Optimizasyonla gemi ön dizaynı ve bilgisayar uygulamaları

Abstract

ÖZET Gemi ön dizaynı bir nonlineer optimizasyon problemi olarak formüle edilmiştir. Matematiksel optimizasyon yöntemleri ve gemi ön dizaynındaki uygulamaları incelenmiştir. Daha sonra dört farklı nonlineer optimizasyon tekniği (Daha iyi Nokta Algoritması, Kompleks Yöntemi, SUMT Yöntemi, Rosenbrock Yöntemi) karşılaştırılmış, bunlar arasından Daha iyi Nokta Algoritması seçilmiştir. Daha iyi Nokta Algoritması gemi ön dizaynına (dökme yük gemisi dizaynı) uygulanmıştır. -vııı-

PRELIMINARY SHIP DESIGN WITH THE AID- OF OPTIMIZATION AND COMPUTER APPLICATIONS SUMMARY Ship design is an engineering field which necessitates to have various engineering knowledge. So naval architect has to follow all technological developments happened in other engineering and science fields. Traditionally, ship design can be divided into two cate gories : a) Preliminary design (or tender design) b) Contract design (or detailed design) In this work, contract design phase will not be consider ed here. Preliminary ship design is the design phase in which ship size, proportions, speed and principal dimen sions are determined. Preliminary design is the main factor whether the ship is to be designed or not. There are many methods used in preliminary design : - trial-error techniques - parametric studies - optimization methods, etc. In this work, preliminary ship design is formulated as a nonlinear optimization problem. For this purpose : - firstly, it is investigated the optimization methods developed different engineering areas (especially used in preliminary ship design) (Chapter 2). - secondly, applications of optimization methods in ship design are examined (Chapter 3). - thirdly, four different optimization techniques are compared and Better Point Algorithm is chosen (Chapter 4, Section 4.1, 4.2). -xx-and finally Better Point Algorithm is applied to ship design and successful results are obtained (Chapter 4, Section 4.3). Chapter 2 explains the optimization methods. -.Optimiza - t ion methods can be divided into three categories as follows : a. Optimization methods for unconstrained functions, b. Optimization methods for constrained functions, c. Optimization methods which exploit system or informa tion flow structure. The methods given in case a find the optimum point for mult i variable, nonlinear functions without any constra ints. The methods in b find the optimum point for multivariable, nonlinear functions with some equality and/or inequality constraints. Dynamic programming can be given as an example of case c. Last case will not be explained here. In below table general classification of optimization methods is shown. Table. Classification of Optimization Methods 1. Optimization Methods for Functions of One Variable a. Calculus b. Root-Finding Procedures for the first derivative of function. Newton ' s Method. False Position Method. Half-Interval Method. Methods for Polynomial Functions c. Searching Schemes cl. Simultaneous Methods. Exhaustive Search. Random Search c2. Sequential Methods. Dichotomous Search. Equal Interval Multi-Point Search -x-. Search by Golden Section. Fibonacci Search 2. Optimization Methods for Functions of Multivariable a. Calculus b. Root-Finding Procedures for the first derivative of function.. Newton- Raphson Method c. Search Methods which use the function values only cl. Simultaneous Methods. Exhaustive Search. Random Search c2. Sequential Methods. Exponential Random Search. Lattice Search. Univariate Search. Rotating Coordinate Method. Direct Search d. Search Methods which use the function values and the values of the first derivative of function. Contour Tangent Methods. Steepest Descent Methods. P artan Methods. Conjugate Gradient Methods e. Search Methods which use the values of : function, first and second derivatives of function. Steepest Descent Methods. Conjugate Gradient Methods 3. Optimization Methods for Constrained Functions a. Linear Programming b. Nonlinear Programming -xi-Variational Calculus : Lagrange Multipliers' Method Quadratic Programming General Nonlinear Problems 4. Optimization Methods which Exploit System or Informa tion Flow Structure a. Dynamic Programming. In Chapter 2, section 2.1 explains classical theory of unconstrained optimization. Section 2.2 describes opti mization methods for functions of one-variable. Explain ed methods are : Newton's Method, Exhaustive Search, Dichotomous Search, Equal Interval Multi-Point Search, Search by Golden Section and Fibonacci Search. Fibonacci Search is found the most effective method between the methods mentioned above. Section 2.3 examines optimiza tion methods for multivariable functions. Explained methods are : Exponential Random Search, Lattice Search, Univariate Search, Rotating Coordinate Method, Direct Search of Hooke and Jeeves, Simplex Method of Nelder and Mead, Complex Method of Box, SUMT Method of Fiacco and Mc Cormick and Rosenbrock's Method. Chapter 3 tells about optimization methods applied in preliminary ship design. Described studies in historical order are : a) Murphy, Sabat and Taylor (1965), b) Mandel and Leopold (1966), c) Meyer-Detring (1969), d) Nowacki, Brusis and Swift (1970), e) Fisher (1972), f) Kupras (1976-1985), g) Lyon and Mistree (1985). In Chapter 4, choosen optimization method is applied to preliminary ship design. Ship is taken as abulk carrier. Section 4.1 tells about Better Point Algorithm. Algo rithm finds the optimum point for multivariable, non - linear functions with some equality and/or inequality constraints. It is assumed that object function is -xii-unimodal. Problem is defined as follows : f(x,,...,x ) : object function which is to be minimized h.(x,,..,x ) = 0 : equality constraints i=l,..,t ` x 1 ' ' n ^ x ''nee g. (x-,,..,x ) 4 0 : inequality constraints where ; t : number of equality constraints nee ^ J t. : number of inequality constraints nxc In preliminary ship design, object function can be : - minimum building costs, - minimum average annual costs, - minimum required freight rate,..., etc.. Equality and inequality constraints can be some design limitations. For example: maximum operating draft, required deadweight, required service speed,..., etc.. In section 4.2 four nonlinear optimization techniques are compared according to execution time, number of function and gradient evaluations and reliability in some test problems. In section 4.3 ship design model is explained and better point algorithm is applied to bulkcarrier design. The main aim of this work is to give an application of optimization methods to preliminary ship design. Author considers that successful results are obtained. -X1X1-