The Further Research on the Application of ABC to the Optimization and Control of Project

A new way of optimization has caught many researchers’attention, namely the heuristic algorithms, including Genetic Algorithm (GA), Simulating Algorithm (SA), Particle swarm optimization (PSO), ant colony optimization (ACO), Artificial Bee Colony Algorithm (ABC) and so on. Some ways of the heuristic algorithms belong to swarm intelligent optimizating algoritms such as PSO, ACO and ABC. ABC is the newest of the swarm intelligent optimizating algorithms, which is not developed perfectly and not be fully employed to a variety of fields. The paper introduces ABC to the optimization of the muli-objective optimization on construction project time-cost-quality and compare the results of ABC with the results of GA or PSO, which not only optimizes the project, but also proves the effectiveness of ABC, extends the applied fields of ABC and puts forword a new effective method of optimizing the construction project time-cost-quality.


Introduce the Problem
Swarm intelligence has become a research interest to many research scientists of related fields in recent years.Dorigo, inspired by the mechanism of organic evolution, proposed ant colony optimization (ACO) by simulating the foraging behavior of ant colonies.Particle Swarm Optimization (PSO) is a swarm intelligence technique developed by Eberhart and Kennedy who were inspired by the social behavior of bird flocking and fish schooling in 1995.Both ACO and PSO are swarm intelligence.In general, an individual is not intelligent.However, the whole biotic population display the ability to solve the complicated problems.Swarm intelligence is the application of the group behaviors in the field of artificial intelligence.
A numerical function optimization algorithm based on foraging behavior of honey bees, called Artificial Bee Colony (ABC) was proposed by Karaboga (2005).Karaboga and Basturk (2008) draw a conclution that ABC had the same good performance as PSO, Differential Evolution (DE) and Evolutionary Algorithm (EA)by comparing ABC to PSO, EA and DE in solving the five standard functions.Fan and Ma (2010) employ ABC to solve 0-1 knapsack problem. A. M. Bernarino and E. M. Bernarino (2010) applied ABC to the problem of weighted loading ring net.Hu, Zhao and Sa (2009) employs ABC to solve JSP and Hu and Zhao (2009) employ ABC to solve TSP, Sundar and Singh (2010) apply ABC to solve quadratic Minimum Degree Spanning Tree Problem, Hsieh, Hsiao & Yeh (2011) use ABC to predict the stock price, Karaboga (2009) employs ABC to design digital IIR filters, Kang, Li and Xu (2009) do structural inverse analysis by hybridsimplex ABC, Ho and Shi-you (2009) solve inverse problems by ABC, Hetmaniok, Slota and Zielonk (2010) get solution of the inverseheat conduction problem by using the ABC algorithm.

Explore Importance of the Problem and Describe Relevant Scholarship
Time, cost, and quality of the project are the three main aims of project management.The optimization of the three objectives can come down to the problem of muli-objective optimization.There are few literature balancing time and cost and quality in recent years.McKim, Hegazy and Attalla (2000) put forward that cost, time and quality are the three main guidelines in evaluating the construction project.These indicators are highly relevant and need being balanced.Rwelamila et al. (1995) proposed that project managers usually try to seek the most effective methods of balancing schedule and cost but rarely analyze the significance of quality.Tang and Qin (1998) introduce the model of simulating the control of construction project TCQ and the ways of analyzing risk based on the technique of PERT.Babua and Suresh (1996) and BaKhang and Mon (1999) make linear model of time,quality and cost in the construction of a specific cement plant and evaluate the effectiveness of this model.Wang, Liu and Luo (2004), Yang, Y. L. Wang and N. M.Wang (2006).and Gao, Hu and Zhong (2007) have made mathematical model on time, cost and quality repectively.Kaheled and Amr (2005) put forward the multi-objective model of balancing time, cost and quality.

State Hypotheses and Their Correspondence to Research Design
This paper presents the time-cost-quality tradeoff optimization model using multi-attribute utility (MAU) function theory and applies ABC to two specific cases based on network planning techniques.Then it compares the results of ABC with the result of GA in Ho and Shi-you (2009) or the result of PSO in (Zhang & Xing, 2010), which show the results of ABC is better than the results of GA and PSO.Therefore, it turns out to be that ABC can obtain the most satisfied decision result and provided a novel and effective way to project managers.In addition, if do many times of experiments, ABC can often obtain not only one best solution vector, which is beneficial for project managers to make reasonable decision flexiblely according to the specific conditions of project implementation.

