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A hybrid mechanism for optimizing construction simulation models
Automation in Construction 14 (2005) 85 – 98 www.elsevier.com/locate/autcon
A hybrid mechanism for optimizing construction simulation models Tao-ming Chenga,*, Chung-wei Fengb, Yan-liang Chena a
Department of Construction Engineering, Chaoyang University of Technology, Taiwan, ROC b Department of Civil Engineering, National Cheng Kung University, Taiwan, ROC Accepted 15 July 2004
Abstract Simulation is a powerful tool for planning and scheduling highly repetitive tasks in a construction project. However, sensitivity analysis has to be utilized to find the best resource combination to execute the construction tasks. By performing the sensitivity analysis, various resource combinations can be evaluated in terms of their effects on the operation’s production and cost. The results of the sensitivity analysis can assist project managers in planning effective resource assignments based on their goals, such as maximizing the system’s production rate or minimizing the system’s unit cost. However, it is time-consuming to conduct the sensitivity analysis if there are a large number of resource alternatives available. This paper proposes a hybrid mechanism that integrates heuristic algorithms and genetic algorithms to efficiently locate the best resource combination for the construction simulation optimization. Results show that this new hybrid mechanism not only locates the optimal solution but also reduces tremendous computational efforts. D 2004 Elsevier B.V. All rights reserved. Keywords: Hybrid mechanism; Construction; Simulation
1. Introduction Simulation is a powerful tool for planning and scheduling highly repetitive tasks in a construction project. Variables of the simulation model, such as the
* Corresponding author. 168 Gifeng E. Road, Wufeng, Taichung County 413, Taiwan, ROC. Tel.: +886 4 23323000x4238; fax: +886 4 23742325. E-mail address: [email protected] (T. Cheng). 0926-5805/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.autcon.2004.07.014
task duration and different resource combinations, can be evaluated in terms of the operation’s production and cost. For example, examining the impact of different resource assignments on the project’s production and cost is useful for the project managers in the planning stage. Conventionally, the project planner has to perform the sensitivity analysis that tests all resource alternatives of the simulation model to determine which resource combinations can produce the highest system’s production rate or the lowest system’s unit cost/total cost. If the simulation model is
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not complicated and has a small number of resource combinations, the sensitivity analysis can be useful to assist the project planner in deciding the best resource assignment. However, if the simulation model is complex and there are a large number of resource combinations available, it becomes time-consuming to perform the sensitivity analysis. Different heuristic algorithms (HAs) have been developed to efficiently search for the most appropriate resource allocation that produces a better system production rate under specified objectives [1]. Even though HA can easily generate a better solution, the solution found by HA is usually the local optimum. In addition, the performance of the HA is problem-dependent. Genetic algorithms (GAs) are also successfully applied as an optimization methodology to search for the optimal resource combination of the simulation model [11]. However, GA conducts the population-wise search, which may require a great amount of computation efforts to find the global optimum solution for largescale simulation problems. Therefore, it is necessary to develop a new mechanism that takes advantages of both HA and GA to find the optimal resource combination of the simulation model. This paper presents a hybrid mechanism that integrates HA and GA to efficiently locate the optimal solution. This hybrid mechanism first applies HA to find several local optimal solutions and then uses GA to search for the global optimal solution from those local optimal solutions. Results show that this new hybrid mechanism not only locates the global optimal solutions but also reduces tremendous computation efforts. In addition, a computer implementation that utilizes the CYCLONE simulation methodology and Visual Basic language is developed to assist project engineers to efficiently find the optimal resource allocation of the simulation model. Details of this new hybrid mechanism and examples that demonstrate the efficiency of this new approach are provided in the following sections.
2. Background Computer simulation techniques have been applied to the field of construction engineering and management near three decades. Several simulation systems have been developed especially for the
construction process. Some of these simulation systems, such as RESQUE [3], UM-CYCLONE [12], COOPS [13], STROBOSCOPE [14], and COST [4], are based on CYCLONE (CYCLic Operation NEtwork) modeling format because of its clear and simple symbolic structure compared to other simulation techniques. Most of these simulation systems focus on analyzing the construction operation in terms of system performances, such as the production rate or the unit cost. Besides analyzing the system performances, searching for the optimal resource combination that produces the best performance is another important issue of the construction simulation. However, these systems take the sensitivity analysis approach, which exhaustively enumerates all resource combinations to find the optimal resource allocation [17]. As a result, if a large number of resource combinations are present, the sensitivity analysis approach becomes inefficient in terms of computation efforts. AbouRizk and Shi [1] proposed an HA, which efficiently locates the most appropriate resource allocation of the simulation system. However, the solution of their heuristic approach is usually the local optimum and the performance is problem-dependent. With the success of integrating GA with different methodologies in many fields, several researchers integrate GA with the simulation system to search for the optimal resource allocation. These researches include applying GA simulation in the optimization of the pastoral dairy farm management [16], shipping and shipyard layout planning [2], hard disk drive production scheduling [18], and ready-mixed concrete trucks dispatching management [6]. In addition, McHaney [15] presented a simple real-coded GA to find better simulation parameters of the hard inverse problem. McHaney reported that GA is relatively adaptable for the discrete event computer simulation environment. Moreover, a general-purpose GA simulation computer system, named GACOST, developed by Cheng and Feng [5] confirms McHaney’s results. Similarly, Hegazy and Kassab [10] used GA simulation technique for resource optimization in construction planning. Although GA is successfully used for the resource optimization of the simulation model, the performance of GA may depend on the initial population, which is randomly generated. It is the purpose of this study to propose a hybrid simulation
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optimization mechanism that integrates HA and GA to more efficiently search for the resource combination that produces the best system performance.
