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AbstractThe design of marine systems is often dominated by aconsiderable number of constraints which are related tothe many competing aspects pertinent to the product’slife cycle. The work presented here originates from au-tomated optimization in which constraints are handled ina formal and unified manner. An analogous approach isproposed for systematic design space exploration on thebasis of parametric design principles. This allows com-prehensive investigations in which constraint monitoringand assessment bring about valuable insight. The con-straint management is illustrated on the basis of a rep-resentative hull design project.KeywordsCAD; Constraint; Geometric modeling; Hull design; Op-timization; Ship design.IntroductionDesigning an object of high complexity implies that quitea few constraints need to be satisfied while several op-posing objectives ought to be maximized (or minimized).This makes design a creative and interesting undertak-ing but also a challenge if many constraints are imposed.Both constraints and objectives usually are of multi-disciplinary character and may stem from hydrodynam-ics, structures, production, operation, economics etc.Design constraints are typically controlled by the personbeing responsible for a certain task. Many constraints re-sult from previous or subsequent tasks carried out by dif-ferent team members or departments. Feed-back is givenonly if one or more constraints are violated. 58416
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The cure toconstraint violation is manifold: Ideally, the constraint inquestion can be slightly relaxed.More typically, however,a compromise needs to be negotiated which means that aloss of performance has to be accepted or a nested changeof many design aspects has to be brought about. In orderto make a rational and well-founded decision comprehen-sive knowledge about the design space, the objectives andthe constraints as well as their dependencies on the designvariables is mandatory. Questions that are usually askedare:• In view of the many constraints, are there any feasi-ble designs at all?• The existence of feasible designs presumed, howclose are favorable designs to one or several con-straints?• Which constraints are dominant and which mighthave no tangible influence (and can thus be dis-carded)?• Which free variables are important and which areinsignificant with respect to both the objectives andthe constraints?If those questions can be answered the number of itera-tions caused by constraint violations will decrease whilethe quality of the design will increase.This paper therefore attempts to address important is-sues of constraint management. Firstly, a theoretical viewon the ideas and concepts is presented so as to intro-duce instruments of constraint assessment. Secondly, apractical application is given to illustrate the feasibil-ity and the merits of the approach. The example con-sidered was realized within FRIENDSHIP-Systems’ op-timization framework applying the fully parametric CADtool FRIENDSHIP-Modeler.Constraint classificationFormal optimizationIn an optimization a good (or the best) solution is de-termined from a set of alternative and feasible solutions.The best solutions – i.e., the Pareto optima – are selectedin terms of the free variables on the basis of problem-oriented criteria. The standard format of mathematicalprogramming is as follows, see Birk and Harries (2003):Free variables: They are the independent decision vari-ables which uniquely describe the problem −→ x T =(x1 x2 . . . xi . . . xn).Objectives: They are the criteria by which a solution isassessed. A criterion is a function of the free vari-ables F(−→ x ). Constraints: They reduce the possible combinations ofthe free variables to the set of feasible combinations.Several types are distinguished:• Bounds ximin ≤ xi ≤ ximax for i = 1, . . . ,n .• Equality constraints hj(−→ x ) = 0 for j =1, . . . ,m .• Inequality constraints gk(−→ x ) ≤ 0 for k =1, . . . , p .This formal treatment of free variables, objectives andconstraints has the key advantage that similar strategiescan be utilized for many optimization problems indepen-dent of their nature. Consequently, it is advantageous toemploy this unified view also for constraint management(even though no automated optimization might actuallybe intended).Constraints in geometric modelingThere are many different types of design constraintswhich relate to all possible aspects of a product. Manyconstraints are of geometric nature or can be ascribedto geometric properties. The authors’ background beinghydrodynamic design of ship hull forms, representativeconstraints shall be discussed in the context of geometricmodeling.Three types of geometric constraints can be distin-guished:• Differential,• Positional,• Integral.Typical positional constraints are maximum dimensions(e.g. breadth must be no greater than ...), collision con-trol (e.g. the hull must remain outside a virtual volume toguarantee minimum propeller clearance) and hard points(e.g. the engine foundation or a container must obviouslynot penetrate the hull and its inner structure). An examplefor collision control is shown in Fig. 1 while a hard pointconstraint can be seen in Fig.