optimization code on dummy variables (worked)

Tuesday afternoon

Author: yangdihan

optmize_dummy.m

@@ -0,0 +1,78 @@
+function [k,P,T,v] = optimize_dummy(l_a,l_b)
+    % scenario based
+    % l_a: lanes for ped on road A
+    % l_b: lanes for ped on road B
+
+    % road A is Balboa Blvd
+    % road B is Newport Blvd
+    % dummy variables/parameters
+
+    % we are using Q directly from liwei right now. We might want to change it
+    % after aug factor done
+
+    q_a_veh = 0.04; % veh/sec
+    q_b_veh = 0.03; % veh/sec
+
+    q_liwei = 1600/3600; % ped/sec
+
+    psg = 4; % ren/veh
+
+    % population in 4 shapes
+    P1 = 200;
+    P2 = 284;
+    P3 = 4000;
+    P4 = 16200;
+
+    V_on = 20000; % veh
+
+    Q_a_ped = l_a*q_liwei; % ped flow on A
+    Q_b_ped = l_b*q_liwei; % ped flow on B
+
+
+    % optimization
+    cvx_begin
+        variables k(1) T_a_veh(1) T_a_ped(1) T_b_veh(1) T_b_ped(1) P_a_ped(1) P_a_veh(1) P_a_out(1) P_b_ped(1) P_b_veh(1) P_b_out(1)
+
+        % k: percentage of people on big island to road A
+
+
+        maximize((4-l_a)*q_a_veh*T_a_veh + (4-l_b)*q_b_veh*T_b_veh)
+        subject to
+
+            % road A
+            P_a_ped == Q_a_ped*T_a_ped; % people get out in ped on A
+            P_a_veh == psg*(4-l_a)*q_a_veh*T_a_veh; % people get out in veh on A
+            P_a_out == P_a_veh+P_a_ped;
+
+            % road B
+            P_b_ped == Q_b_ped*T_b_ped; % people get out in ped on B
+            P_b_veh == psg*(4-l_b)*q_b_veh*T_b_veh; % people get out in veh on B
+            P_b_out == P_b_veh+P_b_ped;
+
+            % in flow = out flow, every one out!
+            P_a_out == P4*k + P1;
+            P_b_out == P4*(1-k) + P2 + P3;
+
+            % time within 4 hours
+            T_a_veh <= 14400;
+            T_a_ped <= 14400;
+            T_b_veh <= 14400;
+            T_b_ped <= 14400;
+            T_a_veh >= 0;
+            T_a_ped >= 0;
+            T_b_veh >= 0;
+            T_b_ped >= 0;
+
+            % count vehicles
+            (4-l_a)*q_a_veh*T_a_veh + (4-l_b)*q_b_veh*T_b_veh <= V_on; % cannot use more cars
+
+            % split factor
+            k >= 0;
+            k <= 1;
+    cvx_end
+    
+    P = [P_a_ped; P_a_veh; P_a_out; P_b_ped; P_b_veh; P_b_out];
+    T = [T_a_veh; T_a_ped; T_b_veh; T_b_ped];
+    v = (4-l_a)*q_a_veh*T_a_veh + (4-l_b)*q_b_veh*T_b_veh;
+    return
+end

scenario.m

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+clear
+clc
+
+P_a_ped = zeros(5);
+P_a_veh = zeros(5);
+P_a_out = zeros(5);
+P_b_ped = zeros(5);
+P_b_veh = zeros(5);
+P_b_out = zeros(5);
+T_a_veh = zeros(5);
+T_a_ped = zeros(5);
+T_b_veh = zeros(5);
+T_b_ped = zeros(5);
+K = zeros(5);
+V = zeros(5);
+
+for l_a = 0:4
+    for l_b = 0:4
+        [k,P,T,v] = optmize_dummy(l_a,l_b);
+        K(l_a+1,l_b+1) = k;
+        V(l_a+1,l_b+1) = v;
+        P_a_ped(l_a+1,l_b+1) = P(1);
+        P_a_veh(l_a+1,l_b+1) = P(2);
+        P_a_out(l_a+1,l_b+1) = P(3);
+        P_b_ped(l_a+1,l_b+1) = P(4);
+        P_b_veh(l_a+1,l_b+1) = P(5);
+        P_b_out(l_a+1,l_b+1) = P(6);
+        T_a_veh(l_a+1,l_b+1) = T(1);
+        T_a_ped(l_a+1,l_b+1) = T(2);
+        T_b_veh(l_a+1,l_b+1) = T(3);
+        T_b_ped(l_a+1,l_b+1) = T(4);
+    end
+end
+
+P_a_ped = int64(P_a_ped);
+P_a_veh = int64(P_a_veh);
+P_a_out = int64(P_a_out);
+P_b_ped = int64(P_b_ped);
+P_b_veh = int64(P_b_veh);
+P_b_out = int64(P_b_out);
+T_a_veh = round(T_a_veh/3600, 1);
+T_a_ped = round(T_a_ped/3600, 1);
+T_b_veh = round(T_b_veh/3600, 1);
+T_b_ped = round(T_b_ped/3600, 1);
+V = int64(V);