Introduction to genetic algorithm Prepared by M .U. Kale Assistant professor Irrigation & Drainage Engineering Dr. P.D.K.V. Akola

What is a Genetic Algorithm (GA)? It is search procedure based on the mechanics of natural selection and natural genetics i.e. survival of the fittests.

Optimization Optimization is the selection of a best element (with regard to some criteria) from some set of available alternatives More generally, optimization includes finding "best available" values of some objective function given a defined domain, including a variety of different types of objective functions and different types of domains.

Potential Benefits of applying optimization to water resource problems Cost minimization Benefit maximization Increase Power, minimum loss maximum release etc.

Linear Programming (LP) LP is common in economy and is meaningful only if it is with constraints. Two forms: Minimize subject to: If the LP minimizer exists it must be one of the vertices of the feasible region. A fast method that considers vertices is the Simplex method. A is p × N and has full row rank (p<N)

Evolutionary Algorithm Evolutionary algorithms (EAs) is population-based metaheuristic optimization algorithms that use biology- inspired mechanisms like mutation, crossover, natural selection, and survival of the fittest in order to refine a set of solution candidates iteratively. The advantage of evolutionary algorithms compared to other optimization methods is their “black box” character. EAs perform consistently well in many different problem categories.

Classification of Evolutionary Algorithms 1. Genetic Algorithms (GA) 2. Genetic Programming (GP)

Genetic algorithms (GA) GAs are a subclass of evolutionary algorithms where the elements of the search space G are binary strings (G = B∗) or arrays of other elementary types. The genotypes are used in the reproduction operations whereas the values of the objective functions f, ∈, F are computed on basis of the phenotypes in the problem space X which are obtained via the genotype-phenotype mapping “gpm”. GAs subsume all evolutionary algorithms which have bit strings as search space G. .

Genetic Programming (GP) : GP includes all evolutionary algorithms that grow programs, algorithms, and similar constructs. All EAs that evolve tree-shaped individuals are instances of Genetic Programming.

Application of GA in water resources Pipe network Design of networks, and analysis Ground water management problems Quantity and quality management models Reservoir operation Single purpose single reservoir Multi-purpose single reservoir Multi-reservoir systems Multi-purpose multi-reservoir systems

Advantages of GA model The GA typically uses a coding of the decision variable set, not the decision variable itself. The GA searches from a population of decision variable sets, not a single decision variable set. The GA uses the objective function itself not the derivative information.

Advantages of GA model 4.The GA algorithm uses probabilistic (not deterministic) search rules. 5.GA takes care of stochasticity also. 6.GA does not requires discretization of state variables. 7.GA does not requires transition probabilities. 8.GA does not have curse of dimensionality problems. 9.GA models results in optimal or near optimal solutions.

Disadvantages of GA model Cannot handle large number of constraints like LP models. Computationally difficult to provide very long string length with binary coding - To some extent overcome by hexagonal coding. Every iteration need objective function evaluation. Difficult to handle mutation. Besides these disadvantages, GA model still provide better solutions than the conventional optimization techniques in developing reservoir operating rules.

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