Optimization of non-stationary Stackelberg models using a self-adaptive evolutionary algorithm

Los modelos de Juegos de Stackelberg engloban una importante familia de problemas de la Teoría de Juegos, que encuentra aplicaciones directas en economía. El principal objetivo es encontrar un equilibrio óptimo entre las decisiones que pueden tomar dos actores que se relacionan jerárquicamente. En general estos modelos son complejos de resolver dada su estructura jerárquica, y la frecuente aparición en estos de funciones objetivos o restricciones intratables analíticamente. Otra causa de dicha complejidad es la existencia de incertidumbre, particularmente debido a la variabilidad en el tiempo de las condiciones del mercado, estrategias de los competidores, entre otras. Un análisis de la literatura relacionada muestra muy pocos trabajos abordando estos problemas de optimización no estacionarios. En este sentido, la presente investigación propone una técnica meta-heurística auto-adaptativa para resolver modelos de Juegos de Stackelberg no estacionarios. Los resultados experimentales obtenidos muestran una mejoría significativa sobre un método existente.Stackelberg’s game models involve an important family of Game Theory problems with direct application on economics scenarios. Their main goal is to find an optimal equilibrium between the decisions from two actors that are related one to each other hierarchically. In general, these models are complex to solve due to their hierarchical structure and intractability from an analytical viewpoint. Another reason for such a complexity comes from the presence of uncertainty, which often occurs because of the variability over time of market conditions, adversary strategies, among others aspects. Despite their importance, related literature reflects a few works addressing this kind of non-stationary optimization problems. So, in order to contribute to this research area, the present work proposes a self-adaptive meta-heuristic method for solving online Stackelberg’s games. Experiment results show a significant improvement over an existing method

An evolutionary computational approach for the dynamic Stackelberg competition problems

Stackelberg competition models are an important family of economical decision problems from game theory, in which the main goal is to find optimal strategies between two competitors taking into account their hierarchy relationship. Although these models have been widely studied in the past, it is important to note that very few works deal with uncertainty scenarios, especially those that vary over time. In this regard, the present research studies this topic and proposes a computational method for solving efficiently dynamic Stackelberg competition models. The computational experiments suggest that the proposed approach is effective for problems of this nature

A Species-based Particle Swarm Optimization with Adaptive Population Size and Deactivation of Species for Dynamic Optimization Problems

Population clustering methods, which consider the position and fitness of the individuals to form sub-populations in multi-population algorithms, have shown high efficiency in tracking the moving global optimum in dynamic optimization problems. However, most of these methods use a fixed population size, making them inflexible and inefficient when the number of promising regions is unknown. The lack of a functional relationship between the population size and the number of promising regions significantly degrades performance and limits an algorithm’s agility to respond to dynamic changes. To address this issue, we propose a new species-based particle swarm optimization with adaptive population size and number of sub-populations for solving dynamic optimization problems. The proposed algorithm also benefits from a novel systematic adaptive deactivation component that, unlike the previous deactivation components, adapts the computational resource allocation to the sub-populations by considering various characteristics of both the problem and the sub-populations. We evaluate the performance of our proposed algorithm for the Generalized Moving Peaks Benchmark and compare the results with several peer approaches. The results indicate the superiority of the proposed method

A survey of multi-population optimization algorithms for tracking the moving optimum in dynamic environments

The solution spaces of many real-world optimization problems change over time. Such problems are called dynamic optimization problems (DOPs), which pose unique challenges that necessitate adaptive strategies from optimization algorithms to maintain optimal performance and responsiveness to environmental changes. Tracking the moving optimum (TMO) is an important class of DOPs where the goal is to identify and deploy the best-found solution in each environments Multi-population dynamic optimization algorithms are particularly effective at solving TMOs due to their flexible structures and potential for adaptability. These algorithms are usually complex methods that are built by assembling multiple components, each of which is responsible for addressing a specific challenge or improving the tracking performance in response to changes. This survey provides an in-depth review of multi-population dynamic optimization algorithms, focusing on describing these algorithms as a set of multiple cooperating components, the synergy between these components, and their collective effectiveness and/or efficiency in addressing the challenges of TMOs. Additionally, this survey reviews benchmarking practices within this domain and outlines promising directions for future research