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involved in a construction operation and their waiting locations: DELAY ðlimiting resourceÞ ¼ MINðall resources
3. The heuristic approach
iÞ
MAXð all waiting locations
jÞ
Dij
ð2Þ
The basic modeling elements of the simulation system are activities and queues. Activities represent the work tasks that need time and resource to perform. Queues are used for modeling the waiting state of resources in the system. AbouRizk and Shi [1] used the DELAY statistic of queue nodes to guide the simulation toward better resource combinations that can maximize the production rate or minimize the unit cost for a system. The resource DELAY statistic is defined as indicated in Eq. (1): DELAY ¼ ðwaiting time=working timeÞ 100%
ð1Þ
where bwaiting timeQ is the total duration that the resource stays in the queues and bworking timeQ is the total duration that the resource stays in the simulation system. The resource DELAY statistic represents the degree of the utilization of the resource in the system. A resource may be used in several activities and wait at several queues. Thus, a resource would have different types of DELAY statistics. Two types of DELAY, as indicated in Eqs. (2) and (3), are defined by AbouRizk and Shi. Eq. (2) describes that the resource with the least DELAY value will limit the production rate for the process. On the other hand, Eq. (3) shows that the resource has enough capacity that will not limit the system production rate under current configuration. Then, the DELAY of a system can be determined as the smallest DELAY value among the resources. Table 1 shows an example of the resources Table 1 Example of resources involved in waiting locations [1] Resource number
1 2 – m
Queue position 1
2
. . .n
D 11 D 21 – Dm1
D 12 D 22 – D m2
. . .D 1n . . .D 2n – . . .D mn
DELAY ðsurplus resourceÞ ¼ MAXðall resources
iÞ
MINð all waiting locations
jÞ
Dij
ð3Þ
3.1. Process of reaching maximum production rate HA can optimize the system by either maximizing the production rate or minimizing the unit cost. The steps for maximizing the production rate of the simulation system are described as follows: 1.
2. 3. 4. 5.
Randomly select a resource combination and conduct a pilot run to determine the current DELAY values for participating resources. Apply Eq. (2) to identify the limited resource. Increase the value of limited resource identified in Eq. (2) within the specified boundaries. Perform the simulation experiment and determine the new production rate. Repeat steps (2)–(4) until the limited resources reach the specified boundaries.
3.2. Process of reaching minimum unit cost Other than maximizing the system production rate, minimizing the unit cost of a simulation system, as defined in Eq. (4), is another goal that the planner usually wishes to achieve: Unit Cost ¼ ½total cost=total production
ð4Þ
where btotal costQ is the total expenditure of resources used in the simulation system and btotal productionQ is the total quantity produced in the simulation system. The steps for minimizing the unit cost rate of a simulation system are described as follows: 1.
Randomly select a resource combination and conduct a pilot run to determine the current DELAY values for participating resources.
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Fig. 1. Generic procedure of GA operations [7].
2.
Apply Eq. (2) to identify the limited resource to be increased. 3. Run simulation for the new resource allocation and evaluate total cost and production as defined in Eq. (4). 4. If the increasing percentage of total cost is less than the one of total production, keep increasing the same limited resource identified in step (2); otherwise, apply Eq. (3) to identify the surplus resource and reduce it, then go to step (3). 5. Repeat steps (2)–(4) until two directions of resources reach their boundaries.
