Upp í vindinn - 01.05.1998, Side 26

Upp í vindinn - 01.05.1998, Side 26
Guðmundur Jón Ludvigsson Stúdent frá MR 1988. C.S. í byggingaverkfræði frá HÍ1992. Vann hjá Lahmeyer International í Þýskalandi, frá 1992 til 1995 M.S. í byggingaverkfræði 1996. Starfandi hjá ICEconsult (LH-tækni) frá 1996 New Approach in Engineering: Global Optimisation of Design Aiming for Maximum Profit of Investment This paper introduces a new approach in development of complex project schemes, with a special emphasis on the design of hydropower plants (Elíasson & Ludvigsson 1996). The goal of this new approach is in all cases to maximise the ben- efit of project investments, by globally optimising the layout and design parameters of the scheme in question. This principle of economical- ly optimal design is no new evidence. It has however been difficult to use it, due to its great complexity. The way out has been to use local optimisation to decide the design parameters. The best known example in hydropower design, is optimisation of tunnel diameters by minimising the sum of construction costs and power losses (Mosonyi 1991). In local optimisation, dependent design variables are optimised as if independent. The weakness of this approach is the substantial risk of miss- ing the true global optimum. In recent years evolutionary methods have proved their worth in optimisa- tion problems, where methods of mathematical analysis are not applica- ble due to system complexity. These methods make it finally possible to apply this new design method. A com- puter model called Hydra, which uses an evolutionary method called Genetic Algorithm to globally optimise hydropower plants is presented. Objective function The objective function is the profit, also called the net present value of the investment, H(xl,..xn): H(x1,..x„) = T(xlv.xn) - K(xlv.xn) - V(xlv.xn) - E(xj,..x„) The function consists of following parts. Each one is calculated for a defined interest rate and lifetime of the investment: • Revenue T(xlv.xn) of the scheme • Project investment K(xu..xn) according to the design parameters x,,..xn • Operation and maintenance cost V(xlv.xn) • Environmental cost (either positive or negative) connected with the scheme E(xlv.xn) The goal is to maximise the objective function. Note that when the revenue is fixed or zero then the goal is simply to minimise the sum: K(X|>..x„) + V(xlv.x„) + E(xlv.xn). Optimisation Procedure The logic of optimisation is mutual for all problems. The goal is to find the minimum or maximum of a defined objective function, where the variables can be subject to some constraints. Mathematically put (maximisation problem): max f(x,, x2, ... xn) a; < x^ < bj for i = 1 to n gj(xu x2, ... x„) < Cj for all j The problem is that the objective func- tion is so complex that conventional mathematical methods can’t solve it. A method that, however, is able to find this global optimum is called Genetic Algorithm (see, e.g., Goldberg 1989; Pirlot 1994). It is based on Charles Darwin’s famous theory ‘Survival of the fittest’. The logic is very briefly as fol- lows: • Each project arrangement is consid- ered an individual (variables encod- ed as genes in a chromosome) with a fitness equal to the profit it pro- duces • Weak individuals tend to die before reproducing, while the stronger ones live longer and bear many off- spring • These offspring often inherit the qualities that enabled their parents to survive • As time passes the individuals in each generation become fitter, i.e. the objective function comes closer to its optimum value. The main strength of the genetic algorithm is that it is independent of the behaviour of the objective function. For example the function does not have to be differentiable in the solution space. Another strength is that the number of optimisation parameters is unrestricted. A minor weakness is that the result is ‘close’ to the real optimum, but this small difference is a negligible factor compared with the unavoidable inaccuracy in the assumptions and cal- culations made in calculating the prof- it. The program ‘Hydra’ is a 32 bit Windows 95 application. £C±2?if It includes a SQL connection to the databases Access 97 or SQL server, where all project data, unit prices, results and documents stored. Also included is a OLE connection to other Windows applications, such as Excel and Word, so results and other data can easily be moved between programs. The functionality is very briefly as foliows (see www.lh.is/ICEconsult/ Hydra). A project is built up by creat- ing and arranging stand alone structure objects (which can be developed and modified by the user outside the pro- gram and "plugged" into Hydra) together at defined coordinates (which also can be free for optimisation). Main 26 ...upp í vindinn

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