The importance of the starting point, the size of initial search region, and the search region reduction rate is examined with respect to the reliability of different direct search optimization procedures in being able to furnish the global optimum for nonunimodal systems. Although, in general, the reliability of an optimization procedure is problem dependent, it is nevertheless clear that reliability cannot be increased simply by selecting larger search regions or by reducing the rate of contraction of the search region. A more efficient means of increasing reliability is to embody a pseudo one‐dimensional search in the optimization procedure to enable the search to leave a local optimum and proceed to a better optimum.

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SUMMARYTwo direct search algorithms for the optimization of non-unimodal systems are presented. One method is interior in nature by using boundary relaxation with pseudo one-dimensional search in the feasible region; the other one is an exterior method which allows the violation of constraints followed by the use of a penalty function to drive the search back into the feasible region. These two methods are usually capable of leaving local optima to reach a better solution if such exists. The application of the proposed approaches to several non-unimodal systems shows that they are better than the existing methods. The proposed methods are also attractive because of the ease of programming and the high probability of reaching the global optimum.