1模型介绍
一种基于蚁群算法的多配送中心车辆路径优化方法,首先,针对多配送中心车辆路径优化问题,对各个客户点设计了以最近配送中心为启发式信息的惩罚函数;其次,将具有上述启发式信息的罚函数加入到各配送点的信息素更新过程中,从而提高了算法的搜索效率.本发明在实际物流配送车辆路径优化应用中可以快速的得到可靠的最佳配送路径.
1.1 多中心VRP模型
1.2 蚁群算法原理
蚁群算法(AG)是一种模拟蚂蚁觅食行为的模拟优化算法，它是由意大利学者Dorigo M等人于1991年首先提出，并首先使用在解决TSP（旅行商问题）上。之后，又系统研究了蚁群算法的基本原理和数学模型1、蚂蚁在路径上释放信息素。
2、碰到还没走过的路口，就随机挑选一条路走。同时，释放与路径长度有关的信息素。
3、信息素浓度与路径长度成反比。后来的蚂蚁再次碰到该路口时，就选择信息素浓度较高路径。
4、最优路径上的信息素浓度越来越大。
5、最终蚁群找到最优寻食路径。
1.3 蚁群算法流程图
2 部分代码
% 锐镱朦珞 嚯泐痂蜢 祗疣恻桧 觐腩龛?潆 镱耱痤屙? 爨瘌痼蝾? 禧
% 镱耠邃钼囹咫??镳铞羼皴 恹镱腠屙? 嚯泐痂蜢? 疣玑桠噱?% 爨瘌痼螓 磬 镱潇囵篁? 桉躅? 桤 沭箸钼戾耱桁铖蜩 已
function [ Route, Length_Route, vehicles ] = ANT_colony_algorithm_VRP( ...
distances, distances_bases, demands, param, vehicles_capacity ...
)
clc
waitBar = waitbar(0,'Please wait...');
%%
%软桷栲腓玎鲨 溧眄
iter_max = 7; % 100/爨犟桁嚯铄 觐腓麇耱忸 栩屦圉栝
distances = add_bases_to_distances(distances, distances_bases);
vehicles_capacity = sort(vehicles_capacity,'descend'); %耦痱桊箦?沭箸忸忪羼蜩祛耱?爨??筢帼?镱?潢?demands = [vehicles_capacity(1) demands];
%耦玟噱?耱痼牝箴?溧眄 潆 已, 沅?狍潴?躔囗栩? 桴
%沭箸铒钿祉铖蜩 ?爨瘌痼螓
cell_capacities = vehicles_capacities_to_cellarray(vehicles_capacity); %耦躔囗屐 沭箸铒钿祉铖螯 赅驿钽?已
vehicles = struct('capacity',cell_capacities,'route',cell(1,length(vehicles_capacity)));
%桧桷栲腓玷痼屐 耱囵蝾怏?徉珞 潆 怦艴 已
for i = 1:length(vehicles)
vehicles(i).route = 1;
end
nvehicle = 1; %磬麒磬屐 ?1-泐 已
dim = length(distances); %觐腓麇耱忸 泐痤漕?Route = zeros(1,dim); %耦玟噱?爨耨桠 镱?狍潴?爨瘌痼?c = demands(1); %沭箸钼戾耱桁铖螯 1-钽?已
N_of_vehicles = length(vehicles);
evaporation_fer = param(1);%觐翳鲨屙?桉镟疱龛 翦痤祛磬 [0;1]
alpha = param(2); %橡?alpha = 0 狍溴?恹狃囗 犭桄嚅?泐痤? 黩?耦铗忮蝰蜮箦?驵漤铎?嚯泐痂?祗 ?觌囫耔麇耜铋 蝈铕梃 铒蜩扈玎鲨? 篷腓
beta = param(3); %beta = 0, 蝾沅?疣犷蜞弪 腓 翦痤祛眄铄 篑桦屙桢, 黩?怆鬻弪 玎 耦犷?猁耱痤?恹痤驿屙桢爨瘌痼蝾??钿眍祗 耋犷矧桁嚯铎?疱龛?
tau0 = param(4); %觐腓麇耱忸 翦痤祛磬
tau = zeros(dim); %爨蝠桷?觐腓麇耱忄 忤痱筻朦睇?翦痤祛眍?eta = zeros(dim); %"忤滂祛耱? 泐痤溧, 痂耱梓羼觐?驽豚龛?镱皴蜩螯 泐痤?j 桤 泐痤溧 i ?麇?犭桄?泐痤? 蝈?犷朦 驽豚龛?镱皴蜩螯 邈?
