Designing chemical engineering processes is inherently connected with mathematical optimisation. Most often deterministic optimization approaches (mathematical programming) are employed such as generalized gradient projection or sequential quadratic programming. This two-part paper shows application of stochastic approach from the class of adaptive random search (ARS) algorithms. In the first part an analysis of ARS methods suggested in the literature is given as well as the so called M-W algorithm developed by the authors. This algorithm allows solving mixed-integer non-linear problems (MINLP). In the second part [1] of this work examples of M-LJ method application are presented for several problems from chemical and process engineering. I has been shown that with proper model formulation the use of very simple M-LJ algorithms allows locating global optimum with high reliability.