A new optimization algorithm based on average and subtraction of the best and worst members of the population for solving various optimization problems

Abstract

In this paper, a novel evolutionary-based method, called Average and Subtraction-Based Optimizer (ASBO), is presented to attain suitable quasi-optimal solutions for various optimization problems. The core idea in the design of the ASBO is to use the average information and the subtraction of the best and worst population members for guiding the algorithm population in the problem search space. The proposed ASBO is mathematically modeled with the ability to solve optimization problems. Twenty-three test functions, including unimodal and multimodal functions, have been employed to evaluate ASBO’s performance in effectively solving optimization problems. The optimization results of the unimodal functions, which have only one main peak, show the high ASBO’s exploitation power in converging towards global optima. In addition, the optimization results of the high-dimensional multimodal functions and fixed-dimensional multimodal functions, which have several peaks and local optima, indicate the high exploration power of ASBO in accurately searching the problem-solving space and not getting stuck in nonoptimal peaks. The simulation results show the proper balance between exploration and exploitation in ASBO in order to discover and present the optimal solution. In addition, the results obtained from the implementation of ASBO in optimizing these objective functions are analyzed compared with the results of nine well-known metaheuristic algorithms. Analysis of the optimization results obtained from ASBO against the performance of the nine compared algorithms indicates the superiority and competitiveness of the proposed algorithm in providing more appropriate solutions.

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“…In ASBO, three movements are conducted sequentially in every iteration [26]. The first movement is toward the average location between the best solution and the worst solution.…”

“…One of the newest metaheuristic algorithms is the average and subtraction-based optimizer (ASBO). This algorithm was proposed by Dehghani in 2022 [26]. The core concept of this algorithm is to move toward the best solution and avoid the worst solution.…”

“…The core concept of this algorithm is to move toward the best solution and avoid the worst solution. This algorithm consists of three sequential movements in every iteration [26]. In the first phase, a movement toward the average between the best and worst solutions is conducted.…”

“…Studies conducted to improve or implement this algorithm have not existed yet. Moreover, in its first publication, ASBO is tested to solve the only theoretical mathematic problem [26]. Through simulation, ASBO outperformed GA, PSO, gravitational search algorithm (GSA), teaching learning-based optimization (TLBO), GWO, WOA, TSA, SHO, and MPA [26].…”

“…Moreover, in its first publication, ASBO is tested to solve the only theoretical mathematic problem [26]. Through simulation, ASBO outperformed GA, PSO, gravitational search algorithm (GSA), teaching learning-based optimization (TLBO), GWO, WOA, TSA, SHO, and MPA [26]. However, this algorithm has not been tested to solve real-world problems.…”