Abstract: A new population - based search algorithm, Line-up Competition Algorithm(LCA) , is presented, which is found to be very efficient in solving non - convex nonlinear programming (NLP) and mixed-integer nonlinear programming (MINLP) problems. In LCA algorithm, there always exist independent and parallel evolutionary families. By two different competition fashions which are the competition for existence inside family and the position competition between the families, population is made to evolve rapidly toward optimal or near optimal region. The concept of competition driving force is proposed and its quantitative description is given. These families are arranged a line - up in the light of the value of their objective function, and allocated the corresponding search space according to their position in the line-up, resulting in the balance of local search and global search. The technique of contracting search space is applied for increasing the convergence speed. The algorithm was tested with a set of typical non - convex NLP and MINLP problems, the results obtained indicate that LCA has obvious advantage over genetic algorithms and simulated annealing algorithms in solution quality and search rate.