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Exploration of multiple roots for a polynomial system

Several problems from engineering, chemistry, medicine, etc. can be formulated as a system of equations. Finding a solution for such a system sometimes requires high computational efforts. There are situations when these systems have multiple solutions. For such problems, the task is to find as many solutions as possible. In this paper, we deal with such systems of equations, which have multiple solutions and we attempt to solve them using two different approaches. Both approaches transform the problem into an optimization problem. The two approaches proposed in are (1) a modified line search and (2) an evolutionary algorithm. Several experiments are performed in order to emphasize the advantages and disadvantages of the two methods.