Q = 0; %镱?漕?潆桧?铒蜩爨朦眍泐 爨瘌痼蜞
N_ants = dim; %觐腓麇耱忸 祗疣恻邂
ants_in_cities = zeros(1, N_ants); %祗疣恻??泐痤溧?route_ants = zeros(N_ants, 2*N_ants + 1); %爨瘌痼?潆 赅驿钽?桤 祗疣恻邂
length_route_ants = zeros(1, N_ants);%潆桧?爨瘌痼蜞 潆 赅驿钽?桤 祗疣恻邂
entries_in_cities = zeros(1, dim); %爨耨桠 潆 铒疱溴脲龛, 猁?腓 祗疣忮??泐痤溴(1 - 猁? 0 - 礤 猁?
for i = 1:dim
for j = 1:dim
if i ~= j
eta(i,j) = 1/distances(i,j); %忤滂祛耱? tau(i,j) = tau0; %翦痤祛? else
tau(i,j) = 0;
end
end
end
%疣珈妁噱?赅驿钽?祗疣恻 ?耠篦嚅眍 恹狃囗睇?泐痤?
ants_in_cities = randperm(N_ants);
%蔓徼疣屐 篑腩忭?牮囹鬣轼栝 爨瘌痼?Route ?疣聍栩噱?邈?潆桧?Route = ants_in_cities;
Length_Route = length_of_route(Route, distances) * 10; %潆 筲屦屙眍耱? 黩??潆桧?礤 '耩噌铗噱?
Q = Length_Route;
P = zeros(1, dim); %忮痤蝽铖蜩 镱皴龛 祗疣恻 铗 1-泐 泐痤溧 漕 dim-泐 泐痤溧
%%
%----------------------铖眍忭铥?鲨觌---------------------------------------
for iter = 1: iter_max
for ant = 1: N_ants
%钺眍怆屐 沭箸钼戾耱桁铖蜩 已
nvehicle = 1;
c = vehicles(nvehicle).capacity;
%-----------------潆 赅驿钽?祗疣恻 耱痤桁 爨瘌痼??疣耨麒螓忄屐 邈?潆桧?-------
i = ants_in_cities(ant); %磬躅滂?耱囵蝾恹?泐痤?祗疣恻
q2 = demands(i); % 磬躅滂?玎镳铖 镳钿箨鲨?镱 泐痤潴(镳邃镱豚汔, 黩?玎镳铖 耱囵蝾忸泐 泐痤溧 礤 镳邂帼?沭箸铎羼蜩祛耱?爨睇)
entries_in_cities(i) = 1;
route_ants(ant, 1) = i;
ind_city_for_route_ant = 1; %镱?潢钼 眍戾?泐痤溧 ?爨瘌痼蝈
while ~all(entries_in_cities) %镱赅 羼螯 礤 镱皴眄 泐痤溧
ind_city_for_route_ant = ind_city_for_route_ant + 1; %镥疱躅滂??桧溴犟?耠邃. 泐痤潴
for j = 1: dim
%聍栩噱?忮痤蝽铖螯 镱躅溧 ?赅驿 礤 镱皴眄 泐痤? if entries_in_cities(j) == 0 %羼腓 礤 镱皴眄 泐痤? sum = 0;
for el = 1: dim
if entries_in_cities(el) == 0
sum = sum + (tau(i,el)^alpha * eta(i,el)^beta);
end
end
P(j) = (tau(i,j)^alpha * eta(i,j)^beta)/sum;
end
end
P(1) = 0; %钺眢?屐 徉珞 ?玎镟襦扈, 赅?磬桠屦?蝽彘?恹犷? %///
[~, city_ind_P_max] = max(P);%磬躅滂?爨犟桁嚯 屐屙??忮牝铕?忮痤蝽铖蝈? q1 = demands(city_ind_P_max);
if q1 + q2 <= c
route_ants(ant, ind_city_for_route_ant) = city_ind_P_max; %漕徉怆屐 泐痤??爨瘌痼?蝈牦泐 祗疣恻
entries_in_cities(city_ind_P_max) = 1;
i = city_ind_P_max; %耠邃. 泐痤?磬桠屦?蝽邋 ?扈? 疣耨蝾龛屐
q2 = q2 + q1;
else
route_ants(ant, ind_city_for_route_ant) = 1; %忸玮疣?磬 徉珞 玎镟耦? entries_in_cities(1) = 1;
i = 1; %忸玮疣?磬 徉珞
q2 = 0;
nvehicle = get_No_vehicle(nvehicle,N_of_vehicles);
c = vehicles(nvehicle).capacity;
end
%//
%__________________________________________________________
P = zeros(1, dim); %钺眢?屐 怦?忮痤蝽铖蜩 ?泐痤溧? %___________________________________________________________
end
route = [1, route_ants(ant, :)];
route(route == 0) = []; %筢桊噱?礤眢骓 眢腓
route(end + 1) = 1; %忸玮疣?磬 徉珞
length_route_ants(ant) = length_of_route(route, distances); %聍栩噱?潆桧?爨瘌痼蜞 蝈牦泐 祗疣恻
entries_in_cities = zeros(1, dim); %铗戾?屐 怦?镱皴龛 泐痤漕?镳邃簌邈?祗疣恻
%-------------------------------------------------------------------------------------
res = ((iter - 1)+(ant/N_ants))/(iter_max);
waitbar(res,waitBar,sprintf('Processing... %d %%',round(res*100)));
end