4. GAs GA is the search algorithm developed by Holland [11], which is based on the mechanics of natural selection and genetics to search through decision space for optimal solutions. The metaphor underlying GA is natural selection. In evolution, the problem that each species faces is to search for beneficial adaptations to the complicated and changing environment. In other words, each species has to change its chromosome combination to survive in the living world. In GA, a string represents a set of decisions (chromosome combination), which is a potential solution to a
problem. Each string is evaluated on its performance with respect to the fitness function (objective function). The ones with better performance (fitness value) are more likely to survive than the ones with worse performance. Then the genetic information is exchanged between strings by crossover and perturbed by mutation. The result is a new generation with (usually) better survival abilities. This process is repeated until the strings in the new generation are identical, or certain termination conditions are met. A generic flow of GA operation is given in Fig. 1. Original parent chromosomes represented as strings are randomly picked. Then, random selection of crossover match chromosome and match cut points are performed. A new group of exclusive substrings from parent chromosomes is formed. In addition, chromosomes are selected randomly to perform mutation operation. As a result, new offsprings of chromosomes are created. The generic operation of GA is depicted as follows. 4.1. Standard GA operations The standard GA operates on a population of bitstrings (genotype) d, and each individual represents a solution coded for all the variables required according to a finite alphabet of cardinality (0 and 1 for binary representation). Each individual yields a decoded solution (phenotype) and is evaluated by a predefined fitness function f. An example of the chromosome representation is given in Fig. 2. Each individual string d is represented in the form d=g(x 1,x 2,x i ,. . .,x n )=g(X). Each bit position x i of the m tuple (length of m for each variable; m depends on the precision required) substrings is designed over a finite alphabet of cardinality k (usually two: 0 and 1). Therefore, there are k nm different strings in the solution space, and those k nm different strings represent k nm different solutions. g is the decoding function that converts the value of x i to the real value.
Fig. 2. Example of chromosome representation.
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Fig. 3. Example of crossover.
4.2. Algorithm Step 1
Step 2
Step 3
Generate random parent population. The parent population P, with N (population size) nm tuple strings, is selected at random with or without replacement from the k nm solution space. The fitness value is evaluated for each string, f( g(X)). Reproduction. The offspring population O of size N is created from P by probabilistically selecting the strings according to their fitness values with replacement. Crossover. With probability P c, each two strings of O undergo a crossover operation on the substring basis. Crossover means that a random selection of a crossover point along the substrings and the exchange of tailing subtuples between the two substrings
Step 4
Step 5
are involved. An example can be seen in Fig. 3. Mutation. With probability P m , the value of the bit position x i in O is changed at random according to the k alphabet of cardinality. This operator is called a mutation operator. Fig. 4 is an example of mutation. Replacement and termination. Replace P by O and evaluate the fitness values of the strings in O, f( g(X)). Repeat steps (2)–(5) until all strings in the population are identical, or until some other termination conditions are met.
Generally, in GA, the accumulated information is exploited by the selection mechanism and new regions of the search space are explored by performing genetic operations (i.e., crossover and mutation).
Fig. 4. Example of mutation.
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However, GA is usually good at global search but slow to converge. Therefore, a common way of overcome this defect is to combine the HAs used to conduct fine-tuning for locating local optima with GA used to perform global search to escape local optima [7]. The proposed new hybrid mechanism for construction simulation optimization is depicted in Section 5.
5. The hybrid mechanism A new mechanism for optimizing the simulation model, named heuristic GAs (HGA), which hybridizes the abovementioned HA and GA, is developed by combining the merits of both algorithms. HGA employs GA to search through the global solution space and applies HA to perform the local search of the selected solution. In addition, the widely used simulation methodology, CYCLONE, is selected to model the construction operation because of its simple modeling symbols. Table 2 indicates the basic modeling elements developed by CYCLONE. Readers may refer to Ref. [9] for details. The proposed hybrid mechanism woks as follows. At first, a CYCLONE model is set up according to the construction operation that needs to be evaluated in terms of resource utilization. The resource variation within the CYCLONE system happens at the queue. Therefore, the chromosome Table 2 CYCLONE system modeling elements [8]
Fig. 5. Chromosome structure proposed in HGA.
structure used in this new simulation mechanism is designed in such a way that the length of the chromosome is equal to the number of the queues and the value of each gene depicts the resource utilization at the queue. Fig. 5 illustrates a string that represents the chromosome structure used in this simulation mechanism. Secondly, numbers of strings P(t), which are defined based on the chromosome structure described above, are randomly generated and evaluated by simulating the CYCLONE model. HA is then employed to alter the resource combination of each string toward a better direction for reaching local optimum. These strings carry the genetic information of resource combinations for the construction operation. Genetic operators, such as crossover and mutation, are applied to those local optimal strings to produce the interim offspring C(t). The fitness value of each string within the interim offspring C(t) can be determined by again simulating the CYCLONE model. Then the new offspring P(t) is generated by selecting the strings from the interim offspring C(t) according to their
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Fig. 6. Summary of HGA.
fitness values. The better is the fitness value of the string, the higher is the chance that the string could be selected. This process is repeated until the termination condition is met. A summary of HGA is given in Fig. 6. 5.1. The computer implementation A computer implementation coded by Microsoft Visual BasicR is developed to streamline the resource optimization process of applying the abovementioned
searching mechanism to the simulation system. This computer implementation utilizes the proposed mechanism as a selection engine to screen out the resource combinations that produce bad system performances. Fig. 7 shows the input interface of the computer implementation. Users can choose the objective to be optimized. Two optimization objectives that maximize system production rate or minimize unit cost are provided by the program. In addition, population size, generation, crossover rate, and mutation rate can be defined by users. Moreover, the convergent diagram
Fig. 7. Interface of HGA parameter input.
