Application of Ant Colony Optimisation Algorithm on Solid Waste Collection: A Case of University of Port Harcourt

Ants are social insects and their behaviour is geared towards the survival of the colony rather than the survival of the individual. Because ants are almost blind, they move along by building chemical trails using a chemical substance called pheromone . These trails are used by ants to find the way to Choba Park by 937.66 m, Delta Park by 1255.99 m, Abuja Park section 1 by 3779.89 m and Abuja Park Section 2 by 1875.15 m representing 33.5%, 31.43%, 51.48% and 32.16%, respectively. However, considering the physical nature of the built environment, a Best Tour Path (BTP) rather than the optimized path was chosen. This gave a total distance reduction of about 16% cumulatively.


INTRODUCTION
Few decades ago, solid wastes were defined as consisting of wastes that are unwanted and useless arising from human and animal activities but now, due to advances in recycling and resource recovery technologies the concept of solid waste has changed. Some of what are known previously to be useless and unwanted are now processed into different valuable products [1]. The term solid waste as used in this research is allinclusive, encompassing the heterogeneous mass of throwaways from the urban community as well as the more homogeneous accumulation of domestic, industrial and educational waste.
The increase in human activities coupled with the increasing rate of population growth has resulted to a significant rise in solid waste generation [2,3]. This poses a challenge on waste management authorities to develop effective ways to manage waste. Route optimization of solid waste collection process remains the most likely option among other solutions. This is likely given its impact on the economic, environment and society at large is very positive when compared with other options. Minimizing waste collection routes are the prime objectives when optimizing waste collection. This implies that for a distinct collection area, waste collection trucks will have to optimize both travelling distance and time. Therefore a major factor in cutting down waste collection cost is by reducing the route time for a waste collection route [4].
In order to properly manage solid waste generated at the University of Port Harcourt, a unit known as the Campus Environmental Beautification and Sanitation (CEBAS) was created [5]. This unit ensures that refuse are collected by contracted waste managers from locations which have been classified into three zones. Each zone has a number of collection points with a final disposal site. With the recent level of economic growth and consumption as a result of increased population, there has been tremendous pressure on the environment and the unhealthy disposal of solid waste is one of the greatest challenges facing the institution and perhaps other developing countries.

Data Collection and Analyses
Semistructured scheduled interview and study group discussion were employed in data collection. Data were collected also from both primary and secondary sources. The location of the disposal sites and collection points, serviceable streets, collection routes, number of trips per day, number and capacities of solid waste collection vehicles were collected. The data were validated by joining some of the trips and by observing same activities within the University. The distance was obtained by computing the Euclidean (or taxicab) distance between each pair of the nodes using the Global Information System (GIS) with the help of the worldwide web and Global Positioning System (GPS) software, Google Earth.

Floyd-Warshall's Algorithm
The FloydWarshall's Algorithm (Table 1) was used to obtain pairs of the shortest distances between the various collection points and the Ant Colony Algorithm was then used to analyze the data in order to arrive at an optimal route for the waste collection points within the University.The pseudo code for FloydWarshall's Algorithm is as presented in the Table 1.

Ant Colony Optimisation (ACO)
The basic idea of ACO algorithms was inspired through the observation of swarm colonies and specifically ants [6]. Most species of ants are virtually considered to be blind but while moving around searching for food they deposit a chemical substance called pheromone [7]. i. the amount of pheromone on arc (i, j),τ ij ii.
desirability of arc (i, j),η ij Where: arc (i, j) denotes the connection between nodes i and j.
At the start of the algorithm an initial amount of pheromone, τ 0 is deposited on each arc: Where: L0 is the length of an initial feasible tour and k is the number of ants. The desirability value (also referred to as visibility or heuristic information) between a pair of nodes is the inverse of their distances; Where: dij is the distance between nodes i and j. So, if the distance on the arc (i, j) is long, visiting city j after city i (or viceversa) will be less desirable.
Each ant constructs its own tour utilizing a transition probability: an ant k positioned at a city i selects the next city j to visit with a probability given by Equation (3) . These positive parameters were assigned the values 1 and 2 respectively as regards to this research. After each ant has completed its tour, the pheromone levels are updated. The pheromone update consists of the pheromone evaporation and pheromone reinforcement. The pheromone evaporation refers to uniformly decreasing the pheromone values on all arcs. The aim is to prevent the rapid convergence of the algorithm to a local optimal solution by reducing the probability of repeatedly selecting certain nodes. The pheromone reinforcement process, on the other hand, allows each ant to deposit a certain amount of pheromone on the arcs belonging to its tour. The aim is to increase the probability of selecting the arcs frequently used by the ants that construct short tours. The pheromone update rule is as follows: In this formulation  (ranges from 0 to ≤ 1) is the pheromone evaporation parameter and  k ij  is the amount of pheromone deposited on arc (i, j) by ant k and is computed as follows: Where: Lk is the tour length constructed by the k-th ant.
Where Q = (maximum distance observed between pairs of nodes) X (total number of nodes) In most of the ant colony based algorithms to Vehicle Routing Problem(VRP), initial pheromone trails,  0 is set equal to the inverse of the best known route distances found for the particular problem. However, it was found that: Where: n = total number of nodes (dump points) considered [10].
A summary of the ACO algorithm is presented in the flow chart (Fig. 2).

