Several real optimization problems are very difficult, and their optimal solutions cannot be found with a traditional method. Moreover, for some of these problems, the large number of decision variables is a major contributing factor to their complexity; they are known as Large-Scale Optimization Problems, and various strategies have been proposed to deal with them. One of the most popular tools is called Cooperative Co-Evolution, which works through a decomposition of the decision variables into smaller subproblems or variables subgroups, which are optimized separately and cooperate to finally create a complete solution of the original problem. This kind of decomposition can be handled as a combinatorial optimization problem where we want to group variables that interact with each other. In this work, we propose a Grouping Genetic Algorithm to optimize the variable decomposition by reducing their interaction. Although the Cooperative Co-Evolution approach is widely used to deal with unconstrained optimization problems, there are few works related to constrained problems. Therefore, our experiments were performed on a test benchmark of 18 constrained functions under 100, 500, and 1000 variables. The results obtained indicate that a Grouping Genetic Algorithm is an appropriate tool to optimize the variable decomposition for Large-Scale Constrained Optimization Problems, outperforming the decomposition obtained by a state-of-the-art genetic algorithm.

Sustainable rural development seeks to balance social, economic, and environmental needs in rural areas, improving the quality of life of communities and the long-term protection of natural resources. Indigenous local solutions give place to grassroots entrepreneurial initiatives, which together with associative and economic integration are key factors for agricultural production, transformation of products, self-consumption, and commercialization. This study was done in Hñähñu communities with the aim to test if participative workshops based on detonating questions are an effective approach for developing entrepreneurship agriculture initiatives of self-managed social enterprises. The initiatives were proposed by the communities to solve local problems. Three initiatives arose: (1) a community seed bank of local species associated with the Milpa including agave; (2) reforestation with agave to produce agave shoots, leaves, and sap; and (3) a company to produce agave-sap syrup. The participants, based on their traditional knowledge, developed the projects, including economic evaluation, risk analysis, and environmental aspects. Some impacts are the conservation of soil and endangered landraces, accessibility to quality seeds not commercially available, building of local organizational and entrepreneurial capacities, strengthening the community, improving the family’s income, recovery of traditional agroecological techniques, and conservation of agrobiodiversity. In conclusion, the methodology is effective for the Indigenous communities to develop initiatives for sustainable self-managed social enterprises.

This work presents a knowledge discovery approach through Causal Bayesian Networks for understanding the conditions under which the performance of an optimization algorithm can be affected by the characteristics of the instances of a combinatorial optimization problem (COP). We introduce a case study for the causal analysis of the performance of two state-of-the-art algorithms for the one-dimensional Bin Packing Problem (BPP). We meticulously selected the set of features associated with the parameters that define the instances of the problem. Subsequently, we evaluated the algorithmic performance on instances with distinct features. Our analysis scrutinizes both instance features and algorithm performance, aiming to identify causes influencing the performance of the algorithms. The proposed study successfully identifies specific values affecting algorithmic effectiveness and efficiency, revealing shared causes within some value ranges across both algorithms. The knowledge generated establishes a robust foundation for future research, enabling predictions of algorithmic performance, as well as the selection and design of heuristic strategies for improving the performance in the most difficult instances. The causal analysis employed in this study did not require specific configurations, making it an invaluable tool for analyzing the performance of different algorithms in other COPs.

The Grouping Genetic Algorithm with Controlled Gene Transmission (GGA-CGT) is among the most effective algorithms for solving the one-dimensional Bin Packing Problem (1D-BPP), a classical NP-hard combinatorial optimisation problem with numerous industrial and logistical applications. This study aims to identify the characteristics that enable a mutation operator to perform better within this algorithm by implementing five state-of-the-art mutation operators: Elimination, Merge & Split, Swap, Insertion, and Item Elimination. Performance was evaluated in terms of the number of optimal solutions obtained. Our findings indicate that the GGA-CGT performs best with the least disruptive operators and that both the gene selection strategy and the item selection strategy can enhance the performance of mutation operators. These findings were validated by redesigning and improving a state-of-the-art item-oriented operator, achieving a 26% improvement over the best baseline version of the same operator.