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Fig. 8. Convergent diagram of HGA computer program.
will be displayed simultaneously along with simulation progress, as shown in Fig. 8.
6. Case verification The verification of HGA for optimizing the simulation model is described in this section. There
are three steps in the verification process. The first step is to obtain the possible optimal solutions that maximize the system production rate and minimize the unit cost without performing any optimization algorithms. This process can be accomplished by using the maximum amount of resources and minimum amount of resources to the simulation model, respectively. It is because, intuitively, the maximal
Fig. 9. Sewer pipeline installation process [9].
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Fig. 10. CYCLONE model for sewer line installation operation.
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are both used to validate this proposed new optimization mechanism.
system production rate may be obtained by using the maximum amount of resources for each work task. Likewise, the minimal unit cost may be reached by employing the minimum amount of resources for each work task. The second step is to employ both HA and GA to obtain the possible optimal solution. Finally, the results obtained from steps (1) and (2) are compared with the solution reported by running HGA in terms of accuracy and efficiency. In addition, two objectives, which are maximizing the system production rate and minimizing the system unit cost,
6.1. The test example The sewer pipeline construction case presented in Fig. 9 is adapted from Halpin and Riggs [9]. This construction operation involves the installation of a sewer line that requires six sequential processes, which are pavement breaking, excavation, pipe laying, backfilling, compaction, and paving. These
Table 3 Initial resource information for the sewer line installation model Initialized at QUEUE
Resource description
Minimum available resource unit
Maximum available resource unit
Cost ($/h or unit)
1 3 4 5 6 10 11 12 13 15
SECTION READY BREAKER IDLE READY FOR EXCAVATE TRUCK WAIT B/H IDLE READY FOR SHORING PIPE STORAGE TRENCH BOX IDEL SMALL CRANE IDLE BED READY FOR BED PREPARE TRUCK IDEL PIPE COMMAND PIPE STOCK PILED CREW IDEL PIPE BED PREPED READY FOR SEAL RDY TO REMOVE TR BOX WAIT BACKFILL B/H IDLE CREW IDEL RDY FOR SURFACE PREP ROLLER RDY SURF RDY FOR PAVEMENT TRUCKS RDY BATCH PLANT IDLE CONCR RDY RDY TO POUR CREW RDY GEN 3 TRKS RDY TO COMPACT CREW DUMMY DUMMY RDY TO PREP SURF DUMMY DUMMY
1 1 0 1 1 0 2000 1 1 0
20 5 0 10 5 0 0 20 10 0
– 2000 – 1000 875 – – – 1000 –
1 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 0 1 1 1 0 1 1
10 0 0 5 0 0 0 0 5 5 0 5 0 10 5 0 0 5 0 0 5 1 1 0 1 1
1000 – – 275 – – – – 875 275 – 275 – 1000 – – – 275 – – 275 – – – – –
16 17 20 22 24 27 29 32 33 34 36 38 40 41 42 45 47 50 54 57 58 60 62 64 60 62
T. Cheng et al. / Automation in Construction 14 (2005) 85–98 Table 4 Activity duration for the sewer line installation model Element number
Activity
2 7 8 14 18 19 21 23 25 26
BREAK PAVEMENT EXCAVATE PAVEMENT TRK BACK CYCLE INSTALL TRENCH BOX LOAD PIPE HAUL TO SITE PLACE PIPE PREPARE PIPE bed TRK TRAVEL TO STACK LEVEL AND HAND BACKFILL HBF INSTALL RUBBER SEAL REMOVED TRENCH BOX BACKFILL WETTED MATERIAL COMPACT MATERIAL LOAD T–M TRK TRAVEL TO SITE PREP FORM WORK PLACE CONCRETE RETURN TO PLANT SPREAD/FINISH DUMMY WEATHER DELAY DUMMY
28 30 35 37 39 43 44 46 48 49 51 53 63 65
Duration (min) 20 45 10 20 20 5 20 5 10 20 20 20 60 6 180 6 10 60 20 10 120 0 600 0
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efforts. Therefore, the aforementioned three steps for verification are taken. Each work task within this test example is first assigned with the maximum amount of resources to obtain the possible maximal system production rate and unit cost. Then each work task is assigned with the minimum amount of resources to obtain the minimal system production rate and unit cost. In addition, this example is simulated in 200 cycles. The result shown in Table 5 indicates that the production rate of using the maximum amount of resources is 0.777 cycles/h, which is about 17 times that of 0.045 cycles/h by using the minimum amount of resources. Moreover, the unit cost of using the minimum amount of resources is $84,503 per section, which is about 42% of $203,323 per section by using the maximum amount of resources. Higher production rate could be reached by using the maximum amount of resource for each work task; however, it is not clear that the production rate obtained so far is the highest one. Similarly, lower unit cost rate could be reached by using the minimum amount of resource for each work task; however, it is also not clear that the unit cost obtained so far is the lowest one. Section 6.2 explains steps (2) and (3) of the verification. 6.2. HGA simulation analysis
