Multi-objective narwhal optimizer: a novel algorithm for multi-criterion optimization

Seyyid Ahmed Medjahed

doi:10.1007/s11227-026-08836-4

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Multi-objective narwhal optimizer: a novel algorithm for multi-criterion optimization

2026-09-01

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Seyyid Ahmed Medjahed *

Mourad Bouatouche

Fatima Boukhatem

DOI：10.1007/s11227-026-08836-4

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Abstract

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Metaheuristic algorithms inspired by natural and biological behaviors have demonstrated strong performance in solving complex optimization problems. However, many existing algorithms are primarily designed for single-objective optimization and, therefore, cannot directly address problems involving multiple conflicting objectives. This paper proposes the Multi-Objective Narwhal Optimizer (MONO), a Pareto-based extension of the recently developed Narwhal Optimizer for solving multi-objective optimization problems. The proposed MONO incorporates Pareto dominance, external archive management, adaptive multi-leader guidance, and crowding-distance-based diversity preservation to effectively balance convergence and exploration throughout the search process. The performance of MONO was evaluated on the CEC benchmark suite and compared with eight representative multi-objective optimization algorithms: NSGA-II, NSGA-III, RVEA, IBEA, SPEA2, MOGWO, MOPSO, and MOEA/D. Experimental evaluation was conducted using three widely adopted performance indicators: Inverted Generational Distance (IGD), Spacing (SP), and Maximum Spread (MS). The results demonstrate that MONO achieves improvements of up to 5.8% in IGD and 5.1% in SP. To demonstrate its practical applicability, MONO was further validated on gene selection tasks using five high-dimensional DNA microarray datasets (Colon, DLBCL, Leukemia, Lung, and Ovarian), on which it successfully identified compact and discriminative gene subsets for cancer classification .

Keywords:

Multi-objective optimization

Evolutionary algorithm

Multi-criterion optimization

Heuristic algorithm

Metaheuristic

Narwhal optimizer