Application of Improved Simulated Annealing Heuristics to Optimization Product Distribution and Wast

www.ijape.org International Journal of Automation and Power Engineering (IJAPE) Volume 4, 2015 doi: 10.14355/ijape.2015.04.004

Application of Improved Simulated Annealing Heuristics to Optimization Product Distribution and Waste Bottle Recycling Ming‐Kuei Yeh1*, Zih‐Ping Ho2 Department of Information Management, National Taipei University of Business No.321, Sec. 1, Jinan Rd., Zhongzheng District, Taipei City 10051, Republic of China 1*c8880@ms21.hinet.net; 2zihpingho@ntub.edu.tw, tp.her@msa.hinet.net

Abstract In today’s post‐industrial society, mass production poses a grave threat onto the world’s ecological system and the human race.

A mountain of waste covers the land which people rely on for survival. Product distributors should deliver goods and recycle waste bottles during the same time periods in order to save energy. Petroleum and other power based energy comsumes lot of natural resources. This study tries to focus on discussing optimization product distribution and waste bottle recycling routes using improved Simulated Annealing heuristics (SAH) approach. The revised and extended mathematic model and new proposed soft computing method are the main topics in this study. Through validations, the study offered foundamental data for optimization of this problem for future study. The industries also can improve their routes using improved SA heuristics approach. Future research suggests comparing more heuristics results with this SAH results.

Keywords Simulated Annealing Heuristics; SAH; Recycling Strategy; Soft Computing; Buniness Intelligence System.

Introduction In today’s post‐industrial society, mass production poses a grave threat onto the world’s ecological system and the human race. A mountain of waste covers the land which people rely on for survival. Product distributors should deliver goods and recycle waste bottles during the same time periods in order to save energy. Petroleum and other power based energy comsumes lot of natural resources.

Ho [8] calculated the profit of orders from recycling products. However, this study extended that research, if only waste bottles were considered and only a limited number of the recycling products were also considered; and if our objective is focused on the routes related issue and we did not consider the profits of selling recycling products, whether this would bring different results? Thus this draft applied intelligence computing to optimize this problem. Intelligence computing has in recent years become a popular problem solving technique. Simulated Annealing (SA) heuristics is one of the soft computing approaches, which resembles the cooling process of molten metal through annealing [14]. This study tries to focus on discussing optimization product distribution and waste bottle recycling routes using an improved SA heuristics approach. The revised and extended mathematical model and new proposed soft computing method are the main topics in this study.

Literature Review Product Distribution and Waste Recycling Related Literatures A geographical information system has become popular due to the 3G techniques of the recent intelligent phone trend. Such products as Google releasing Google Global Maps API, it would make it possible to see any local map on earth; furthermore, proceed with more value‐added applications. The previous literatures which were related to this study were as follows.

Fang et al. [5] presented a new mathematical programming model of a flow shop scheduling problem that

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International Journal of Automation and Power Engineering (IJAPE) Volume 4, 2015 www.ijape.org

considers peak power load, energy consumption and associated carbon footprint in addition to cycle time.

Chaabane et al. [3] proposed a mixed‐integer linear programming based framework for solid and liquid wastes, gases and transportation systems. The results showed that carbon management strategies would help decision makers to achieve sustainability objectives.

Although several literatures were related to waste and product production, there is only a limited amount of literature available on waste recycling and product distribution, most of them are turning wastes to bio‐energy topics.

Simulated Annealing Heuristics Related Literatures Simulated Annealing resembles the cooling process of molten metal through annealing. At high temperature, the atoms in a molten metal can move freely with respect to each other, when the temperature is reduced, the movement of the atoms gets restricted [14]. It was introduced by Kirkpatrick et al. [9] and Cerny [2]. An SA algorithm repeats an iterative neighbor generation procedure and follows search directions that improve the objective function value. In each iteration, for a current solution compared with a historical one , the objective difference is evaluated [1]. If the new solution improves the objective value, then it is accepted. If it is worse than the current one, it can still be accepted depending on a so‐called probability of accepting worse solution [12]. The probability is obtained from the Boltzman distribution P (E) = e



E kT

(1)

where P (E) is the probability of the optimization process to keep a modification that incurs an increase E of the objective function. k is a parameter of the process, and T is the instantaneous “temperature” of the process [13].

A cooling rate  is used to reduce the temperature of the annealing process [4].

Popovic et al. [10] ever used a hybrid SA and mixed integer linear programming algorithm for optimizing planning of radial distribution networks with distributed generation. Haridass et al. [6] applied SA for scheduling a log transport system problem. Therefore, SA is still a popular approach for solving many optimizing problems.

Problem Formulation This research adapts finding the minimal penalty of product distribution and waste bottle recycling, cij , as the model. A dynamic selection model [7][8], previous research, helps this study construct a more precise problem formulation. In this study, let N denote set of nodes. Let n denote number of nodes. Let i, j denote node number, i  j . Let ct (i, j ) denote cost function from transportation node i to node j. Let ced (i, j ) denote ED penalty cost from transportation node i to node j, it’s also an Early and Delay job optimization sub problem. Let cw(i, j ) denote waste penalty cost from transportation node i to node j, it means carriage waste bottle cost and storage cost of waste bottle on the customer side. Let cij denote penalty function from node i to node j. Let xij denote a binary decision variable. The model is shown as follows.