processes are programmed in series with no shared resources and transportation and feedback loops. The CYCLONE model for the sewer line operation is shown in Fig. 10. The test data, which include the duration of each work task, available resources, and related cost information, are listed in Tables 3 and 4, respectively. As it can be estimated, the total number of resource combinations is 7.81251012 (=202 10458). Consequently, it is not economical to exhaustively enumerate all resource combinations to obtain the optimal solutions in terms of computational
In steps (2) and (3), the test example is also optimized by HA, GA, and HGA for allocating optimal resource combinations, respectively. In addition, two objective functions, which are maximizing the system production rate and minimizing the system unit cost, are used to verify the results of HGA in terms of accuracy and efficiency. Running GA and HGA involves setting up parameters (i.e., population size, generation number, crossover rate, and mutation rate). Based on the suggestion from the experiments of Cheng and Feng [5], the population size, generation
Table 5 Best guess of both the production rate and unit cost of the sewer line installation system Item
Guess of possible worse result
Guess of possible best result
System production rate System unit cost Resource combination [number of Q (quantity)]
0.045 (cycles/h) $203,323/section Q 1 (1), Q 3 (1), Q 5 (1), Q 6 (1), Q 12 (1), Q 13 (1), Q 16 (1), Q 22 (1), Q 33 (1), Q 34 (1), Q 38 (1), Q 41 (1), Q 42 (1), Q 50 (1), Q 58 (1)
0.777 (cycles/h) $84,503/section Q 1 (20), Q 3 (5), Q 5 (10), Q 6 (5), Q 12 (20), Q 13 (10), Q 16 (10), Q 22 (5), Q 33 (5), Q 34 (5), Q 38 (5), Q 41 (10), Q 42 (5), Q 50 (5), Q 58 (5)
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number, crossover rate, and mutation rate are set to 50, 50, 0.5, and 0.1, respectively. In addition, although generating a single pilot resource combination is sufficient for performing HA optimization, 50 pilot resource combinations are randomly generated to locate the possible optimal solutions simultaneously for the purpose of comparing GA and HGA in terms of accuracy and efficiency. Moreover, in order to fairly compare three methodologies, the termination condition for running HA is also determined by generation rather than blimited resource reaching specific boundary.Q The results are analyzed as follows. 6.2.1. Comparisons based on the object of maximizing the system production rate When the objective is defined to maximize the system production rate, the results obtained by conducting HA, GA, and HGA optimization are 0.86, 0.87, and 0.88 units per cycle, respectively. It is clear that HGA generates the best system production rate compared to the results reported by HA and GA. Moreover, as indicated in Fig. 11, HGA takes only 17 generations to find the best system production rate, which is the fastest one among the three algorithms. Furthermore, only 2500 (=50 50) resource combinations are explored. In other words,
only 3.21010 (=2500/(7.81251012)) of the total solution space is explored by running HGA. As the results indicate, HGA can find the better solution with less computational efforts. 6.2.2. Comparisons based on the object of minimizing system unit cost In addition, HA, GA, and HGA are employed to minimize the system unit cost of the test example. The results of the unit cost of the test example generated by HA, GA, and HGA are $38,555, $28,657, and $28,103 per section, respectively. Again, HGA reports the minimal unit cost among the three algorithms. HGA also takes the least number of generations to converge to the optimal solution, as shown in Fig. 12. 6.3. Sensitivity analysis Since running HA, GA, and HGA all requires the random selection of initial resource combinations, it is necessary to see whether the random selection will affect the final optimum solution. Table 6 lists 10 different independent simulation results when the population size and the number of generation are, respectively, set to 50 and 50 for running all three methods. In addition, the crossover rate and the
Fig. 11. Convergent curve for maximizing system production rate.
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Fig. 12. Convergent curve for minimizing system unit cost.
combinations could result in the same system production rate. Furthermore, the average solutions of running HA, GA, and HGA for minimizing the system unit cost are 33,667, 30,367, and 29,488 ($/ unit), respectively. The optimal solution (i.e., 26,484) is gained by the fourth run in running HGA. In these tests, HGA decreases the system unit cost by 12.4% ([33,667–29,488]/33,667) and 2.9% ([30,367– 29,488]/30,367) compared with HA and GA, respectively. The sensitivity analysis results indicate that HGA outperforms HA and GA in optimizing both the production rate and the system unit cost.