Bee Clony in Nature
Bee clony in nature: self-organization and division of labour are necessary and sufficient properties to obtain swarm intelligent behaviour such as distributed problemsolving systems that self-organize and adapt to the given environment: a) Self-organization can be defined as a set of dynamical mechanisms, which result in structures at the global level of a system by means of interactions among its low-level components.These mechanisms establish basic rules for the interactions between the components of the system.The rules ensure that the interactions are executed on the basis of purely local information without any relation to the global pattern.Bonabeau et al. have characterized four basic properties on which self organization relies: Positive feedback, negative feedback, fluctuations and multiple interactions.Positive feedback is a simple behavioural "rules of thumb" that promotes the creation of convenient structures.Recruitment and reinforcement such as trail laying and following in some ant species or dances in bees can be shown as the examples of positive feedback.Negative feedback counterbalances positive feedback and helps to stabilize the collective pattern.In order to avoid the saturation which might occur in terms of available foragers, food source exhaustion, crowding or competition at the food sources, a negative feedback mechanism is needed.Fluctuations such as random walks, errors, random task switching among swarm individuals are vital for creativity and innovation.Randomness is often crucial for emergent structures since it enables the discovery of new solutions.In general, self organization requires a minimal density of mutually tolerant individuals, enabling them to make use of the results from their own activities as well as others.b) Division of labour namely simultaneous task performance by cooperating specialized individuals is believed to be more efficient than the sequential task performance by unspecialized individuals and enables the swarm to respond to changed conditions in the search space.The foraging bees are classified into three categories employed, onlookers and scouts.All bees that are currently exploiting a food source are classified as the employed bees.The employed bees bring loads of nectar from the food source to the hive and may share the information about food source with onlooker bees.'Onlookers' are those bees that are waiting in the hive for the information to be shared by the employed bees about their food sources and 'scouts' are those bees which are currently searching for new food sources in the vicinity of the hive.

Basic Thought of ABC
In the beginning of foraging behavior,all the bees have know nothing about the food sources,namely all the bees are scouts who seek randomly food sources near beehives, this stage is like the population initialization in optimizing phase; After a while, half of the bees find food source and become employed bees, the employed bees begin to spread the food information or give up the found food source and become scouts at some rate, the stage is like the stage of seeking feasible solutions in optimizating process, in which stage some solutions don't meet the constraint condition will be replaced randomly; Another half bees who haven't found food source become onlookers, the onlookers wait for the food information from employed bees and receive the food information at some probability.The probability is positively correlated to the specific information on food resource(such as sugar content and so on), this stage is like natural selection,the bigger value of fitness is more likely to be received, the received feasible solution can mutate to get the better solution.Later,the onlooker will check if the number of failure time is beyond the limited number, if the number is bigger than the limited ,then gives up the current food source for it is probable to be far away from beehive, this stage is like the verification stage in the optimizing process, in which if the current solution is not easy to be found and then it will be replaced with a new generated solution.Bee colony will not stop repeating the steps above (except the initial stage)until maximum iteration or minimum criteria is attained, it's the same story in the optimizing phase.
The specifications are shown as Figure 1 and Figure 2.
(k is a solution in the neighbourhood of I,  is a random number in the range [-1,1])and evaluate them; 6: Apply the greedy selection process between i x and i v ; 7: Calculate the probability values i P for the solutions i x by means of their fitness values using equation (1) The employed Bees begin to spread the food information or give up the found food source and become scouts at some rate and record the currently best food source.
The onlookers wait for the food information from employed bees and receive the food information at some probability.Update the currently best food source.
The onlooker will check if the number of failure time is beyond the limited number, if the number is bigger than the limited, then give up the current food source for it is probable to be far away from beehive.Update the currently best food source.
Reach the maximum iteration.
Get the best food source .

Yes
No Scouts who seek randomly food source Seek feasible solutions, some solutions don't meet the constraint condition will be replaced randomly and record the currently best solution.
Natural selection, the bigger value of fitness is more likely to be received, the received feasible solution can mutate to get the better solution.Update the currently best solution.
Verify if the feasible solution is beyond the maximum iteration times, it will be replaced with a new randomly generated solution if it is beyond the limited times.Update the currently best solution.
Reach the maximum iteration.
Get the best solution.

