Solver is an add-in tool in Excel that can help you find the optimal solution for a problem by changing the values of certain variables. There are three types of solving techniques available in Solver:
Linear Programming (LP): Linear programming is a technique for solving optimization problems that can be expressed in linear equations. LP assumes that the relationships between variables are linear, and the objective function is a linear combination of the decision variables. The LP technique is suitable for problems that have a linear structure, such as transportation and production planning.
Nonlinear Programming (NLP): Nonlinear programming is a technique for solving optimization problems that cannot be expressed in linear equations. NLP allows for more complex relationships between variables, such as quadratic or exponential relationships. The NLP technique is suitable for problems that have a nonlinear structure, such as portfolio optimization and supply chain optimization.
Evolutionary Solvers: Evolutionary solvers are a class of optimization techniques that are based on the principles of natural selection and genetic algorithms. Evolutionary solvers work by creating a population of potential solutions, evaluating them based on a fitness function, and then selecting the best solutions to generate new ones. This process is repeated until an optimal solution is found. Evolutionary solvers are useful for solving complex optimization problems that may have multiple local optima.
Solver offers several algorithms within each of these three types of solving techniques. For example, the linear programming technique in Solver includes Simplex LP and GRG Nonlinear. The nonlinear programming technique includes Generalized Reduced Gradient (GRG) and Evolutionary. The evolutionary solver includes both genetic and swarm optimization methods.
When using Solver, it is important to choose the appropriate solving technique and algorithm for your problem. The choice of technique and algorithm will depend on the structure of the problem, the number of decision variables, and the constraints involved.