mutation rate for running GA and HGA are set to 0.5 and 0.1, respectively. When the objective is to maximize the production rate, the average solutions of 10 runs for HA, GA, and HGA are 0.861, 0.869, and 0.881 (cycle/h), respectively. The maximum value of 0.91 is obtained in the sixth run in running HGA. In those 10 runs, none of the production rates obtained by HGA was below 0.87, which indicates that HGA can keep a good performance. It is also interesting to note that, in these tests, the system production rate is usually dominated by the resource that has the lowest output rate. It is possible that different resource Table 6 Sensitivity analysis for running HA, GA, and HGA Run
Objective and method Maximize production rate (cycles/h)
1 2 3 4 5 6 7 8 9 10 Average
Minimize unit cost ($/unit)
HA
GA
HGA
HA
GA
HGA
0.86 0.84 0.88 0.87 0.87 0.84 0.87 0.87 0.84 0.87 0.861
0.87 0.87 0.88 0.87 0.87 0.81 0.88 0.88 0.88 0.88 0.869
0.88 0.88 0.88 0.88 0.88 0.91 0.88 0.87 0.87 0.88 0.881
38,555 32,562 33,547 34,040 27,636 38,392 31,305 28,443 37,853 34,340 33,667
28,657 30,658 31,988 28,412 28,197 30,369 34,157 27,235 31,099 32,893 30,367
28,103 26,437 33,083 26,484 30,514 28,657 29,228 31,775 26,501 34,107 29,488
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7. Conclusions Computer simulation techniques have been applied to the field of construction engineering and management for predicting the performance of the construction operation with predefined resource combination. Conventionally, the sensitivity analysis is conducted to find the optimal resource combination, in which all possible resource combinations are exhaustively enumerated to find the suitable resource combination that produces the optimal system performance. If the potential resource combinations are small in size, the sensitivity analysis would not cost too much computational efforts. However, when a large size of resource combinations is presented in the simulation model, such a sensitivity analysis process is no longer appropriate. This paper proposes a hybrid optimization mechanism that integrates HAs and GAs, named as HGA, to efficiently generate the resource combination that produces the optimal system performance. Case study shows that this new hybrid mechanism, along with the implemented computer program, can efficiently and accurately generate the optimal solution to help construction engineers streamline the planning process of construction operations.
Acknowledgements This work was partially supported by the National Science Council, Taiwan (grant no. NSC91-2211-E324-021).
References [1] S. AbouRizk, J. Shi, Automated construction–simulation optimization, Journal of Construction Engineering and Management, ASCE 120 (2) (1994) 374 – 385. [2] S.S. Bruzzone, Simulation and genetic algorithms for ship planning and shipyard layout, Simulation 71 (2) (1998) 74 – 83.
[3] D. Chang, RESQUE, PhD thesis, University of Michigan, Ann Arbor, MI, 1987. [4] T.-M. Cheng, S.-T. Wu, COST User’s Manual, Department of Construction Engineering, Chaoyang University of Technology, Taiwan, 2001. [5] T.-M. Cheng, C.-W. Feng, An effective simulation mechanism for construction operations, Automation in Construction 12 (3) (2003) 227 – 244. [6] C.-W. Feng, T.-M. Cheng, H.-T. Wu, Optimizing the schedule of dispatching RMC trucks through genetic algorithms, Automation in Construction 13 (3) (2004) 327 – 340. [7] M. Gen, R. Cheng, Genetic Algorithms and Engineering Optimization, Wiley, New York, 2002. [8] D.W. Halpin, CYCLONE-method for modeling job site processes, Journal of the Construction Division, ASCE CO3 (1977) 489 – 499. [9] D.W. Halpin, L.S. Riggs, Planning and Analysis of Construction Operations, Wiley, New York, 1992. [10] T. Hegazy, M. Kassab, Resource optimization using combined simulation and genetic algorithms, Journal of Construction Engineering and Management, ASCE 129 (6) (2003) 698 – 705. [11] J. Holland, Adaptation in Natural and Artificial System, University of Michigan Press, Ann Arbor, MI, 1975. [12] P.G. Ioannou, UM-CYCLONE User’s Guide, Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, MI, 1989. [13] L.Y. Liu, P.G. Ioannou, Graphical object-oriented discrete-event simulation system, Proceedings of the 1992 Winter Simulation Conference, Association for Computing Machinery, Arlington, VA, December, 1992, pp. 1285 – 1291. [14] J.C. Martinez, P.G. Ioannou, General-purpose systems for effective construction simulation, Journal of Construction Engineering and Management, ASCE 125 (4) (1999) 265 – 276. [15] R. McHaney, Integration of the genetic algorithm and discreteevent computer simulation for decision support, Simulation 72 (6) (1999) 401 – 411. [16] R.S. Parmar, R.W. McClendon, W.D. Potter, Farm machinery selection using simulation and genetic algorithms, Transactions of the American Society of Mechanical Engineers 39 (5) (1996) 1905 – 1909. [17] L.S. Riggs, Sensitivity analysis of construction operations, PhD thesis, Georgia Institute of Technology, Atlanta, GA, 1979.[18] [18] Z.Y. Zhao, R. de Souza, Genetic production line-balancing for the hard disk drive industry, International Journal of Advanced Manufacturing Technology 16 (2000) 297 – 302.