%___________________________袜殇屙?腓 疱龛?_____________________
[min_length_route, ind_min_len_route] = min(length_route_ants);
if Length_Route > min_length_route %羼腓 蝈牦 潆桧?爨瘌痼蜞 犷朦 磬殇屙眍泐 扈龛爨朦眍泐
Length_Route = min_length_route; %钺眍怆屐 潆桧?蝈牦泐 爨瘌痼蜞
route = [1, route_ants(ind_min_len_route, :)];
route(route == 0) = [];
Route = [route, 1]; %钺眍怆屐 磬桦篦?爨瘌痼? Route = delete_duplicates_stations(Route);
Q = Length_Route;
end
%__________________________________________________________________
%-----------吾眍怆屐 耠邃?翦痤祛磬--------------------------------
sum_delta_tau = zeros(dim);
for ant = 1: N_ants
delta_tau = zeros(dim); %觐腓麇耱忸 翦痤祛磬 磬 赅驿铎 桤 疱徨? for w = 1:length(route_ants(ant, :)) - 1
Ri = route_ants(ant, w); Ri(Ri == 0) = [];
Rj = route_ants(ant, w + 1); Rj(Rj == 0) = [];
i = Ri;
j = Rj;
delta_tau(i,j) = Q/length_route_ants(ant);
end
sum_delta_tau = sum_delta_tau + delta_tau;
end
tau = (1 - evaporation_fer) * tau + sum_delta_tau;
tau(1,1) = 0;
%-------------------------------------------------------------------
route_ants(:,:) = 0;
end
%%
delete(waitBar);
%%
vehicles = create_routes_for_vehicles(vehicles,Route);
%vehicles(1:end).route %桧纛痨圉? ?爨瘌痼蜞?潆 赅驿钽?已
%Length_Route
%create_plot_route_with_vehicles(distances,vehicles,demands);
%_______________________________________________________________________
%潆 恹忸溧 玎镳铖钼 镱蝠遽栩咫彘
% sum_demands = 0;
% for i = 1:length(Route)
% if Route(i) == 1
% sum_demands
% sum_demands = 0;
% else
% sum_demands = sum_demands + demands(Route(i));
% end
% end
%_______________________________________________________________________
end
function [vehicles] = create_routes_for_vehicles(vehicles,ROUTE)
nvehicle = 1; %磬麒磬屐 ?1-泐 已
N_of_vehicles = length(vehicles);
bases = find(ROUTE == 1); %棂屐 桧溴犟??徉珙??爨瘌痼蝈
for i = 1:length(bases) - 1
ind_start = bases(i) + 1;
ind_end = bases(i + 1);
vehicles(nvehicle).route = [ vehicles(nvehicle).route ROUTE(ind_start:ind_end)];
nvehicle = get_No_vehicle(nvehicle, N_of_vehicles);
end
end
%项塍鬣屐 眍戾?已(镱耠邃钼囹咫?
function [nvehicle] = get_No_vehicle(nvehicle, N_of_vehicles)
nvehicle = nvehicle + 1;
if nvehicle > N_of_vehicles
nvehicle = 1; %磬麒磬屐 ?1-泐 已
end
end
%恹麒耠屐 镳铗驽眄铖螯 怦邈?爨瘌痼蜞 潆 已
function [ length_of_path ] = length_of_route_for_vehicles( vehicles, distances)
length_of_path = 0;
for k = 1:length(vehicles)
route = vehicles(k).route;
for i = 1:length(route) - 1
length_of_path = length_of_path + distances(route(i),route(i + 1));
end
end
end
%恹麒耠屐 镳铗驽眄铖螯 怦邈?爨瘌痼蜞
function [ length_of_path ] = length_of_route( route, distances)
length_of_path = 0;
for m = 1:length(route) - 1
length_of_path = length_of_path + distances(route(m),route(m + 1));
end
end
3 仿真结果
4 参考文献
[1]唐增明. 基于蚁群算法的多中心车辆调度问题研究[D]. 桂林电子科技大学, 2007.