## Overview of whale optimization algorithm

Whale Optimization Algorithm (WOA) is a meta heuristic algorithm based on humpback whale hunting method proposed by Mirjalili in 2016. It has been successfully applied to various complex discrete optimization problems, such as resource scheduling problem, construction site workflow planning, location and path planning, neural network training and so on. In terms of algorithm improvement and application, Yan Xu et al. Proposed a hybrid stochastic quantum Whale Optimization Algorithm to solve TSP problem; Teng Deyun and others improved Whale Optimization Algorithm by combining Whale Optimization Algorithm with topology to solve multi-objective reactive power optimization scheduling problem; Tu Chunmei et al. Proposed chaotic feedback adaptive optimization algorithm; Liu zhusong et al. Proposed positive co chaotic double string optimization algorithm (CSCWOA); Zhong Minghui et al. Proposed an efficient optimization algorithm for randomly adjusting control parameters

## WOA

WOA can be used to solve continuity optimization problems. Therefore, by investigating the express delivery situation of several express companies in Jinzhou City, it is found that customer satisfaction and distribution efficiency are not ideal, mainly because each customer point has different time periods for receiving express mail, resulting in the back and forth of couriers and unnecessary time waiting, which not only greatly reduces the distribution efficiency of couriers, At the same time, it also greatly reduces customer satisfaction. Therefore, this paper introduces the greedy exchange mechanism into the whale optimization algorithm, establishes the express terminal distribution path model with time window based on the greedy whale optimization algorithm (GWOA), and solves the example. The results show that GWOA has better convergence speed and better local optimization ability.

## Express terminal distribution

Description of routing problem the express terminal distribution routing problem can be described as: the courier starts from the distribution center (express distribution network), sends the customer's goods to each customer point along a specific route, and then needs to return to the starting point (express distribution network point) before a fixed time. During this period, couriers can choose short distance and time-saving routes to complete express delivery according to their own experience, or give priority to some customers according to their special needs. The premise is to ensure that all customer points are served before the specified time and can only be served once. Therefore, the express terminal distribution path should be reasonably planned to achieve the shortest distribution time, shortest distribution route distance, lowest distribution cost and maximum customer satisfaction under the constraints of meeting customer time window, customer demand, load limit of distribution vehicles and maximum driving distance of express vehicles.

tic clear clc %% use importdata This function reads the file data=importdata('input.txt'); cap=160; %% Extract data information vertexs=data(:,2:3); %Coordinates of all points x and y customer=vertexs(2:end,:); %Customer coordinates cusnum=size(customer,1); %Number of customers v_num=3; %Initial number of vehicles used demands=data(2:end,4); %requirement h=pdist(vertexs); dist=squareform(h); %Distance matrix %% Whale optimization algorithm parameters NIND=100; %Population number MAXGEN=300; %Maximum number of iterations N=cusnum+v_num-1; %Whale individual length=Number of customers+Maximum number of vehicles used-1 belta=10; %Penalty function coefficient for violation of load constraint %% Population initialization init_vc=init(cusnum,demands,cap,dist); %structure OVRP Initial solution population=init_pop(NIND,N,cusnum,init_vc); %% Route and total distance of output random solution obj=obj_function(population,cusnum,cap,demands,dist,belta); [min_obj,min_index]=min(obj); disp('Optimal individual in initial population:') [currVC,NV,TD,violate_num,violate_cus]=decode(population(min_index,:),cusnum,cap,demands,dist); %Initial decoding disp(['Number of vehicles used:',num2str(NV),'，Total vehicle distance:',num2str(TD),'，Number of constraint violation paths:',num2str(violate_num),'，Number of customers violating constraints:',num2str(violate_cus)]); disp('~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~') %% Main cycle gen=1; %Counter initialization bestInd=population(min_index,:); %Initialize global optimal individual bestObj=min_obj; %Initial global optimal individual objective function value BestPop=zeros(MAXGEN,N); %Record the global optimal individual in each iteration BestObj=zeros(MAXGEN,1); %Record the objective function value of the globally optimal individual in each iteration BestTD=zeros(MAXGEN,1); %Record the total distance of the globally optimal individual in each iteration while gen<=MAXGEN %% Update whale population location for i=1:NIND p=rand; %0~1 Random number between if p<0.5 population(i,:)=cross1(population(i,:),bestInd,cusnum,cap,demands,dist,belta); elseif p>=0.5 population(i,:)=cross2(population(i,:),bestInd,cusnum,cap,demands,dist,belta); end end %% Local search operation population=local_search(population,cusnum,cap,demands,dist,belta); %% Calculate the objective function value of the current whale population obj=obj_function(population,cusnum,cap,demands,dist,belta); [min_obj,min_index]=min(obj); minInd=population(min_index,:); %% Update the global optimal individual if min_obj<bestObj bestInd=minInd; bestObj=min_obj; end BestPop(gen,:)=bestInd; BestObj(gen,1)=bestObj; %% Displays the distribution scheme information decoded by the current global optimal individual disp(['The first',num2str(gen),'Generation global optimal solution:']) [bestVC,bestNV,bestTD,best_vionum,best_viocus]=decode(bestInd,cusnum,cap,demands,dist); disp(['Number of vehicles used:',num2str(bestNV),'，Total vehicle distance:',num2str(bestTD),'，Number of constraint violation paths:',num2str(best_vionum),'，Number of customers violating constraints:',num2str(best_viocus)]); fprintf('\n') BestTD(gen,1)=bestTD; %% Update calculator gen=gen+1; end %% Print the total cost change trend of the global optimal solution of each iteration of the outer loop figure; plot(BestObj,'LineWidth',1); title('Variation trend of individual objective function value of global optimal whale') xlabel('Number of iterations'); ylabel('Objective function value'); %% Print the global optimal solution roadmap. 1 means satisfied and 0 means dissatisfied draw_Best(bestVC,vertexs); toc