A hybrid mechanism for optimizing construction simulation models Tao-ming Chenga,*, Chung-wei Fengb, Yan-liang Chena a
Department of Construction Engineering, Chaoyang University of Technology, Taiwan, ROC b Department of Civil Engineering, National Cheng Kung University, Taiwan, ROC Accepted 15 July 2004
Abstract Simulation is a powerful tool for planning and scheduling highly repetitive tasks in a construction project. However, sensitivity analysis has to be utilized to find the best resource combination to execute the construction tasks. By performing the sensitivity analysis, various resource combinations can be evaluated in terms of their effects on the operation’s production and cost. The results of the sensitivity analysis can assist project managers in planning effective resource assignments based on their goals, such as maximizing the system’s production rate or minimizing the system’s unit cost. However, it is time-consuming to conduct the sensitivity analysis if there are a large number of resource alternatives available. This paper proposes a hybrid mechanism that integrates heuristic algorithms and genetic algorithms to efficiently locate the best resource combination for the construction simulation optimization. Results show that this new hybrid mechanism not only locates the optimal solution but also reduces tremendous computational efforts. D 2004 Elsevier B.V. All rights reserved. Keywords: Hybrid mechanism; Construction; Simulation
1. Introduction Simulation is a powerful tool for planning and scheduling highly repetitive tasks in a construction project. Variables of the simulation model, such as the
* Corresponding author. 168 Gifeng E. Road, Wufeng, Taichung County 413, Taiwan, ROC. Tel.: +886 4 23323000x4238; fax: +886 4 23742325. E-mail address: [email protected] (T. Cheng). 0926-5805/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.autcon.2004.07.014
task duration and different resource combinations, can be evaluated in terms of the operation’s production and cost. For example, examining the impact of different resource assignments on the project’s production and cost is useful for the project managers in the planning stage. Conventionally, the project planner has to perform the sensitivity analysis that tests all resource alternatives of the simulation model to determine which resource combinations can produce the highest system’s production rate or the lowest system’s unit cost/total cost. If the simulation model is
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not complicated and has a small number of resource combinations, the sensitivity analysis can be useful to assist the project planner in deciding the best resource assignment. However, if the simulation model is complex and there are a large number of resource combinations available, it becomes time-consuming to perform the sensitivity analysis. Different heuristic algorithms (HAs) have been developed to efficiently search for the most appropriate resource allocation that produces a better system production rate under specified objectives [1]. Even though HA can easily generate a better solution, the solution found by HA is usually the local optimum. In addition, the performance of the HA is problem-dependent. Genetic algorithms (GAs) are also successfully applied as an optimization methodology to search for the optimal resource combination of the simulation model [11]. However, GA conducts the population-wise search, which may require a great amount of computation efforts to find the global optimum solution for largescale simulation problems. Therefore, it is necessary to develop a new mechanism that takes advantages of both HA and GA to find the optimal resource combination of the simulation model. This paper presents a hybrid mechanism that integrates HA and GA to efficiently locate the optimal solution. This hybrid mechanism first applies HA to find several local optimal solutions and then uses GA to search for the global optimal solution from those local optimal solutions. Results show that this new hybrid mechanism not only locates the global optimal solutions but also reduces tremendous computation efforts. In addition, a computer implementation that utilizes the CYCLONE simulation methodology and Visual Basic language is developed to assist project engineers to efficiently find the optimal resource allocation of the simulation model. Details of this new hybrid mechanism and examples that demonstrate the efficiency of this new approach are provided in the following sections.
2. Background Computer simulation techniques have been applied to the field of construction engineering and management near three decades. Several simulation systems have been developed especially for the
construction process. Some of these simulation systems, such as RESQUE [3], UM-CYCLONE [12], COOPS [13], STROBOSCOPE [14], and COST [4], are based on CYCLONE (CYCLic Operation NEtwork) modeling format because of its clear and simple symbolic structure compared to other simulation techniques. Most of these simulation systems focus on analyzing the construction operation in terms of system performances, such as the production rate or the unit cost. Besides analyzing the system performances, searching for the optimal resource combination that produces the best performance is another important issue of the construction simulation. However, these systems take the sensitivity analysis approach, which exhaustively enumerates all resource combinations to find the optimal resource allocation [17]. As a result, if a large number of resource combinations are present, the sensitivity analysis approach becomes inefficient in terms of computation efforts. AbouRizk and Shi [1] proposed an HA, which efficiently locates the most appropriate resource allocation of the simulation system. However, the solution of their heuristic approach is usually the local optimum and the performance is problem-dependent. With the success of integrating GA with different methodologies in many fields, several researchers integrate GA with the simulation system to search for the optimal resource allocation. These researches include applying GA simulation in the optimization of the pastoral dairy farm management [16], shipping and shipyard layout planning [2], hard disk drive production scheduling [18], and ready-mixed concrete trucks dispatching management [6]. In addition, McHaney [15] presented a simple real-coded GA to find better simulation parameters of the hard inverse problem. McHaney reported that GA is relatively adaptable for the discrete event computer simulation environment. Moreover, a general-purpose GA simulation computer system, named GACOST, developed by Cheng and Feng [5] confirms McHaney’s results. Similarly, Hegazy and Kassab [10] used GA simulation technique for resource optimization in construction planning. Although GA is successfully used for the resource optimization of the simulation model, the performance of GA may depend on the initial population, which is randomly generated. It is the purpose of this study to propose a hybrid simulation
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optimization mechanism that integrates HA and GA to more efficiently search for the resource combination that produces the best system performance.
