Elsevier

Computer-Aided Design

Volume 45, Issue 6, June 2013, Pages 991-1004
Computer-Aided Design

Educated search—A generic platform for partial modification at conceptual design phase of multidisciplinary problems

https://doi.org/10.1016/j.cad.2013.02.001Get rights and content

Abstract

This paper presents a goal programming algorithm utilising a weight-free aggregate function for producing enhanced design alternatives and a knowledge-based procedure for the selection of the final solution from a pool of enhanced alternatives. Normally, in a multi-disciplinary design problem several teams of designers with different preference and background knowledge are involved in the decision making processes, such as constructing aggregate functions for multi-objective optimisation and trade-off study towards selecting the final solution. In constructing an aggregate function, designers need to identify how important each objective is with respect to the other objectives. However, in the absence of a final decision maker with expertise in all disciplines, the predicates such as “as important as” or “more important than” cannot be used to compare objectives from different disciplines, and therefore the establishment of a weighted aggregate function is not viable. Introducing the concepts of unsatisfactoriness and tolerated margin, “how important is a design quality with respect to other design qualities” is replaced with “to what extent can the unsatisfactoriness of a design quality be tolerated”. This removes the predicament arising from the usual subjective decision making when forming an aggregate function and also transforms the final solution selection from a negotiation process to a straightforward and knowledge based procedure. A software tool comprising of two modules, a multi-deme genetic algorithm, for producing enhanced alternatives, and an assessment module, which includes visualisation, ranking and filtering facilities, is developed and its performance is shown using an illustrative multi-disciplinary design space.

Graphical abstract

Highlights

► Modification of multidisciplinary design candidates at conceptual design phase. ► Goal programming algorithm utilising a weight-free aggregate function. ► Knowledge-based procedure for multidisciplinary design alternative assessment. ► A decision support system minimising interferences between various subspaces. ► Interactive search with a robust multi-deme genetic algorithm.

Introduction

Multi-disciplinary design is becoming dominant in many engineering fields, such as automotive [1], building construction [2], naval structures [3] and aircraft design. The largest number of applications can be found in the field of aircraft design; for instance see [4], [5], [6], [7] and the references therein. A multi-disciplinary design problem has three main features: (i) Designers consider some or all relevant disciplines included in the design problem simultaneously. Exploiting the interaction between disciplines shall lead to a consistent result, which is of better quality compared to the results obtained by designing each discipline individually. Traditional sequential design of multi-disciplinary design problems is not efficient and may even lead to non-optimal results [8], [9]; (ii) Multi-disciplinary designs are normally carried out by several design teams and normally no single design team is expert in all disciplines. For example, as shown in Fig. 1, the aircraft physical design space can be divided into ten different subspaces, requiring several design teams with different background and field of expertise working interactively towards generating design concepts and modifying/enhancing a design candidate. Here, multiple decision makers are involved in the design process, making decision making rather complicated; (iii) Multi-objective optimisation is an indivisible element of multi-disciplinary designs as products are assessed based on several assessment criteria (design qualities or objectives), most of them conflicting.

Conducting a multi-disciplinary optimal design, designers may face several challenges in practice, as explained below.

There are three main approaches being adopted in performing a multi-objective optimal design. In the first approach, known as a priori method, a multi-objective optimisation problem is transformed to a single objective problem by combining all design objectives using a weighting system and forming a single aggregate or cost function. Weighting systems comprise of a set of weighting factors and/or tuning exponents representing the relative degree of importance of design objectives. At the end of a successful search process, the design alternative that minimises the cost function is entitled the optimum solution. This solution is a single point on the Pareto frontier of the corresponding original problem. The weighting factors have significant influence on the location of the final solution on the Pareto frontier, as the search is directed towards the points closer to endpoints corresponding to objectives that have been judged to be more important. A comprehensive summary of different types of weighting systems can be found in [11]. Methods that have been proposed and are being used can be categorised as either direct weighting or fuzzy preference [12], [13], [14]. In a direct weighting approach, the designer either sets the weighting factors directly or employs a transformation heuristic to convert his numerical inputs to weighting factors [15]. In fuzzy preference methods, (sometimes inaccurately called weight-free methods), the designer starts with assigning the fuzzy preference relations between objectives but eventually employs a “words to numbers transformation” [12] to find the weighting factors.

