ارائه الگوريتم جست‌وجوي گرانشي مقيد و حل مسأله مسيريابي وسايل نقليه

Proposing a Constrained-GSA for the Vehicle Routing Problem

اﻣﺮوزه ﻣﺴﺄﻟﻪ ﻣﺴﯿﺮﯾﺎﺑﯽ وﺳﺎﯾﻞ ﻧﻘﻠﯿﻪ، ﯾﮑﯽ از ﻣﻮﺿﻮﻋﺎت ﭘﺮﮐﺎرﺑﺮد در ﻣﻮﺿﻮﻋﺎت ﺻﻨﻌﺘﯽ، ﻧﻈﺎﻣﯽ و ﺣﺘﯽ اﻣﻨﯿﺘﯽ اﺳﺖ و ﺑﺮاي اﻓﺰاﯾﺶ ﮐﺎراﯾﯽ و ﺑﻬﺮهوري ﺳﺎﻣﺎﻧﻪﻫﺎي ﺣﻤﻞ و ﻧﻘﻞ ﺗﻌﺮﯾﻒ ﺷﺪه اﺳﺖ. ﻣﺴﺄﻟﻪ ﻣﺴﯿﺮﯾﺎﺑﯽ وﺳﯿﻠﻪ ﻧﻘﯿﻠﻪ ﺑﺎ ﺷﺮاﯾﻂ ﺑﺮداﺷﺖ و ﺗﺤﻮﯾﻞ ﻫﻢزﻣﺎن ﻣﺤﻤﻮﻟﻪ از ﺟﻤﻠﻪ اﯾﻦ ﻣﺴﺎﺋﻞ اﺳﺖ. اﯾﻦ ﻣﺴﺄﻟﻪ از ﻧﻈﺮ ﭘﯿﭽﯿﺪﮔﯽ ﻣﺤﺎﺳﺒﺎﺗﯽ در ﻣﺠﻤﻮﻋﻪ ﻣﺴﺎﺋﻞ ﺳﺨﺖ )NP-hard( ﻗﺮار ﻣﯽ ﮔﯿﺮد؛ ﺑﻨﺎﺑﺮاﯾﻦ ﻣﺤﺎﺳﺒﻪ ﺑﻬﺘﺮﯾﻦ ﭘﺎﺳﺦ ﺑﺮاي اﯾﻦ ﻣﺴﺄﻟﻪ، در زﻣﺎن ﻣﺤﺎﺳﺒﺎﺗﯽ ﻧﻤﺎﯾﯽ اﻧﺠﺎم ﺧﻮاﻫﺪ ﺷﺪ و در ﻣﺴﺎﺋﻞ اﺟﺮاﯾﯽ ﻗﺎﺑﻞ اﺳﺘﻔﺎده ﻧﺨﻮاﻫﺪ ﺑﻮد. اﺳﺘﻔﺎده از اﻟﮕﻮرﯾﺘﻢﻫﺎي ﻓﺮااﺑﺘﮑﺎري ﯾﮑﯽ از روشﻫﺎﯾﯽ اﺳﺖ ﮐﻪ ﺑﻪوﺳﯿﻠﻪ آﻧﻬﺎ ﻣﯽﺗﻮان ﺟﻮابﻫﺎﯾﯽ ﻣﻨﺎﺳﺐ و در زﻣﺎن ﻣﺤﺎﺳﺒﺎﺗﯽ ﻗﺎﺑﻞ ﻗﺒﻮل ﺑﻪدﺳﺖ آورد. در روشﻫﺎي ﻣﻮﺟﻮد، ﻗﯿﻮد ﻣﻮﺟﻮد در ﻣﺴﺄﻟﻪ، ﺑﺎ اﺳﺘﻔﺎده از روش ﺟﺮﯾﻤﻪ ﺑﻪ ﺗﺎﺑﻊ ﻫﺪف ﻣﺴﺄﻟﻪ اﺿﺎﻓﻪ ﺷﺪه و ﻣﺴﺄﻟﻪ ﺑﻬﯿﻨﻪﺳﺎزي ﺗﮏﻫﺪﻓﻪ ﺗﻌﺮﯾﻒ ﻣﯽﺷﻮد. ﺿﻤﻦ اﯾﻦﮐﻪ ﺗﻌﺪاد ﺑﻬﯿﻨﻪ وﺳﺎﯾﻞ ﻧﻘﻠﯿﻪ ﻣﻮرد ﻧﯿﺎز ﺑﺮاي ﺣﻞ ﻣﺴﺄﻟﻪ در ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﻧﻤﯽﺷﻮد. در اﯾﻦ ﻣﻘﺎﻟﻪ، اﻟﮕﻮرﯾﺘﻢ ﺟﺴﺖوﺟﻮي ﮔﺮاﻧﺸﯽ ﺑﻬﺒﻮدﯾﺎﻓﺘﻪ ﺑﺮاي ﺣﻞ ﻣﺴﺎﺋﻞ ﻣﻘﯿﺪ ﻣﻌﺮﻓﯽ ﺷﺪه اﺳﺖ. ﻫﻤﭽﻨﯿﻦ ﺑﻪﻣﻨﻈﻮر ﮐﻨﺘﺮل ﻗﺎﺑﻠﯿﺖﻫﺎي اﻟﮕﻮرﯾﺘﻢ ﻧﻈﯿﺮ ﮐﺎوش و ﺑﻬﺮهوري از ﯾﮏ ﮐﻨﺘﺮﻟﺮ ﻓﺎزي ﺑﺮاي ﺗﻌﯿﯿﻦ ﭘﺎراﻣﺘﺮﻫﺎي ﻣﻮﺟﻮد در اﻟﮕﻮرﯾﺘﻢ اﺳﺘﻔﺎده ﺷﺪه ، ﺳﭙﺲ، ﺑﺎ اﺳﺘﻔﺎده از اﯾﻦ اﻟﮕﻮرﯾﺘﻢ، روﺷﯽ ﺑﺮاي ﺣﻞ ﻣﺴﺄﻟﻪ ﻣﺴﯿﺮﯾﺎﺑﯽ وﺳﺎﯾﻞ ﻧﻘﻠﯿﻪ ﺑﺎ ﺷﺮاﯾﻂ ﺑﺮداﺷﺖ و ﺗﺤﻮﯾﻞ ﻫﻢزﻣﺎن اراﺋﻪ ﺷﺪه اﺳﺖ. ﺑﺎ اﺳﺘﻔﺎده از اﯾﻦ روش، ﻋﻼوه ﺑﺮ ﻣﺤﺎﺳﺒﻪ ﻣﺴﯿﺮﻫﺎي ﻣﻨﺎﺳﺐ ﺑﺮاي اﻧﺠﺎم ﺧﺪﻣﺎت، ﺗﻌﺪاد ﺑﻬﯿﻨﻪ وﺳﺎﯾﻞ ﻧﻘﻠﯿﻪ ﺑﺮاي ﻓﺮآﯾﻨﺪ ﺧﺪﻣﺎﺗﯽ ﻧﯿﺰ ﺗﻌﯿﯿﻦ ﻣﯽﺷﻮد. ﺑﺮاي ارزﯾﺎﺑﯽ ﮐﺎراﯾﯽ روش ﭘﯿﺸﻨﻬﺎدي در اﯾﻦ ﻣﻘﺎﻟﻪ، روش ﭘﯿﺸﻨﻬﺎدي ﺷﺒﯿﻪﺳﺎزي ﺷﺪه و روي ﻣﺠﻤﻮﻋﻪ دادة اﺳﺘﺎﻧﺪاردي ﮐﻪ ﺑﺮاي اﯾﻦ دﺳﺘﻪ از ﻣﺴﺎﺋﻞ ﺗﻌﺮﯾﻒ ﺷﺪه، اﺟﺮا ﺷﺪه اﺳﺖ. ﻧﺘﺎﯾﺞ ﺗﺠﺮﺑﯽ و ﺷﺒﯿﻪﺳﺎزي ﻧﺸﺎن ﻣﯽدﻫﺪ ﮐﻪ اﯾﻦ روش، ﺑﺎ وﺟﻮد ﺳﺎدﮔﯽ در روش ﭘﯿﺎدهﺳﺎزي و اﺟﺮا، داراي ﮐﺎراﯾﯽ ﺑﻬﺘﺮي ﻧﺴﺒﺖ ﺑﻪ اﻟﮕﻮرﯾﺘﻢﻫﺎ و روشﻫﺎي ﺑﺮرﺳﯽ ﺷﺪه اﺳﺖ.

