Applying genetic algorithms for construction quality auditor assignment in public construction projects

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Applying genetic algorithms for construction quality auditor assignment in public

construction projects

Yu-Ren Wang

a,

⁎

, Siang-Lin Kong

b a

Dept. of Civil Engineering, National Kaohsiung University of Applied Sciences, 415 Chien-Kung Road, Kaohsiung 807, Taiwan

b_{Construction Ofﬁce, Public Works Bureau, Kaohsiung City Government, No.2 Shiwei 3rd Rd., Kaohsiung 802, Taiwan}

a b s t r a c t

a r t i c l e i n f o

Article history:

Accepted 27 November 2011 Available online 26 December 2011 Keywords:

Assignment problem Quality audit Optimization Genetic algorithms

Random third party quality audits are mandatory by the regulations for public construction projects in Tai-wan. This project and auditor selection process is normally carried out based on personal experience and the quality of the selection outcome is hard to predict and control. This is a difﬁcult work assignment problem because there are normally hundreds of projects and dozens of auditors to choose from. The purpose of this research is to establish a genetic algorithm-based model to assist with the project selection and auditor as-signment process. The model is set up toﬁnd the optimal match between the project characteristics and au-ditor expertise from approximately 5.09E + 29 possible combinations. Information provided by the Kaohsiung County Government is used to validate the model. The results show that the model is not only valid but also able to produce a“much better match” between projects and auditors when comparing to man-ual assignment.

1. Introduction

In order to improve the quality of the public construction projects, the Taiwan government has enforced a three-level quality manage-ment system since 1993. The goal is to promote the awareness of the importance of construction quality among all the participants in the public construction projects. Theﬁrst level is the quality control system carried out by the contractor. The second level is the construc-tion quality assurance system implemented by the local government construction department. The third level is quality audit system enforced by the national government construction department[1]. The structure of the three-level quality management system is shown inFig. 1.

To conduct the third-level quality audit, a quality audit committee is established in the Kaohsiung County Government. The committee is composed of one chairperson, two vice-chairperson, one secretary andﬁve staffs, 17 internal auditors and 45 external auditors. The au-ditors are nominated by the committee and approved by National Construction Council. Approved auditors are either experienced ex-perts (from government or from private sector) or knowledgeable scholars. The quality audit committee is responsible for selecting pub-lic projects to be audited and assign auditors for quality audits every month. In general, there are more than 150 construction projects in the list and eight projects are to be selected for audit each month. For each project, three auditors (one internal and two external)

should be assigned from the approved auditor list to conduct the quality audit. This is a complex assignment problem as there are many potential project and auditor combinations (approximately 5.09E + 29) to choose from. It is a very tough task confronting the quality audit committee and at times, the committee just randomly (or by gut feelings) selects projects and assigns auditors. As a result, some auditor expertise might not match the project characteristics well and thus the“quality” of the construction quality audit is in jeopardy.

To assist with this assignment problem, this research adopts ge-neric algorithms to develop a public construction project selection and auditor assignment model that aims atﬁnding optimal matches between the auditor expertise and project characteristics. With data provided by the Kaohsiung County Government, the model is proven to provide better recommendations regarding project selection and auditor assignment when comparing with traditional manual selec-tion and assignment process. Built in the MS Excel environment, this model can be easily utilized by the members in the quality audit committee to assist with the public construction project quality audit process.

In Japan, the Metropolitan Government of Tokyo also conducts au-dits on public construction projects to ensure no wasteful spending, shoddy workmanship and so forth at each stage of project execution [2]. The proposed model can be adopted to assist the Tokyo City of ﬁ-cials select projects for audit and assign appropriate auditors. In other countries, private companies (often consulting companies) hired by the public agencies would perform the quality audits for public con-struction projects. With some customization, these private companies will be able to use the modi_{ﬁed model to assist the quality audit} Automation in Construction 22 (2012) 459–467

⁎ Corresponding author. Tel.: +886 7 3814526x5250; fax: +886 7 3831371. E-mail addresses:yrwang@cc.kuas.edu.tw(Y.-R. Wang),dozekidd@kcg.gov.tw

(S.-L. Kong).

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process. With a better match between auditor expertise and project characteristics, it is expected that the“quality” of the quality audit will be improved.

