Update moo_stripped.ipynb

book/pages/moo_stripped.ipynb

@@ -1745,12 +1745,12 @@
     "#### Goal attainment\n",
     "If we define two fails for the power and CO<sub>2</sub> emissions, we can apply goal attainment. Those goals could be $460 \\text{ kW}$ for the generated power and $640 \\text{ g/kWh}$ for the CO<sub>2</sub> emissions. Now the objective function can as:\n",
     "\n",
-    "$$ \\mathop {\\min }\\limits_x \\left( 460 - \\max \\left( f_{\\text{power}}\\left( x \\right), f_{\\text{CO}_2\\text{ emissions}} \\left( x \\right) - 640 \\right) \\right)$$\n",
+    "$$ \\mathop {\\min }\\limits_x \\left( {\\max \\left( {460 - {f_{{\\rm{power}}}}\\left( x \\right),{f_{{\\rm{C}}{{\\rm{O}}_2}{\\rm{ emissions}}}}\\left( x \\right) - 640} \\right)} \\right)$$\n",
     "\n",
     "#### Pareto front\n",
     "Finally, we can find the pareto front by defining the problem as:\n",
     "\n",
-    "$$ \\mathop {\\min }\\limits_x \\left( {{\\delta }_{i}} \\cdot f_{\\text{power},\\text{normalized}}\\left( x \\right) +  \\delta_j \\cdot f_{\\text{CO}_2\\text{ emissions},\\text{normalized}}\\left( x \\right) \\right) $$\n",
+    "$$  \\mathop {\\min }\\limits_x \\left( - {{\\delta }_{i}} \\cdot f_{\\text{power},\\text{normalized}}\\left( x \\right) +  \\delta_j \\cdot f_{\\text{CO}_2\\text{ emissions},\\text{normalized}}\\left( x \\right) \\right) $$\n",
     "\n",
     "For normalization, we could take the value from our plot, but for more real-life complex problems the dimensions are higher and you cannot find the maximum and minimum of each single objective function. Therefore, let's estimate the maxima and minima as:\n",
     "\n",