Final Program EXPRES 2012 - Conferences

V. OBJECTIVE FUNCTIONThe objective function in analyzed case is the COP ofthe heating systemIn the above function each term depends on the massflow rate.Maximum value of COP is obtained optimalcombination of mass flow rate of well water, heatingwater and mass flow rate of Freon.For optimization is applied numerical procedure, themethod of genetic algorithm.The application of classical optimization procedureusing the first derivative at mass flow rates is verycomplicated and difficult to implement.VI. MATHEMATICAL OPTIMIZATIONPROCEDUREA. Genetic algorithmsMethods of evolutionary computation are widely usedfor optimisation of problems [5-7] which can be multimodel,non-differentiable, non-continuous, also in thedomain of heating, ventilation and air conditioning [8].Genetic algorithms proved to be very useful foroptimization of multicriteria and multiparameterproblems as presented problem of optimization ofheating cooling system with heat pump. Evolutionarycomputation employs the vocabulary taken from theworld of genetics itself, and as a result solutions referto organisms of a population. Each organism representsthe code of a potential solution to a problem. A furtherimportant characteristic of GAs is that they work bymaintaining a set (population) of potential solutions,where as the other search methods process a singlepoint of the search space.Traditional analytical or numerical based approachesgenetic algorithms are based on building of solution.Because this is in the case of optimization of heatingsystem with water-water heat pump impossible we cantake different approach. The combination of allindependent variables used in the mathematical modelfor calculation of COP we can designate as solution.And previously stated mathematical formulation forcalculation of COP can be designated as targetfunction. The solution is feasible combination ofindependent variables not only the optimal solution.Representation of organism is:Our desire is to advance during evolution of solutionsto the optimal solution. In the world of evolutionarycomputation, solution is called organism. And set ofsolutions created in one step is called generation. Thisbasically means we are searching for such combinationof , and that the COP will, be at hismaximum. We could check all possible combinationsof , and . Unfortunately this is impossiblebecause of infinite size of search space. An exhaustivesearch method or an exhaustive search methodcombined with conventional gradient based methodscan be applied to find the optimal solutions, eventhough it is impractical in real time applications forsuch a complicated problem due to its time consumingnature.With genetic algorithms we can manage this problem.Genetic algorithms are effective at search in such largespace. It works on set (generation) of possible solutionand afterwards it checks the quality of solution (valueof COP). The creation of new set of solution (offspringgeneration) is based on principles of evolution andgenetics which takes into account the value of COP.Basic steps of genetic algorithm which repeat for everygeneration are (Figure 2):1. Creation of an initial set of solutions (initialgeneration of organisms).In our case organismrepresent combination of mass flows of cooling/heatingmedia. Organism it’s a set of numerical values. Firstgeneration of solution is created at random from theinterval of possible values.2. Evaluation of organisms by means of a fitnessfunction. This basically means calculation of COPvalue for all solutions (organism).3. Execution of evolutionary (reproduction andcrossover) and genetic (mutation) operations onsolutions (organisms) which solve the problem aboveaverage in current generation.In our model of optimization the tournament selectionis used. Tournament selection randomly chooses fromthe population at least two organisms and the onewhich represents better solution (COP in our case) isused for creation of new solution by crossover andmutation. It was used simple one point crossover, forexample:The mutation is based on the randomly insertion ofnew random value:The biggest advantage of search for solution bygenetic algorithms is possibility to use mathematicalcorrect definition of COP, without need forsimplification. Traditional methods of solving complexreal-world problems are based on simplification. Atsimplification process we have to deal with possibilitytoo simplify too much. With genetic algorithms we cantry evolutionary created solutions in the real world, inour case mathematical formulation of COP.19