Optimizing Route for Hazardous Materials Logistics (ORHML) belongs to a class of problems referred to as NPHard, and a strict constraint of it makes it harder to solve. In order to dealing with ORHML, an improved hybrid ant colony algorithm (HACA) was devised. To achieve the purpose of balancing risk and cost for route based on the principle of ACA that used to solve TSP, the improved HACA was designed. Considering the capacity of road network and the maximum expected risk limits, a route optimization model to minimize the total cost is established based on network flow theory. Improvement on route construction rule and pheromone updating rule was adopted on the basis of the former algorithm. An example was analyzed to demonstrate the correctness of the application. It is proved that improved HACA is efficient and feasible in solving ORHML.
Hazardous materials, which have different physical and chemical properties, have high risk during transportation, as a series of problems may arise in this process. Route optimization is a complex combinatorial optimization problem, which is a typical NPcomplete problem and difficult to come up with a direct answer. It is a practical problem in urgent need of solution in which we can find the optimal plan under the restrictions quickly, accurately, safely, and economically.
Optimizing Route for Hazardous Materials Logistics (ORHML) can be described as follows. Given a set of hazardous materials and an underlying network consisting of a number of nodes and capacitated arcs, we wish to find an optimal routing plan to ship the hazardous materials through the network at lowest cost without violating the capacity limits. ORHML models also appear as subproblems in more complicated models, such as distribution system design and capacitated network design.
ORHML has attracted the attention of many OR researchers. Kara et al. [
In general, in spite of their more realistic assumption, most of the exact versions of risk models have some puzzling properties and these models may not be suitable for hazmat transportation planning. We suggest that researchers and practitioners consider the properties of the risk models carefully.
Successful ant colony algorithms have been developed for several combinatorial optimization problems, such as Traveling Salesman Problem (TSP) and Vehicle Routing Problem (VRP).
Based on the successful application of ant colony algorithm to TSP, a new ACA was adopted in solving ORHML. A collaborative metaheuristic approach is inspired by the foraging behavior of real colonies of ants. The basic ACA application is a large number of simple artificial agents that are able to build good solutions for hard combinatorial optimization problems through lowlevel based communications. Real ants cooperate in their search for food by depositing chemical traces (pheromones) on the floor.
ORHML optimization model can be demonstrated as follows:
Based on the risk analysis theory, the risk of hazardous materials
(1) Casualties along the road
(2) Casualties in the vehicle
(3) Property damage
(4) Traffic interruption
(5) Evacuation
(6) Environmental damage
HACA goal is to find the shortest tour. In HACA
Improvement process of solution strategy.
When ant
In the HACA, original version formula for
The number of next nodes which ant
The sum of ants is represented by
Using for reference the idea of ant
The algorithm constructs two ant colonies to realize the goal of optimization: minimize the cost and risk of the hazardous materials transportation. These two ant colonies are the HACARISK and HACACOST, which are used to determine the optimal route. In consideration of the two together, we may find better solutions to the problem. After getting the improved solution, the overall pheromone update would be used to get the exchange of information concerning the advantages and disadvantages of the solution [
The HACARISK optimization process is to get the feasible solution which uses one less risk than
If the least cost has been figured out by this algorithm, the HACARISK optimization process can be stopped, and then we shift to the HACACOST optimization process.
In the HACACOST we introduce an integer vector
The HACACOST optimization process is similar to the traditional HACA optimization process which is to optimize the utilization of the load capacity and volume of RISKs.
The optimizing process can be divided into two parts: first, the ants move between the various points in search of the optimal solution; second, decompose the optimal solution into
The movement of ants in the HACACOST and HACARISK is similar to each other. At the beginning of the algorithm, ants are randomly distributed among all the nodes. From the initial node, the ants determine the next move within the scope of available points, on the basis of the probability and the restrictions on RISK load capacity and volume. The time and cost of all nodes to the virtual origin node are 0, and no direct connection between the virtual origin nodes is allowed. Once the ants arrive the terminal node, thus begins the construction of the next subset. After traversing all the nodes, the ants return to the initial node to form a loop, that is, feasible solution.
In the HACACOST optimization process, a feasible solution
When the above process was being completed, the obtained solution may still be incomplete (and may have missed points), so the insertion process is needed as further optimization. Insertion process is mainly to deal with the point that has not been included in the existing solution. The process determines the optimal feasible insertion position (the shortest path) for each point until the plug cannot find a viable location [
As can be seen in Figure
Parameter value.









