Efficient Genetic Algorithms for Target Set Selection with Power-Law Parameters and Greedy Heuristics

핵심 개념

Simple randomized parameter choices and elementary greedy heuristics can outperform complex algorithms and costly parameter tuning for the target set selection problem.

초록

The content presents two modifications to the biased random-key genetic algorithm (BRKGA) for solving the target set selection (TSS) problem, which is an NP-hard graph optimization problem.

The first modification is to choose the BRKGA parameters randomly during the run, using a power-law distribution. This avoids the need for costly parameter tuning, as done in the original BRKGA. The second modification is a simple greedy heuristic called reverseMDG, which aims to reduce the size of valid target sets by greedily removing low-degree vertices.

The authors show that the BRKGA with these two modifications, called fastBRKGA+rev, consistently outperforms the state-of-the-art algorithms, including the original tuned BRKGA, the max-min ant system (MMAS), and the MMAS with Q-learning and a graph convolutional network. This is achieved without any costly offline computations.

The results demonstrate that easy adjustments can significantly improve the quality of TSS heuristics. The insights on using power-law distributed parameter choices and simple problem-specific heuristics are not limited to the TSS problem and can be applied to other optimization problems as well.

통계

The number of vertices |V| and edges |E| for the various social network instances used in the experiments.

인용구

"Besides providing a superior algorithm for the TSS problem, this work shows that randomized parameter choices and elementary greedy heuristics can give better results than complex algorithms and costly parameter tuning."
"Our first modification is to simply choose all parameters of the BRKGA in each iteration randomly from a power-law distribution. The resulting parameterless BRKGA is already competitive with the tuned BRKGA, as our experiments on the previously used benchmarks show."
"We then add a natural greedy heuristic, namely to repeatedly discard small-degree vertices that are not necessary for reaching the whole graph. The resulting algorithm consistently outperforms all of the state-of-the-art algorithms."

핵심 통찰 요약

Superior Genetic Algorithms for the Target Set Selection Problem Based on Power-Law Parameter Choices and Simple Greedy Heuristics

by Benjamin Doe... 게시일 arxiv.org 04-08-2024

https://arxiv.org/pdf/2404.04018.pdf

더 깊은 질문

How can the power-law parameter tuning approach be extended to other optimization problems beyond the target set selection problem?

The power-law parameter tuning approach can be extended to other optimization problems by adapting the concept of choosing parameter values from a power-law distribution dynamically during the optimization process. This approach can be applied to various optimization algorithms, such as genetic algorithms, particle swarm optimization, simulated annealing, and more. By replacing the traditional fixed parameter values with dynamically chosen values from a power-law distribution, the algorithm can adapt and explore a wider range of parameter settings, potentially leading to better performance and convergence. This method can be particularly useful in optimization problems where the optimal parameter values are not known in advance or may vary during the optimization process.

What are potential drawbacks or limitations of relying solely on greedy heuristics like reverseMDG for the target set selection problem?

While greedy heuristics like reverseMDG can be effective in quickly finding locally optimal solutions, they have limitations that may impact their overall performance in the target set selection problem. Some potential drawbacks include:

Local Optima: Greedy heuristics are prone to getting stuck in local optima, especially in complex optimization landscapes where the globally optimal solution may not be reachable through a series of locally optimal choices.

Lack of Exploration: Greedy heuristics tend to exploit the current best solution without exploring other potential solutions. This can lead to suboptimal results, especially in problems with a large search space where exploration is crucial.

Limited Solution Quality: Greedy heuristics may not always find the best possible solution, as they make decisions based on immediate local improvements rather than considering the global optimization goal.

Sensitivity to Initial Solution: Greedy heuristics are sensitive to the initial solution provided, and a poor initial solution can lead to suboptimal results.

While reverseMDG can be a valuable component in optimization algorithms, it is essential to complement it with other strategies, such as randomization, diversification, and intensification, to overcome these limitations and improve the overall performance of the algorithm.

What other types of simple, problem-specific heuristics could be combined with genetic algorithms to further improve their performance on the target set selection problem?

In addition to reverseMDG, several other simple, problem-specific heuristics can be combined with genetic algorithms to enhance their performance on the target set selection problem. Some of these heuristics include:

Degree-based Selection: Prioritizing vertices with higher degrees during the selection process to increase the likelihood of activating more vertices in the target set.

Community Detection: Identifying and targeting communities or clusters within the graph to optimize the spread of influence and reachability of the target set.

Centrality Measures: Utilizing centrality measures like betweenness centrality or closeness centrality to identify critical vertices for inclusion in the target set.

Diversity Maintenance: Implementing mechanisms to maintain diversity in the population to prevent premature convergence and explore a wider range of solutions.

Local Search Operators: Incorporating local search operators to refine and improve candidate solutions found by the genetic algorithm, enhancing the quality of the final target set.

By combining these simple, problem-specific heuristics with genetic algorithms, researchers can leverage domain knowledge and problem characteristics to design more effective and efficient optimization strategies for the target set selection problem.