When employing an aggregate function, the key assumption is that all objectives incorporated in the function are comparable and therefore it is possible to assign/calculate a weighting factor for each objective. The validity of this assumption, as discussed below, becomes the main concern when utilising this approach for a multi-disciplinary optimisation. On one hand, selection of weighting factors is highly subjective as it is based on subjective factors, such as designer’s preferences and background knowledge. On the other hand, in a multi-disciplinary design problem several teams of designers, with different preference and background knowledge are involved in the decision making process. In the absence of a final decision maker, who is an expert in all disciplines, the predicates such as “as important as” or “more important than” [12] cannot be used to compare objectives from two different disciplines, and therefore establishment of a weighting system with a commonly accepted set of weighting factors is not viable. A design candidate having poor qualities with respect to one design subspace might be discarded if the designers of that subspace are in charge of defining the weighting system, on the other hand it might be deemed a remarkable design candidate by the designers of other design subspaces. One may argue that, assuming that all design subspaces have the same level of importance, objectives with the same rank from different design subspaces can be related by the fuzzy preference relation of “as important as”. Obviously, this method of comparison fails if the number of objectives in different subspaces is not the same. For example, assume that objectives of two design subspaces are ranked from 1 to 6 and 1 to 4. The fourth objective of subspace 2, on one hand becomes as important as the fourth objective of subspace 1, while at the same time it can be seen as the last objective of subspace 2 and therefore as important as the sixth (last) objective of subspace 1.

In the second approach, known as a posteriori methods, no weighting system is used and the search process forms the Pareto frontier itself, or its best viable approximation. Here the first goal is to find Pareto front solutions. Depending on the type and size of problem, the number of Pareto solution can be enormous making it practically impossible to find all of them. Moreover, in many cases such as combinatorial optimisation problems proof of the optimality of solutions is computationally impossible. A practical approach is to form a set of best-known solutions representing the Pareto front. The best-known Pareto front should be ideally a subset of the Pareto optimal set, uniformly distributed and diverse over of the Pareto front.

A final decision maker evaluates the generated design alternatives against the assessment criteria and looks for trade-off solution. Most of the existing multi-disciplinary optimisation algorithms fail or do not perform well for problems with large number of objectives [16], [17]. The high computational time required to produce enough uniformly distributed Pareto solutions for very large real world problems, together with the lack of a final decision maker capable of performing a multi-criteria assessment, are the drawbacks of this approach when adopted for multi-disciplinary design problems.

In the third approach of multi-objective optimisation, by treating all-but-one design objectives as constraints, the multi-objective optimisation problem is transformed to a single objective one. This method is most suited for cases in which one objective is dominant and other objectives either have known target values or have known upper and/or lower bounds. In the case of conflicting objectives, solution obtained by this method is again a single point on the Pareto frontier of the original problem, while unlike the first approach the designer actually directly imposes constraints on the locus of the solution prior to commencing the optimisation. Although this is an accepted approach for optimal design of well-documented and standardised design problems, but since the search is directed in favour of the dominant objective, it cannot be applied to multi-disciplinary design where there are several objectives, which do not outperform one another.

It is well recognised that, decisions made in conceptual design phase are amongst the most influencing decisions in a design process, affecting the cost of the design process as well as the quality of the result [18], [19]. However, multi-objective optimisation of a real world multi-disciplinary problem becomes even more challenging in the conceptual phase due to (i) the greatest uncertainty exists in this phase; (ii) usually low fidelity models and methods of analysis are used in this phase; (iii) feedback from preliminary and detail design phases may cause significant changes to design concepts, leading to invalidity of the optimality of a solution; and (iv) in the early stages of design concept generation it is difficult to visualise, capture and transfer a design concept between different design teams [19]. That is, in conceptual design phase, using the term modification may be more accurate, as optimisation in its strict deterministic form is not practical.

In multi-disciplinary design problems there are cases in which only one or few design subspaces have poor design qualities and therefore modification should be focused only on those subspaces (in this paper, referred to as partial modification) rather than the entire design space (here, referred to as total modification). It is obvious that in order to enhance the poor qualities of one design subspace, employing a total modification, in which all design subspaces are considered for modification, is not an efficient and practical approach. Ideally, modification process should be directed in favour of the design qualities corresponding to a particular design subspace, or a combination of two or more design subspaces. In this paper, the term “local zone” refers to one or, a combination of two or more design subspaces while the union of other design subspaces is referred to as “non-local” zone. A partial modification, however, has a major drawback. When modifying a design candidate partially the designers need to be aware of, and when possible control, the effect of this partial modification of design variables on design qualities of the non-local zone.