N: set of nodes n: number of nodes i, j: node number, i  j ct (i, j ) : cost from transportation node i to node j ced (i, j ) : ED penalty cost from transportation node i to node j, it’s also an Early and Delay job optimization sub

problem. cw(i, j ) : waste penalty cost from transportation node i to node j, it means carriage waste bottle cost and storage

cost of waste bottle on the customer side.

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cij : penalty function from node i to node j

cij = f (i, j ) = ct (i, j )  ced (i, j )  cw(i, j ) xij 



1, the path goes from node i to node j 0, otherwise



The MINLP (Mixed integer non‐linear programming) model to minimize the penalty of product distribution and waste bottle recycling is as follows: Min   cij xij (2) iN jN

s.t. n

 xij = 1 

i 0

n

j (3)

 xij = 1 

i (4)

xij  {0,1} 

i , j (5)

j 0

The objective (2) is to find a minimal penalty of product distribution and waste bottle recycling. In Eq. (3) and (4), each node should visit at one time. Eq. (5) declares artificial binary decision variable constraints.

Improved Simulated Annealing Algorithm The SA Algorithm for this problem is as follows: The decision variables is xij .

Step 1: Initialization Randomizing an initial solution The solution represents the path flow in the whole system.

Step 2: Objective function evaluation Evaluating the objective function for the initial solution Step 3: Neighbour solution generation Based on previous solution to generate a new solution Step 4: Objective function evaluation Evaluating the objective function for the neighbour solution Step 5: Comparison If the new solution is better than the original one, then replace it. Otherwise, using the Boltzman distribution (see Eq.1) for determining whether to accept the new solution or rejecting dependent on relative magnitude of E and T values.

Step 6: Cooling In each temperature, the procedure generates a fixed number of neighbour solutions, then  would reduce the temperature of the annealing process.

Step 7: Stopping Has iteration reached a pre‐defined number? If yes, then Stop the searching process. Otherwise, the procedure goes back to step 3.

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International Journal of Automation and Power Engineering (IJAPE) Volume 4, 2015 www.ijape.org

In this study, step 3 and 5 were improved and extended, the software let MP denote the memory of the previous path sets (Eq. 6). xij  MP (6)

Besides, the neighbour solution generation keeps the top 10 paths as a candidate neighbour. In each iteration,it randomly selects one of these ten candidate neighbours as a previous solution in Step 3.

This study also revised Step 1, the initial solution is setting geographical constraints. The nodes which belong to the same distinct must be preferentially allocated. It would accelerate the searching efficiency in the initial step.

Computer Results and Discussion In this section, the algorithm was coded in Visual Basic computer language with Celeron (R) Dual‐Core CPU at 2.10 GHz and 1GB of RAM memory. This MINLP model is a strong NP‐hard problem [11]. Since the proposed model is a new problem, no published solution method is available for comparison. Thus, this research conducted an experimental design, at different nodes, for comparing the performance of heuristics. The parameters of SA were listed in Table 1. The research results are also showed in Figure 1.

TABLE 1 SET OF PARAMETERS FOR SA

Parameter Cooling Rate 

Value 0.90

T0

100℃

Tn

0℃

Iterations at the Ti

10

Threshold Rate to P (E)

0.50 0 10

Tabu Termination time (sec)

FIG. 1 COMPARISON SAH RESULTS AT DIFFERENT NODES

Conclusions In previous research, there is only a limited amount of literature available on waste recycling and product distribution. This study establishes a pioneer research about optimization product distribution and waste bottle recycling routes using an improved SA heuristics approach. Through validations, the study offered foundamental data for optimization of this problem for future study. The industries also can improve their routes using improved SA heuristics approach.

Future research suggests comparing more heuristics results with these SAH results.

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[1]

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[2]

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[7]

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[9]

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Ming‐Kuei Yeh received his Ph.D. in Computer Science and Information Engineering from National Central University, Taiwan in 2010. He joined Nanya Institute of Technology as a Lecturer in 2003 and became an Associate Professor in 2012. He is currently with the Department of Information Management, National Taipei University of Business, and leads the Business Intelligence Research Center. His current research interests include RFID system, IOT, pervasive computing, computer network and network management. E‐mail: c8880@ms21.hinet.net Zih‐Ping Ho is an researcher fellow in the Business Intelligence Research Center, Dept. Information Management, National Taipei University of Business, Taipei City, Republic of China; also an associate editor in BIOINFO Renewable & Sustainable Energy in the United States. He received his Ph.D. in Industrial Engineering and Enterprise Information, Tunghai University on Jan. 2010. He was an associate researcher in Taiwan Research Institute, Taipei City on 2013.1 ‐ 2014.1; a post doctor fellow in Information Technology Center in National Taiwan Normal University on 2011.8‐2012.12; an assistant professor in Taiwan Tourism College, East Taiwan on 2010.8 ‐ 2011.7; an associate editor of World Research Journal of Energy Technology and Policy from 2012.10.15 to 2014.7; and listed in Who’s Who in the World, Marguis Company on March 2013 – 2015.

E‐mail: zihpingho@ntub.edu.tw; tp.her@msa.hinet.net

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