AB  80  500  16  400  19000  0.0000018  0.000002 
AC  35  1000  20  730  6000  0.0000055  0.0000069 
AD  60  700  34  500  12000  0.0000035  0.0000044 
BA  70  400  40  250  18000  0.0000015  0.0000019 
BD  50  800  52  670  14000  0.0000035  0.0000044 
BE  70  700  18  370  15000  0.0000025  0.0000031 
CF  15  800  42  850  5000  0.0000065  0.0000081 
CG  30  1200  68  680  9000  0.0000045  0.0000056 
DF  20  2000  48  970  0  0.0000075  0.0000094 
EF  25  1800  36  750  6000  0.0000055  0.0000069 
EH  65  800  44  350  18000  0.0000015  0.0000019 
FG  40  900  24  500  12000  0.0000035  0.0000044 
FH  50  700  18  380  16000  0.0000025  0.0000031 
GH  35  400  16  250  12000  0.0000015  0.0000019 
HG  65  300  12  250  18000  0.0000015  0.0000019 
Road network.
Set freight = 0.5 yuan/km/unit,
The probabilities of hazard losses.









0.4  0.8  0.6  0.4  0.1  0.2 

0.7  0.6  0.3  0.4  0.7  0.7 
Total expected risk
Total expected risk.

AB  AC  AD  BA  BD  BE  CF  CG 


1495.61  2527.264  2448.515  847.7595  2496.6  2256.487  978.3397  2412.688 

744.24  1408.428  1373.803  480.7152  1402.368  1250.897  540.918  1337.213 
 
DF  EF  EH  FG  FH  GH  HG  
 

2880.29  3249.342  1574.389  2098.725  1663.237  349.7931  590.3967  

1590.48  1810.836  892.7568  1177.546  922.467  197.7444  334.7838 
Set Fright = 0.5 yuan/km/unit. The cost
The cost.
AB  AC  AD  BA  BD  BE  CF  CG  DF  EF  EH  FG  FH  GH  HG  


40  17.5  30  35  25  35  7.5  15  10  12.5  32.5  20  25  17.5  32.5 
In view of complexity of this problem, the whole level optimization solutions are obtained based on the random searching and evolution process of the improved ant colony algorithm. The solution can be seen in Figure
Solution.
Solving the ORHML is to determine route plans that can make a minimum of risk and safety under the premise of restrictions of the placements. That is, to seek a safe routing plan that could obtain the lowest cost with the conditions has been known.
A new ant colony optimization based approach to solve ORHML was introduced. In particular, the algorithm has been designed to solve ORHML with a balance between the safe and the cost. Pinpointing the characteristics of this problem, our algorithm introduces a new methodology for optimizing multiple objective functions. We consider the optimization of the safe and the cost at the same time. This paper analyzes the differences of the ant colony algorithms in solving the restricted ORHML. In order to deal with ORHML, an improved HACA was devised. Pinpointing the characteristics of this problem, we consider the optimization of cost and risk together. The basic idea is to coordinate the activity of different ant colonies, each of them optimizing a different objective. These colonies work by using independent pheromone trails but they collaborate by exchanging information. Furthermore, the integrated use of HACASAFE and HACACOST has been applied as the improvement of the solving strategy.
Finally, the feasibility and effectiveness of this method has been scrutinized with practical examples. From the result on the test problem, we can conclude that the model and the heuristic procedures are quite successful in solving ORHML.
The research is supported by Basic Scientific Research Funding of Beijing Jiaotong University (Project name: Collaborative optimization for hazardous materials transportation route choice and logistics center location).