RESULTS
The results from the analyses of the data collected from the three campuses on applying FloydWarshall's algorithm is presented in Tables A1-A4 (Appendix A), representing the shortest distance between collection points (nodes) of the three campuses (Choba Park Campus, Delta Park Campus and University Park Campus). Note that the University Park Campus was divided into two sections as a matter of convenience.
Taking the Choba Campus, for illustration on flow chart ( Fig. 2) computation outputs, an initial pheromone (Table A1.1) was computed for all the nodes using Equation (6) and the heuristic values (Table A1.2) for the various nodes were computed by applying the resulted shortest distance between collection points (nodes) presented in Table A1 into Equation (2). On applying the computed initial pheromone and heuristic values for the various nodes into Equation (3), the resulted routes (Table A1.3) were obtained. After the first iteration, the initial pheromone for each node was updated (Table  A1.4) using Equation 4. Also the resulted routes with respect to these updated pheromone on each arc trail is presented in Table A1.5; when reapplied into Equation (3) for the second iteration. The route with the minimum stable distance is taken as the proposed optimised route for the waste collection crew.
Similar to the results exemplified by Choba Park campus in Tables A1.1 A1.6, are those of the other two campuses (Delta Park and University Park in two subcampuses or sections). The results printed out for Delta Park and University Park except for Tables A2 -A4 are unnecessary, given the result details as provided by Choba Park campuses illustration.
The summary of the resulting optimum route for each campus on the application of the Ant Colony Optimization algorithm (ACO) is represented in Table 2. However, considering the physical nature of the system (the feasibility of these paths and vehicle capacity), the Best Tour Path (BTP) for each campus was obtained.
The plot of the optimal route on relative co ordinates for the various campuses are as shown in Figs. 36.

DISCUSSION
It can be seen from Tables A1A4 (which represent the pair of the shortest distance between each nodes within each campuses of the institution as analyzed using FloydWarshall's algorithm), that the nodes are numbered from 1, 2, 3…61 representing the total waste collection points within the Institution but with exception of nodes 12, 29, 62 which represent the dump site within Choba, Delta and University Park campuses, respectively. Waste collection points (nodes) within Choba campus are labeled 1, 2, 3…11. Delta Park campus has nodes labeled 13, 14, 15…28. While the University Park has nodes labeled 20, 31, 32…61.
The result obtained from the application of Floyd Warshall's algorithm (Tables A1A4) usually result to the formation of a kind of graph, whose vertices is equal to the number of collection points having its major diagonals equal to zero. This is so because the shortest distance between a collection point and itself will always be zero. Table 2 there is significant reduction in the total distance travelled along the routes in the various campuses when the ACO was applied. For the case of Choba Park, the optimum tour path started with node 1 and ended with node 8 giving a total reduction in length of about 937.66 m representing 33.5% reduction in total length of tour path when compared with the tour path usually used by the waste collectors within the campus.

As seen in
In Delta Park, the optimal tour started with node 25 and terminates with node 21 giving a total reduction in length of about 1255.99 m, representing 31.43% reduction in total length of tour path when compared with the tour path usually used by the waste collectors within the campus.
In University Park, Section 1 and Section 2 recorded 3779.89 m and 1875.15 m reduction in length representing 51.48% and 32.16% reduction in total length of tour path when compared with the tour path usually used by the waste collectors within the campus.
Given the availability of the road network, the vehicle capacity and nearness to the various dump sites the Best Tour Path (BTP) for each of the three campuses gave the percentage reduction. The BTP gave a total distance reduction of 2%, 6%, 32% and 8%, respectively for Choba, Delta, University Park sections 1 and 2, respectively. Cumulatively, a total distance X y reduction of about 16% was obtained when considering the Best Tour Path.

CONCLUSION
The following conclusion can be made from the application of the Ant Colony Optimization Algorithm in the optimization of Solid waste Collection within the University of Port Harcourt: i.
The Ant Colony Optimization (ACO) is very powerful tool in network or route optimization in general; and ii.
The Ant Colony Optimization (ACO) was able to achieve approximately40% reduction in total route distance travelled by solid waste collectors cumulatively for the whole institution.
The implication of this reduction in distance is that it has a direct relationship with time and overall reduction in both operational and maintenance (O & M) cost which in turn would mean an increase in profit for the waste management firm or company involved in the daily collection of waste for the University.

RECOMMENDATION
Solid waste collection is one of the six functional elements of Municipal Solid Waste Management (MSWM) System. In some cases it has been referred to as the most sensitive or important of the entire elements. Based on the results from this research it is recommended that: i.
The solid waste collection process within the University of Port Harcourt should be properly routed using the application of the Ant Colony Optimization algorithm; ii.
The capacity of the solid waste collection trucks should be increased so as to reduce the number of collection trips and perhaps reduce the overall operation and maintenance cost; and iii.
The University management should use the Ant Colony Optimization algorithm as a decision tool to aid the siting of solid waste collection points and dump sites within the campuses.

COMPETING INTERESTS
Authors have declared that no competing interests exist.