Abstract
Search trajectory networks (STNs) were proposed as a tool to analyze the behavior of metaheuristics in relation to their exploration ability and the search space regions they traverse. The technique derives from the study of fitness landscapes using local optima networks (LONs). STNs are related to LONs in that both are built as graphs, modelling the transitions among solutions or group of solutions in the search space. The key difference is that STN nodes can represent solutions or groups of solutions that are not necessarily locally optimal. This work presents an STN-based study for a particular combinatorial optimization problem, the cyclic bandwidth sum minimization. STNs were employed to analyze the two leading algorithms for this problem: a memetic algorithm and a hyperheuristic memetic algorithm. We also propose a novel grouping method for STNs that can be generally applied to both continuous and combinatorial spaces.
Highlights
O BSERVING the inner dynamics of metaheuristics is crucial for a better understanding of how these algorithms differentiate from each other on the way they explore the search space, and how those differences relate to their performance under specific scenarios
For constructing the search trajectory networks (STNs), we record the transitions between representative solutions that occur when the memetic algorithm (MA) and dynamic multi-armed bandit (DMAB)+MA algorithms, described in Section IV, are used for solving the selected cyclic bandwidth sum problem (CBSP) instances
Search space partitioning is an essential step during the construction of STNs models, which consists in mapping
Summary
O BSERVING the inner dynamics of metaheuristics is crucial for a better understanding of how these algorithms differentiate from each other on the way they explore the search space, and how those differences relate to their performance under specific scenarios This is increasing in relevance, as in recent years numerous novel metaheuristics have been proposed. Very promising results have been obtained by such proposals, causing a growing interest in extending their applications and increasing the need for analysis tools to effectively characterize their behavior On this matter, search trajectory networks (STNs) [15], [16] are a relatively novel analysis tool for gaining a better perspective on the inner search dynamics of metaheuristics in relation to how they explore the search space of a particular problem instance. STNs constitute a metaphor-free attempt at profiling metaheuristics
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