2. Assignment problem

Generalized assignment problem (GAP) deals withfinding the op-timal solution among many different combinations, which are con-cerned with assigning n jobs to m agents under constraints. Every agent has different capabilities and resource constraints. When per-forming each job, the cost occurred and efficiency achieved is differ-ent for each agdiffer-ent. The purpose of solving GAP is to assign appropriate agent to complete the n jobs so that the lowest total cost or the highest overall profit is achieved. It can be expressed in the following equations[3]:

Maximize or minimize f xð Þ ¼X m i¼1 Xn j¼1 cijxij ð1Þ subject to X m i¼1 xij¼ 1; j¼ 1;2;…;m ð2Þ Xn j¼1 rijxij≤ bi; i ¼ 1;2; …;n ð3Þ

Eq.(1)is the objective function and Eqs.(2) and (3)are problem constraints. n is the total number of jobs to be performed and m is the total number of agent available to perform the jobs. Cijrefers to

the cost occurred or proﬁt obtained for agent i to complete job j. When Xijequals one, it means that agent i is assigned to perform

the job j. On the other hand, when Xijequals zero, agent i is not

appointed to perform the job j. rij is the resource consumed by

agent i to perform the job j and biis the total resource available for

agent i. Eq.(2)makes sure that each job is performed by only one

agent and Eq.(3)makes sure that the resource consumed by each

agent does not exceed the capacity limit.

This research intends to investigate effective techniques for assigning auditors and selecting projects for public construction audit under constraints. That is, to optimize the match between audi-tor expertise and project characteristics. Several researches have been conducted to solve this sort of assignment problems with different techniques/algorithms. Nevertheless, none has been applied to solve quality auditor assignment problem before. Algorithms aiming at re-solving assignment problems can be summarized as exact algorithms and heuristic algorithms, which will be discussed in the following sections.

2.1. Exact algorithms

Exact algorithms are one of the algorithms used to_{find exact} solu-tions to optimization problems. Savelsbergh proposed a Branch-and-Price algorithm tofind the maximum profit when assigning n jobs to m agents under capacity constraints[4]. The algorithm considers the linear programming relaxation of the disaggregated formulation for the generalized assignment problem (GAP) and allows column gener-ation at any node of the branch and bound tree. The optimal integer solutions to a set partitioning formulation of the problem can thus be obtained[5]. Narciso and Lorena applied Lagrangean/surrogate re-laxation to the problem of maximum profit assignment of n tasks to m agents (n > m), such that each task is assigned to only one agent sub-ject to capacity restrictions on the agents[5].

A Branch-and-Bound algorithm is proposed by Haddadi and Ouzia to solve the generalized assignment problem with largest-upper-bound-next branching strategy[6]. Lagrangean relaxation is achieved by dualizing the second set of constraints. An upper bound is obtained using a standard subgradient method at each node of the decision tree to solve the lagrangean dual. By solving a smaller generalized as-signment problem, the algorithm exploits the solution of the relaxed problem[6].

Gomar et al. proposed a linear programming model to optimize the multi-skilled workforce assignment and allocation process in con-struction[7]. Their objective is toﬁnd the minimum total number of workforce, switching and hires/ﬁres. The model is able to suggest ac-tivity assignments that minimize switching and can be used to set strategic targets for combination of multi-skills[7].

2.2. Heuristic algorithms

Different from the exact algorithms, heuristic algorithms only_ﬁnd approximate solutions to the problem. As a result, optimal solutions are not guaranteed under heuristic search but“good” solutions can still be obtained within reasonable run times. Pearl states that heuris-tic methods are based upon intelligent search strategies to control problem solving in human beings and machines[8].

Chu and Beasley proposed a genetic algorithm (GA)-based heuris-tic for solving generalized assignment problem[3]. Comparing to other heuristic algorithms in terms of solution quality, the GA-based algorithm is able to provide the best possible heuristic solutions when assigning n jobs to m agents under capacity constraints. The re-sults show that the near-optimal solutions found are on average less than 0.01% from optimality[3].

Diaz and Fernandez applied Tabu search heuristic to solve the GAP [9]. Different from other search techniques, Tabu search enhances the performance of a local search method by using memory structures. The proposed algorithm uses recent and medium-term memory to dynamically adjust penalty weights when constraints are violated. The most distinctive feature of the proposed algorithm is the permis-sion of solution search in the infeasible solution space. Comparing to other heuristic methods, the Tabu search heuristic provides good quality solutions in competitive computation times[9].

A GA-based algorithm is proposed by Tororslu and Arslanoglu to solve an extended version of the standard assignment problem, which has additional constraints for matching the nodes of the parti-tions[10]. When solving the GAP, both the hierarchical-ordering and set-restriction constraints are taken into consideration for large hier-archical organizations. The results show that GA-based algorithm provides good solutions for the multi-objective optimization problem [10].

Exact algorithms are only effective in certain GAP instances where the constraints are loose. For highly capacitated problems, exact algo-rithms can only solve problems involving up to a few hundred vari-ables before the search trees grow prohibitively large. The large-sized problems are often tackled by applying heuristics to obtain

Fig. 1. Three-level quality management system.

