In global-optimisation tasks, trapping the population at local minima (LM), and long stagnation periods at each of minima may lead to difficulties in achieving a satisfactory convergence of the algorithm. Hard or soft dynamic penalty functions (PFs) can be built into the definition of the cost function in any evolutionary global-search algorithm in order to limit the search area and so to improve the convergence. The concept, kinds and use of PFs have been reviewed in detail in [1]. The PFs are built in the general utility genetic-algorithm packages such as LHG [2] or BASIC [3], and their use  in specific problems has been reported e.g. in [4,5]. In general, the choice of PF parameter values should be influenced by the extremum shape and extent in the given class of optimisation tasks. In [5], the use of varying-in-time soft penalty has permitted to improve the convergence for a powder-pattern indexing (PPI) task; the concept from [5] will be presented here in more detail and the influence of PF parameters on the convergence will be discussed. The applied definition of the PF discourages the algorithm from exploration of the earlier found LMs, moreover, a list of such minima is created. The PF varies smoothly in order to prevent against the loss of genetic information at the stage of birth of the next generation. Its use leads to reduction of the time of stagnation at the given LM, enabling thus to find numerous LMs and to select the global one from among them. It will be shown for the PPI example studied, how the choice of the PF parameter values influences the opportunity of finding the global optimum in a short cpu time.

[1] C.A.C. Coello, Comp. Meth. Appl. Mech. Eng. 191 (2002) 1245-1287.

[2] R. Östermark, Eur. J. Operat. Res.b152 (2004) 195-214.

[3] E.G. Shopova, N.G. Valdieva-Bancheva, , Comput. Chem. Eng. 30 (2006) 1293-1309.

[4] K. Wang, A. Salhi, E.S. Fraga, Chem. Eng. Process. 43 (2004) 663–675.

[5] W. Paszkowicz, Mater. Sci. Forum 228 (1996) 19–24.