روش اﭘﺴﯿﻠﻦ ﻣﺤﺪودﯾﺖ اﺻﻼحﺷﺪه ﺑﺮاي ﻣﺴﺎﺋﻞ ﺑﻬﯿﻨﻪﺳﺎزي دو ﻫﺪﻓﻪ: ﮐﺎﻫﺶ ﭘﯿﭽﯿﺪﮔﯽ ﻣﺤﺎﺳﺒﺎﺗﯽ و اﻓﺰاﯾﺶ ﮐﺎراﯾﯽ

Modified ε-constraint method for bi-objective optimization: Reduce computational complexity and increase efficiency

ﯾﮑﯽ از روشﻫﺎي ﻣﺆﺛﺮ در ﺣﻞ ﻣﺴﺎﺋﻞ ﺑﻬﯿﻨﻪﺳﺎزي ﭼﻨﺪﻫﺪﻓﻪ، روش -ﻣﺤﺪودﯾﺖ ﻣﯽﺑﺎﺷﺪ ﮐﻪ ﺑﺮ ﺧﻼف روش ﻣﺠﻤﻮعوزندار ﺷﺪه ﻗﺎدر ﺑﻪ ﯾﺎﻓﺘﻦ ﻧﻘﺎط ﻏﯿﺮﻣﻐﻠﻮب در ﻗﺴﻤﺖﻫﺎي ﻧﺎﻣﺤﺪب از ﻣﺮز ﻏﯿﺮﻣﻐﻠﻮب اﺳﺖ. از ﻣﻌﺎﯾﺐ ﻋﻤﺪهي اﯾﻦ روش ﯾﺎﻓﺘﻦ ﻧﻘﺎط ﻏﯿﺮﻣﻐﻠﻮب ﺗﮑﺮاري ﺑﻪ ازاي اﻧﺘﺨﺎب ﭘﺎراﻣﺘﺮﻫﺎي ﻣﺘﻔﺎوت و در ﻧﺘﯿﺠﻪ اﻓﺰاﯾﺶ ﭘﯿﭽﯿﺪﮔﯽ ﻣﺤﺎﺳﺒﺎﺗﯽ اﻟﮕﻮرﯾﺘﻢ و ﮐﺎﻫﺶ ﮐﺎراﯾﯽ آن در ﺣﺎﻟﺖ ﮐﻠﯽ اﺳﺖ ﮐﻪ ﺑﻪ ﻟﺤﺎظ زﻣﺎن و ﻫﺰﯾﻨﻪ ﭘﯿﺎدهﺳﺎزي ﻣﻘﺮون ﺑﻪﺻﺮﻓﻪ ﻧﯿﺴﺖ. در اﯾﻦ ﻣﻘﺎﻟﻪ اﺻﻼﺣﯽ ﺑﺮ روش -ﻣﺤﺪودﯾﺖ اﻧﺠﺎم ﻣﯽﮔﯿﺮد ﮐﻪ ﺑﻪ واﺳﻄﻪي ﻫﻮﺷﻤﻨﺪﺳﺎزي اﻟﮕﻮرﯾﺘﻢ، ﻧﻮاﺣﯽ ﻏﯿﺮﺿﺮوري ﮐﻪ ﻣﻨﺠﺮ ﺑﻪ ﺗﻮﻟﯿﺪ ﻧﻘﺎط ﻏﯿﺮﻣﻐﻠﻮب ﺗﮑﺮاري ﻣﯽﺷﻮﻧﺪ، از ﻫﻤﺎن اﺑﺘﺪا ﺣﺬف ﻣﯽﮔﺮدﻧﺪ و در ﻧﺘﯿﺠﻪ ﻟﺰوم ﺗﻼشﻫﺎي ﻣﺤﺎﺳﺒﺎﺗﯽ اﺿﺎﻓﯽ ﺟﻬﺖ ﯾﺎﻓﺘﻦ ﻧﻘﺎط ﻏﯿﺮﻣﻐﻠﻮب ﺗﮑﺮاري ﻣﻨﺘﻔﯽ ﻣﯽﺷﻮد. ﻣﺒﺎﺣﺚ و ﺟﺰﯾﯿﺎت روش ﭘﯿﺸﻨﻬﺎدي ﺑﻪ ﻫﻤﺮاه اﻟﮕﻮرﯾﺘﻢ آن، اراﺋﻪ ﺷﺪه و در ﺑﺨﺶ ﻣﺜﺎل ﻋﺪدي، ﮐﺎراﯾﯽ روش ﭘﯿﺸﻨﻬﺎدي در ﻣﻘﺎﯾﺴﻪ ﺑﺎ روش -ﻣﺤﺪودﯾﺖ، ﻣﻮرد ﺑﺮرﺳﯽ ﻗﺮار ﻣﯽﮔﯿﺮد.

One of the effective method for solving the multi-objective optimization problems is the ε-constraint method which, unlike the weighted sum method is able to find non-dominated points in non-convex parts of the non-dominated frontier. The main disadvantages of this method are finding similar non-dominated points for choosing different parameters and thus increasing the computational complexity of the algorithm and reducing its overall performance, which is not cost-effective in terms of time and cost. In this paper, a modified is made to ε-constraint method, which, due to the intelligence of the algorithm, the unnecessary areas that lead to the production of the same non-dominated points are eliminated from the beginning. Therefore, additional computational efforts are eliminated to produce the same non-dominated points. Discussions and details of the proposed method, with its algorithm, are presented and in the numerical examples section, the efficiency of the proposed method is compared with the ε-constraint method.