Population initialization
In order to calculate the fitness values of solutions we employed the following equation ( 2) Normalize i P values into [0,1]; 8: Produce the new solutions (new positions) i v for the onlookers from the solutions i x , selected depending on i P , and evaluate them; 9: Apply the greedy selection process for the onlookers between i x and i v ; 10: Determine the abandoned solution (source), if exists, and replace it with a new randomly produced solution i x for the scout using the equation ( 3) (3) 11: Memorize the best food source position (solution) achieved so far; 12: cycle=cycle+1; 13: until cycle= Maximum Cycle Number (MCN).

The Basic Principles of Multiple Attribute Utility
Multiple attribute utility (MAU) which originated in the eighteenth century was developed by Zeng, Jie and Cun (2004).MAU theory is an analytical method for decision-making based on multiple criteria.Applications of MAU in the construction field include the studies on procurement route selection (Chang & Ive, 2002) and performance assessing of construction engineering.
Attribute utility means a measure of the desirability of outcomes associated with an alternative action.An alternative may be chosen according to the preference of decision-makers or the importance of each single criterion or performance.Each alternative to be evaluated is measured through multiple attribute functions that respectively represent each single criterion and are composed using a series of weights.Such a weight may reflect the preference of decision-makers or the importance of each performance.
If there are J≥1 criteria for each alternative, then let   denote a vector of performances for an alternative, then the composite attribute utility for measuring this alternative can be obtained as (4) Where j u is the single attribute utility function for the performance j and is scaled from 0 to 1. j w is the weight for the performance j and the sum of all the weights is equal to 1, i.e . The risk neutral utility function is commonly used and is defined as (5) (5) Where j a and j b are the constants and can be determined based on the best and the worst performances where their measure levels respectively reach the lowest value 0 and the highest value 1.

The Method of Creating the Multiple Attribute Utility Function of TCQ
With regards to the project performances such as time, cost and quality associated with a combination of construction methods, the equations for computing the single utility values for time, cost and quality of a project can be expressed as ( 6), ( 7), (8): Where T, C and Q respectively represent the time, cost and quality of a project. T and  T respectively represent the longest and shortest project durations;  C and  C respectively represent the maximum and minimum total cost;  Q and  Q respectively represent the maximum and minimum overall quality of a project.If the weights for the three performances are T w , C w and Q w respectively, then the composite attribute utility can be obtained through ( 9) The optimal alternative should be the one that has the largest composite attribute utility.The network-planning diagram is shown as Figure 3, specific parameters are shown as Table1.

The Creation of MAU Function of Case
, take them into (10), ( 11), ( 12), get While T w , C w and Q w is calculated by experts grading method,they respectively are , take them into (13) and get ( 14)

The Introduction of the Specific Case II
The network-planning diagram is shown as Figure 4, specific parameters are shown as Table 2.   Take the data in to(10)～( 12), get a=1, b=1/64, c=1, d=1/23340, e=0, f=1/0.148 While T w , C w and Q w is calculated by experts grading method,they respectively are , take them into (15), get ( 16)

Best solutions
The maximum utility ABC GA in (Ho& Shi-you,2009) The results of various algorithms is in Table 3. Compare optimal solution of the ABC algorithm to GA in (Ho & Shi-you, 2009), we can see that the solution quality of ABC algorithm is better and robuster than the optimum solutions of GA algorithm.

The Choice of Parameter
The number of population namely NP=20; The number of food source namely Foodnumber=10; The maximum times of failure namely Limit=100; The maximum cycling times nameyMax=2500; The number of parameters: D=39.

The Analysis of the Result
The results of various algorithms is in Table 3, Compare optimal solution of the ABC algorithm to PSO in (Zhang & Xing, 2010), we can see that the solution quality of ABC algorithm is better and robuster than the optimum solutions of GA algorithm.

Discussion and Conclusion
This paper presents the time-cost-quality tradeoff optimization model using multi-attribute utility (MAU) function theory and applies ABC to two specific cases based on network planning techniques.Then it compares the results of ABC with the result of GA in (Ho & Shi-you, 2009)or the result of PSO in (Zhang & Xing, 2010), which not only show the results of ABC is better than the results of GA and PSO but also display the robustness of ABC.In conclusion, the paper not only proves the effectiveness of ABC, extends the applied fields of ABC, but also puts forword a new effective method for project managers to optimize the construction project time-cost-quality.

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Figure 3.The Network-planning diagram

Figure 4 .
Figure 4.The Network-planning diagram Figure 5.The result of ABC algorithms Figure 6.The result of ABC algorithms

Table 1 .
Specific parameters

Table 2 .
Specific parameters

Table 4 .
The analysis of the results