1 內容介紹

非傳統的優化工具已經證明了它們在解決各種優化問題方面的潛力。這些問題處理單個目標或多個/多個目標。倭黑猩猩優化器（BO）是一種智能自適應元啟發式優化算法，靈感來自倭黑猩猩的社會行為和繁殖策略。文獻中沒有研究擴展這個 BO 來解決多目標優化問題。本文提出了一種多目標 Bonobo 優化器 (MOBO) 來解決不同的優化問題。本文提出了三個不同版本的 MOBO，每個版本都使用不同的方法，例如自適應網格方法的非支配排序；一種使用擁擠距離方法對人口進行排序的排序方案；分解技術，其中解決方案是通過將一個多目標問題分解為多個單目標問題來獲得的。提議的 MOBO 的所有三個不同版本的性能已經在一組 30 個多樣化的基準測試功能上進行了測試，并將結果與文獻中可用的其他四種著名的多目標優化技術的結果進行了比較。獲得的結果表明，與其他算法相比，所提出算法的前兩個版本在收斂性和多樣性方面表現出色或具有競爭力。

tled attacker, barrier, chaser, and driver are employed for simulating the diverse intelligence. Moreover, the four main steps of hunting, driving, blocking, and attacking, are implemented. Afterward, the algorithm is tested on 30 well-known benchmark functions, and the results are compared to four newly proposed meta-heuristic algorithms in term of convergence speed, the probability of getting stuck in local minimums, and the accuracy of obtained results. The results indicate that the ChOA outperforms the other benchmark optimization algorithms.

2 仿真代碼

% This is the matlab code for the optimization algorithm, namely Bonobo Optimizer (BO).

% This is written for solving unconstrained optimization problems. However, it can also solve constrained optimization

% problems with penalty function approaches.?

% Moreover, this for solving minimization problems.

% For details of the BO algorithm, kindly refer and cite as mentioned below:

% A. K. Das and D. K. Pratihar, "Bonobo optimizer (BO): an intelligent heuristic with selfadjusting parameters over continuous spaces and its applications to engineering problems,"?

% Applied Intelligence, 2021, DOI: 10.1007/s10489-021-02444-w

% For any query, please email to: amit.besus@gmail.com

clc;close all;clear all;

tic;? ?% CPU time measure

CostFunction = @(x)MyObjectiveFunction(x); % Objective function?

d=4;? % No. of Variables

Var_min=[-100 -100 -100 -100];? % Lower variable Boundaries

Var_max=[100 100 100 100];? ?% Upper variable Boundaries

%% Common parameters of? BO similar to? other optimization algorithms

N=30; % No. of bonobos in the population, i.e. population size

max_it=100;? % Maximum number of iterations

[bestcost,alphabonobo,convergence_curve]=BO(N,d,Var_min,Var_max,max_it,CostFunction);

disp(['Best Cost: ' num2str(bestcost)]);

disp(['Bestsolution: ' num2str(alphabonobo)]);

figure

plot (1:max_it,convergence_curve,'-*')

title('Convergence Curve')

xlabel('Number of iterations')

ylabel('Evolution of best objective value')

toc;

3 運行結果

4 參考文獻

[1] Das A K ,? Nikum A K ,? Krishnan S V , et al. Multi-objective Bonobo Optimizer (MOBO): an intelligent heuristic for multi-criteria optimization[J]. Knowledge and Information Systems, 2020, 62(6).?

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