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approximate solutions[3]. Based on the literature reviewed and the complexity of the problem scheme, this research adopts heuristic search method to solve the auditor assignment and project selection problem. In this research, genetic algorithms are chosen as the heuris-tic search technique for its good quality of solution generated and competitive computation times when solving the complex GAP. In the proposed GA model, infeasible solutions are allowed by introduc-ing penalties in theﬁtness function to improve the performance of this model.

3. Genetic algorithms

First introduced by Dr. John Holland in 1975, the concept of ge-netic algorithms (GAs) is based on Darwin's theory of biological evolution by natural selection[11]. GA is one of the optimization methods and is also an effective random search method. It adopts the principles of natural genetic evolution and selection process, by which traits that make it more likely for an organism to survive and successfully reproduce will pass on to successive generations

in order to have offspring with “better-ﬁtness” for survival.

When encountering with complex problem, GAs are able to search for optimal solutions by adopting this“best-ﬁt survived” principle [12]. Similar to the evolution by natural selection, the genetic al-gorithm searches for the best-ﬁt solutions to a problem through a series of reproduction, crossover, mutation and selection pro-cess.Fig. 2illustrates this process. Before applying the genetic al-gorithm to solve a problem, the problem must be transformed into an objective function in mathematical format. Based on the prob-lem itself, potential solutions are represented by chromosomes

and coded into genes. The ﬁtness of each individual solution is

evaluated by the objective function. Then the GA process of selec-tion, reproducselec-tion, crossover and mutation is repeated to obtain an optimal solution.

3.1. Problem formulation

The biggest challenge when applying the genetic algorithms is the problem formulation. At this early stage, an objective function or ﬁt-ness function must be formulated to prescribe the optimality of a

solution to the problem. Theﬁtness function should correlate closely with the objective of the problem to be solved[13]. For example, in

the typical Traveling Salesman Problem (TSP), a _{ﬁtness function}

must be constructed to describe the sequence of the cities visited and calculate the total travel distance. In this particular example, the_{ﬁtness of one possible solution refers to the total travel distance} obtained under the predetermined sequence of cities visited. In the GA process, solutions (sequence of cities visited) are represented as chromosomes, which consist of bit strings (genes). One typical way is to code the solutions in binary as strings of 0s and 1s.Fig. 3 illus-trates three typical ways of coding in the GA process: (a) binary cod-ing, (b) numerical codcod-ing, and (c) symbolic coding.

3.2. Initial population

After the problem formulation, the_{fitness function is established} and potential solutions are generically represented. The next step is to generate an initial population of solutions as a start point of the search process. Typically, these individual solutions are randomly generated from the solution space to form the initial population. In general, the total number of individuals in each generation remains the same during the GA process. The size of population depends on the nature of the problem and the length of the chromosome. For chromosomes with n genes, it can be viewed as a solution space of n dimensions. If the population size is too small, the search could con-verge faster and make it more likely tofind local optimal solutions. This will limit the capability of GAs to search for optimal solutions. On the other hand, if the population size is large, it will take more time to compute and thus makes it longer for the model to_{find the} optimal solution. In addition, if thefitness values in the initial popula-tion are good, it is easier for the model tofind the optimal solution. Therefore, the size of initial population and their corresponding fit-ness values will have direct impact on computing time and quality of model output[14].

3.3. GA operators

After the initial population has been generated, individualfitness will be evaluated by thefitness function. A selection process which is based on individualfitness will be implemented to choose the

“par-ents” for the next generation. The new generation is generated

through crossover and mutation of the selected individuals from the previous generation. Theﬁtness values of the new generation will be calculated and this process (selection, reproduction, crossover and mutation) will repeat until model termination criteria are reached. Common terminating conditions are: (a) a solution meets the objective, (b) aﬁxed number of generations are

gener-ated, (c) aﬁxed computing time is reached and (d) improvement

ofﬁtness value becomes very small in successive generations. 3.3.1. Selection and reproduction

In the selection process, solutions with betterﬁtness values (as measured by theﬁtness function) are more likely to be selected as

Fig. 2. Generic algorithm process. Fig. 3. Typical variable coding schemes.

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[10] I.H. Toroslu, Y. Arslanoglu, Genetic algorithm for the personnel assignment with multiple obectives, Information Sciences 177 (2007) 787–803.

[11] J. Holland, Adaption in Natural and Artiﬁcial Systems, The University of Michigan Press, Ann Arbor, MI, 1975.

[12] Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer, New York, 1996.

[13] D.E. Goldberg, Genetic algorithms in search, Optimization and Machine Learning, Addison Wesley, Reading, MA, 1989.

[14] D.A. Coley, An introduction to genetic algorithms for scientists and engineers, WorldScientiﬁc, Singapore, 1999.

[15] Government Kaohsiung County, 2008 Project Audit Plan, Kaohsiung, Taiwan, 2008, 2008

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