The transition from continuous swarm intelligence algorithms to discrete combinatorial domains remains a critical challenge in bio-inspired computing. Traditional binarization techniques frequently induce premature convergence in highly constrained landscapes. This paper presents a chaotic discretization framework that replaces the classical behavior of the two-step binarization technique to regulate the balance between exploration and exploitation. The proposal systematically integrates three leading continuous metaheuristics in the literature, with twenty-four binarization configurations, across three distinct NP-hard problem archetypes: capacity-constrained (0–1 Knapsack), sparse (Set Covering), and mathematically degenerate flat landscapes (Unicost Set Covering). Nonparametric statistical tests confirm that chaotic discretization acts as a powerful regulator in the landscape (p < 0.05). Empirical evidence shows that the highest-performing chaotic mapping is heavily influenced by the specific landscape morphology evaluated: the 0–1 Knapsack Problem is statistically optimized by the Circle map under standard rules; the Set Covering Problem achieves optimal median performance with the Tent map under elitist formulations, although severe matrix constraints ultimately force statistical ties; and the Unicost Set Covering Problem utilizes the nonlinear sequences of the sinusoidal map under complementary operators to break convergence stagnation.
Felipe Cisternas-Caneo, Broderick Crawford, Jorge Mendoza et al.· Biomimetics· 0 citations
Bio-inspired swarm metaheuristic algorithms constitute a widely used tool for solving complex optimization problems. However, the experimental characterization of their emergent behavior remains a methodological challenge. This study proposes an experimental framework for characterizing emergent behavior through swarm collective dynamics. The framework integrates complementary dynamic indicators and establishes relative diversity loss as a homogeneous criterion for defining equivalent comparison states across different search processes. The framework was evaluated using the Reptile Search Algorithm (RSA) and Draco Lizard Optimizer (DLO) as case studies, with Particle Swarm Optimization (PSO) serving as a reference algorithm. The results showed that swarm collective dynamics were associated with both the mathematical properties of the search landscape and the search mechanisms of each metaheuristic. Furthermore, relative diversity loss enabled the comparison of different metaheuristics within a common reference framework. In RSA, swarm reorganization occurred during the first iterations. DLO exhibited a more gradual evolution, whereas PSO showed an intermediate behavior between both dynamics. The proposed experimental framework provides a methodological basis for the experimental characterization of emergent behavior in swarm metaheuristics.
Solving problems associated with the efficient distribution and organization of resources has generated increasing interest in the scientific community. One of the most commonly used approaches consists of approximate solution techniques, which have been able to solve complex covering problems within acceptable computational time and cost. One of the benchmarks used to evaluate these approaches is the Set Covering Problem, which is an NP-hard combinatorial optimization problem. Among the techniques that have been investigated, metaheuristics play an important role. These methods are commonly developed for continuous search spaces and, in order to be applied to covering problems, must be modified to operate in discrete domains. This modification presents an important challenge: finding an appropriate transformation method that translates continuous solutions into binary solutions. This issue has been addressed through two main strategies: binarization using two-step schemes, and, in our proposal, the use of repair operators orchestrated according to their performance through an Adaptive Repair Selection Mechanism based on the multi-armed bandit framework. To evaluate our proposal, we selected the Binary Hunger Games Search metaheuristic because the relative quality of each individual determines its hunger level, which in turn regulates the movement of the population and the influence of the best solution found. Infeasible solutions are handled through a set of Tabu Search-based repair operators. Instead of applying a single repair rule throughout the entire execution, the proposed approach dynamically selects among these operators according to their observed contribution during the search. Each repair operator also incorporates Tabu memory to discourage repetitive decisions during feasibility restoration. The experiments were conducted using the classical Beasley benchmark instances for the Set Covering Problem.
Broderick Crawford, Hugo Caballero, Gino Astorga et al.· Biomimetics· 0 citations
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