**5. Conclusions and future work**

In this chapter the basic elements of a GA were reviewed to describe its application for different logistics and manufacturing problems. The routing problems, beyond the transportation context, can be applied on machine maintenance schemes or material changing services within production plants to minimize operational times. Also, they can be applied to improve the material flow through the warehouse, which is a main facility within the SC. Operations such as order-picking and bin-shelving can be optimized by modeling them as TSP instances [28].

On the other hand, the KP for selection of items is a problem shared with other contexts such as waste reduction in cutting processes, selection of investments and portfolios, decisions for capital budgeting and asset-backed securitization [29]. The

#### *Search Algorithms on Logistic and Manufacturing Problems DOI: http://dx.doi.org/10.5772/intechopen.96554*

PFSP has been also extended on other fields such as in scheduling of quality control tasks on different machines [30].

Thus, the relevance of solving these combinatorial problems, particularly those of large scale, is very important due to their impact in other science and industrial fields.

Within the search algorithms, the GA can provide very suitable results for these problems. However, as presented in Sections X.2, X.3., and X.4, final performance depends of the type of problem. While the GA can achieve mean error gaps under the 10% mark for TSP/CVRP, for the PFSP the GA can achieve near optimal results under the 1% mark.

These results were supported by extensive experiments which were performed with well-known test databases or libraries. In practice, these experiments also provide important feedback to consider alternative meta-heuristics or develop hybrid approaches for improvement of performance.

This is because, as reviewed, a single meta-heuristic or search algorithm may not be enough to solve all problems if near-optimality is required. In this case, hybridization between different methods have improved on the search mechanisms of meta-heuristics, either deterministic or stochastic. Also, the integration with mathematical programming (which implies an exact solving method) has provided innovative proposals to solve NP-hard problems [31].

Future work is extensive on this field because:


Thus, as a concluding remark, it can be stated that any advance on these algorithms can impact on different fields. Just to mention an important field within the current industry, meta-heuristics are playing an important role on the implementation of dynamic decision models within Industry/Manufacturing 4.0 systems. Within this context, recent works have reported the application and improvement of these search algorithms for cost-efficient deployment of computing systems in logistics centers [32], dynamic CVRP [33], and development of Digital-Twin platforms [34].