In a multi-disciplinary design problem, normally, each design subspace has a different share of contribution in the conceptual design phase. For instance, currently, the Stability and Control subspace plays a minor role in the conceptual design phase of aircraft design space. This is mainly due to the fact that some stability and control design aspects, such as the architecture of the Flight Control System, are initiated in the subspace itself primarily based on the information provided by previous design practices rather than the information generated in other design subspaces. The stability and control design aspects, however, affect other subspaces during the initial stages of design development; hence integration of this subspace into the conceptual design phase directly influences the quality of the final design and the cost of design process [20], [21]. In order to integrate a new design subspace in a real world practice, the main concern is that the interaction between different disciplines, if not directed and managed properly, can cause interference between different design teams, increase the number of costly iterations between disciplines, and therefore affects the overall cost of the design process adversely.

In view of the above discussion, with the motivation of integrating design subspaces in the conceptual phase of multi-disciplinary design problems, while producing minimum interferences between various subspaces, a decision support system, capable of performing a multi-criteria modification has been developed in MATLAB. Since most multi-disciplinary engineering design practices are based on employing the available resources towards the enhancement of the current products, the designer decision support system is focused on modifying an initial design candidate rather than generating innovative concepts. Design candidate modification is based on an interactive target-directed approach in which partial modifications of an initial design candidate by the designers in charge of the local zone is carried out using the knowledge implemented in the software by the designers in charge of the non-local zone. In this paper, this concept is referred to as “Educated Search”.

Section snippets

Educated search

Educated search (ES) is a modification-based design enhancement process founded based on a weight-free goal programming method. Application of goal programming in conceptual design of multi-disciplinary problems is not new. The majority of the reported works employ goal programming methods for multi-criteria assessment of alternatives and to aggregate decision information where multiple decision makers are involved (e.g. see [22], [23], [24], [25], [26]). The application of goal programming in

Physical design space and its subspaces

In a multi-disciplinary design problem, the physical design space is constructed of several design subspaces, each representing one discipline. A physical design space is defined through its N design subspaces. A design subspace s,(s1,,N) is defined by the followings:

  • The vector of qs design qualities Ys={yj},j=1,,qs, corresponding to that subspace. Design qualities are those measurable features of a design candidate that are used to assess a design candidate. Equality and inequality

Loss function: unsatisfactoriness of a design candidate with respect to a design quality

By using a flat aggregate function, in which no design quality is superior to others, no strict evaluation can be performed at the stage of generating enhanced alternatives. An alternative design solution, which has some unsatisfactory design qualities, cannot be discarded unless it is known that, those design qualities have such level of importance that their violation cannot be tolerated. In other words, using the normal satisfactory boundaries of design qualities as a reference to reject

Secondary assessment and selection of the final solution

After concluding production of a population of enhanced alternatives, there can be three possibilities: (i) there is only one enhanced alternative with all qualities satisfactory, including the special case in which all of qualities meet target values; (ii) there is no solution with all qualities satisfactory; and (iii) there are more than one enhanced alternatives with all qualities satisfactory. In the first case, no further assessment is required and the alternative with all qualities

The background search tool for producing enhanced alternatives

The first part of this section presents the genetic algorithm-based search tool developed for generating enhanced alternatives. The second part of this section elaborates on further enhancements that can be made to boost the search performance.

Discussion and concluding remarks

In constructing an aggregate function, the key assumption is that all objectives incorporated in the function are comparable, and therefore it is possible to assign/calculate a weighting factor for each objective. The validity of this assumption becomes the main concern when applied to a multi-disciplinary optimisation. In a multi-disciplinary design problem several teams of designers, with different preference and background knowledge are involved in the decision making process and therefore

Acknowledgements

The research reported in this paper was supported by the EU FP6 funded project, SimSAC (Simulating Aircraft Stability and Control Characteristics for Use in Conceptual Design) under Contract number AST5-CT-2006-030838.

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    1

    Formerly: Aerospace Vehicle Architecture and Design Integration Research Group, Department of Aerospace Engineering, University of Bristol, UK.

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