[1.0 - 0.92]
[0.0 - 0.07]
[0.87 – 1.0]
Market segment
90
Weight
Pareto design solution
Vector
(module combination)
number
cost
85
1
(1.0, 0.0)
7b
11
2
12
5
3b
8
6
2 3 4
(0.85, 0.15) (0.5, 0.5) (0.05, 0.95)
7b
11
4
5
3
8
6
0
7b
11
4
5
3b
8
6
0
7b
11
4
9
3
8
6
0
Table 3. Pareto design selected for different market segment 80
Selected solution
75 350
355
360
365
370
375 weight
380
385
390
395
400
Product platform
Modules set for the whole product family
Module 7b,11,6,8
Module 2,3,4,5,6,8,9,11,12, 3b,7b,8b,
Figure 5. Pareto optimal solution for weight vector (0.85, 0.15) Table 4. Product platform and Module set for whole product family for the example problem
Acknowledgements This work is supported in part by the National Science Foundation grant DMI #9900226.
References 1. 2.
3.
4.
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6.
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