Since the nature is the principle source for proposing some new optimization methods such as genetic algorithms (GA), simulated annealing (SA) and ant colony (AC) the main contribution of this study is that it proposes a novel optimization method relies on the aspect of Beam and Detector (BD). Inspired by this idea, an optimization algorithm is constructed, which will be called BD method that starts with an initial guess to find a local optimum using any simple optimization method. (Simplex algorithm is used in this study). Then, a nonlinear system of equations will be formed that contains objective function and constrains and auxiliary equations. Degree of freedom of the nonlinear system of equations determines the number of auxiliary equations. In this system, the objective function equals to the value of the last local optimum. All constrains are transformed to the equations. Auxiliary equations will be used to complete the system of the equations respect to the degree of freedom. The special form of auxiliary functions guarantees that they just cross the same roots as stay in the objective equation. So the guarantee of reaching the global optimum comes to the ability of finding all roots of the system of equations. For seeking all solutions to the system of equations, a new homotopy method, Fixed-Point Newton (FPN) homotopy is presented. This homotopy is the combination of the fixed-point and the Newton homotopies. The original system of equations is changed to the new system of equations by multiplying the (x-x0) term. When x0 is selected as starting point and FPN homotopy is applied, Bifurcation points are generated. After finding all Bifurcation points, it is necessary to switch to other branches which are bifurcated from these points to find all roots of the new system of equations. The novel concept of the optimization algorithm is that it never uses differentiation of the objective function to convert a nonlinear optimization problem to the system of nonlinear equations. On the other hand, this algorithm guarantees the global optima, not searching all the decision variables space like traditional evolutionary algorithms.

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