## 6 Results Discussion and Conclusions  
This study investigated the performance of CGAs with respect to the automatic parameter adjustment of inventory control strategies in logistic networks that have complex, mesh-type topologies. Two such strategies were examined: the classical OUT policy implemented in a distributed way and a centralized one that took into account the network connectivity structure. The analytical study, which was confirmed by the conducted numerical experiments, demonstrated that the centralized decision-making allowed one to lower the holding costs while maintaining the requested service level relative to the distributed approach. The performed numerical studies confirmed that the CGA-based optimization was an effective tool for the optimization of logistic networks, even in the case of complex interconnection structures. It allowed one to reduce the computational time and effort (relative to the full-search approach), while yielding a near-optimal outcome. Moreover, the CGA-based optimization provided a considerable improvement over the typically applied MC approach in terms of accuracy and convergence time. Figure 12: Relation of holding cost with respect to the network complexity in terms of the policy used and the customer satisfaction. Figure 13: Fitness function improvements. Hence, it can be considered as a viable alternative to the traditional tuning procedures, especially in systems with irregular topologies. For the sake of clearer visualization, the reported numerical studies showed systems consisting of a relatively small number of nodes, i.e., a few, or a dozen. This scale may either reflect a small distribution network, e.g., a regional store network, or serve as a projection of an extended one (e.g., a continent divided into countries or a country divided into states). Strenuous tests of the CGA-based optimization of the interconnection structures involving hundreds or thousands of nodes is an area for further research. The analysis of the execution time indicated that such structures might require parallelization techniques to conduct the computations. From the managerial perspective, the conducted research offered a few important insights. First, it was evidenced that in the considered class of systems, the application of a centralized OUT policy was economically more efficient than the distributed one, although it required a common view of the system. The greater the structural complexity, the bigger the economic profits that were gained in the centralized approach. The CGA-based optimization may be flexibly adapted according to diverse system requirements. The applied fitness function allows system managers to smoothly balance the optimization objectives, notably, the customer satisfaction vs. the operational costs, using just two numerical coefficients. In particular, a simultaneous increase of both coefficients enables achieving full customer satisfaction with maximum economic savings. Moreover, in the proposed framework, the objectives can be redefined, or replaced, without altering the computational scheme itself. The framework can also be customized to support other inventory control policies besides OUT, albeit with different search-space constraints and other fitness functions that balance the optimization goals would need to be specified. There are a few directions in which the presented research could be extended. One may address the robustness issues, e.g., how to adjust the CGA for a yet more involved case of networks with uncertain, time-varying parameters and topologies (inaccurate inventory records, node failures, etc.). Furthermore, other evolutionary algorithms may be implemented and compared with the discussed CGA-based optimization with respect to the time and efficiency when seeking the optimal solution. Since in inventory management problems, one typically faces a number of conflicting goals, multi-objective optimization algorithms may also be considered. Conceptualization, P.I. and L.W. ; methodology, P.I. ; software, L.W. ; validation, L.W.