Three on Three Optimizer: A New Metaheuristic with Three Guided Searches and Three Random Searches

Abstract

This paper presents a new swarm intelligence-based metaheuristic called a three-on-three optimizer (TOTO). This name is chosen based on its novel mechanism in adopting multiple searches into a single metaheuristic. These multiple searches consist of three guided searches and three random searches. These three guided searches are searching toward the global best solution, searching for the global best solution to avoid the corresponding agent, and searching based on the interaction between the corresponding agent and a randomly selected agent. The three random searches are the local search of the corresponding agent, the local search of the global best solution, and the global search within the entire search space. TOTO is challenged to solve the classic 23 functions as a theoretical optimization problem and the portfolio optimization problem as a real-world optimization problem. There are 13 bank stocks from Kompas 100 index that should be optimized. The result indicates that TOTO performs well in solving the classic 23 functions. TOTO can find the global optimal solution of eleven functions. TOTO is superior to five new metaheuristics in solving 17 functions. These metaheuristics are grey wolf optimizer (GWO), marine predator algorithm (MPA), mixed leader-based optimizer (MLBO), golden search optimizer (GSO), and guided pelican algorithm (GPA). TOTO is better than GWO, MPA, MLBO, GSO, and GPA in solving 22, 21, 21, 19, and 15 functions, respectively. It means TOTO is powerful to solve high-dimension unimodal, multimodal, and fixed-dimension multimodal problems. TOTO performs as the second-best metaheuristic in solving a portfolio optimization problem