Introduction

Non-traditional optimization tools have proved their potential in solving various types of optimization problems. These problems deal with either single objective or multiple/many objectives. Bonobo Optimizer (BO) is a metaheuristic optimization algorithm inspired from the social behaviour and reproductive strategies of Bonobos. There is no study in literature to extend this BO to solve multi-objective optimization problems.

This project is an experiment to extend the proposed and well-performing Bonobo Optimizer to solve multi-objective optimization problems (MOPs).

# Solution Approach

Multi-Objective Bonobo Optimizer (MOBO) was proposed to solve different multi-objective optimization problems. Three different versions of MOBO each using a different approach, such as non-dominated sorting with adaptation of grid approach to maintain diversity; a ranking scheme for sorting of population with crowding distance approach to maintain diversity; decomposition technique, wherein the solutions are obtained by dividing a multi-objective optimization problem into a number of single objective problems. The algorithms were developed in MATLAB.

The performances of all three different versions of the proposed MOBO had been tested on a set of thirty benchmark test functions, such as DTLZ functions, ZDT functions, etc , taken from literature. The results were compared with four other famous and well-performing multi-objective optimization algorithms available in literature, such as Non-Dominated Sorting Genetic Algorithm - II (NSGA-II), Multi-Objective Particle Swarm Optimization (MOPSO), Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) and Multi-Objective Grey Wolf Optimizer (MOGWO). Performance indices like inverse generational distance (IGD), Maximum Spread (MS), Spacing Metric (SP) and HyperVolume (HV) were used for comparison. These standard metrics basically evaluates how the algorithms perform based upon their exploration and exploitation tendency.

Non-parametric statistical tests were conducted to determine the relative ranks of the algorithms based on their performances. These statistical tests include Friedman, Aligned Friedman and Quade tests for multiple comparisons. Contrast estimation results were obtained for the algorithms.

The performance of the MOBO was found to be dependent not only on performance of BO but also on the framework or strategy used for converting BO into MOBO. From our experiments, it was found out that the MOBO with non-dominated sorting with adaptation of grid approach to maintain diversity performed superior in comparison to other algorithms.

TODO: Add images

Link to MOBO paper

Link to BO paper