In the past decades, vehicle routing problem (VRP) has gained considerable attention for its applications in industry, military, and transportation applications. Vehicle routing problem with simultaneous pickup and delivery is an extension of the VRP. This problem is an NP-hard problem; hence finding the best solution for this problem which is using exact method, take inappropriate time, and these methods are not useful in real-world applications. Using meta-heuristic algorithms for calculating and computing the solutions for NP-hard problems is a common method to contrast this challenge. The objective function defined for this problem, is a constrained objective function. In previous algorithms, the penalty method was used as constraint handling technique to define the objective function. Determining the value of parameters and penalty coefficient is not easy in these methods. Moreover, the optimal number of vehicles was not considered in the previous algorithms. So, the user should guess number of vehicles and compare the result with other values for this variable. In this paper, a novel objective function is defined to solve the vehicle routing problem with simultaneous pickup and delivery. This method can find the vehicle routes such that increases the performance of the vehicles and decreases the processes’ costs of transportation. in addition, the optimal number of vehicle in this problem can be calculated using this objective function. Finding the best solution for this optimization problems is an NP-hard and meta-heuristic methods can be used to estimate good solutions for this problem. Then, a constrained version of gravitational search algorithm is proposed. In this method, a fuzzy logic controller is used to calculate the value of the parameters and control the abilities of the algorithm, automatically. Using this controller can balance the exploration and exploitation abilities in the gravitational search algorithm and improve the performance of the algorithm. This new version of gravitational search algorithm is used to find a good solution for the predefined objective function. The proposed method is evaluated on some standard benchmark test functions and problems. The experimental results show that the proposed method outperforms the state-of-the-art methods, despite the simplicity of implementation.