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involved in a construction operation and their waiting locations: DELAY ðlimiting resourceÞ ¼ MINðall resources
3. The heuristic approach
iÞ
MAXð all waiting locations
jÞ
Dij
ð2Þ
The basic modeling elements of the simulation system are activities and queues. Activities represent the work tasks that need time and resource to perform. Queues are used for modeling the waiting state of resources in the system. AbouRizk and Shi [1] used the DELAY statistic of queue nodes to guide the simulation toward better resource combinations that can maximize the production rate or minimize the unit cost for a system. The resource DELAY statistic is defined as indicated in Eq. (1): DELAY ¼ ðwaiting time=working timeÞ 100%
ð1Þ
where bwaiting timeQ is the total duration that the resource stays in the queues and bworking timeQ is the total duration that the resource stays in the simulation system. The resource DELAY statistic represents the degree of the utilization of the resource in the system. A resource may be used in several activities and wait at several queues. Thus, a resource would have different types of DELAY statistics. Two types of DELAY, as indicated in Eqs. (2) and (3), are defined by AbouRizk and Shi. Eq. (2) describes that the resource with the least DELAY value will limit the production rate for the process. On the other hand, Eq. (3) shows that the resource has enough capacity that will not limit the system production rate under current configuration. Then, the DELAY of a system can be determined as the smallest DELAY value among the resources. Table 1 shows an example of the resources Table 1 Example of resources involved in waiting locations [1] Resource number
1 2 – m
Queue position 1
2
. . .n
D 11 D 21 – Dm1
D 12 D 22 – D m2
. . .D 1n . . .D 2n – . . .D mn
DELAY ðsurplus resourceÞ ¼ MAXðall resources
iÞ
MINð all waiting locations
jÞ
Dij
ð3Þ
3.1. Process of reaching maximum production rate HA can optimize the system by either maximizing the production rate or minimizing the unit cost. The steps for maximizing the production rate of the simulation system are described as follows: 1.
2. 3. 4. 5.
Randomly select a resource combination and conduct a pilot run to determine the current DELAY values for participating resources. Apply Eq. (2) to identify the limited resource. Increase the value of limited resource identified in Eq. (2) within the specified boundaries. Perform the simulation experiment and determine the new production rate. Repeat steps (2)–(4) until the limited resources reach the specified boundaries.
3.2. Process of reaching minimum unit cost Other than maximizing the system production rate, minimizing the unit cost of a simulation system, as defined in Eq. (4), is another goal that the planner usually wishes to achieve: Unit Cost ¼ ½total cost=total production
ð4Þ
where btotal costQ is the total expenditure of resources used in the simulation system and btotal productionQ is the total quantity produced in the simulation system. The steps for minimizing the unit cost rate of a simulation system are described as follows: 1.
Randomly select a resource combination and conduct a pilot run to determine the current DELAY values for participating resources.
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Fig. 1. Generic procedure of GA operations [7].
2.
Apply Eq. (2) to identify the limited resource to be increased. 3. Run simulation for the new resource allocation and evaluate total cost and production as defined in Eq. (4). 4. If the increasing percentage of total cost is less than the one of total production, keep increasing the same limited resource identified in step (2); otherwise, apply Eq. (3) to identify the surplus resource and reduce it, then go to step (3). 5. Repeat steps (2)–(4) until two directions of resources reach their boundaries.
4. GAs GA is the search algorithm developed by Holland [11], which is based on the mechanics of natural selection and genetics to search through decision space for optimal solutions. The metaphor underlying GA is natural selection. In evolution, the problem that each species faces is to search for beneficial adaptations to the complicated and changing environment. In other words, each species has to change its chromosome combination to survive in the living world. In GA, a string represents a set of decisions (chromosome combination), which is a potential solution to a
problem. Each string is evaluated on its performance with respect to the fitness function (objective function). The ones with better performance (fitness value) are more likely to survive than the ones with worse performance. Then the genetic information is exchanged between strings by crossover and perturbed by mutation. The result is a new generation with (usually) better survival abilities. This process is repeated until the strings in the new generation are identical, or certain termination conditions are met. A generic flow of GA operation is given in Fig. 1. Original parent chromosomes represented as strings are randomly picked. Then, random selection of crossover match chromosome and match cut points are performed. A new group of exclusive substrings from parent chromosomes is formed. In addition, chromosomes are selected randomly to perform mutation operation. As a result, new offsprings of chromosomes are created. The generic operation of GA is depicted as follows. 4.1. Standard GA operations The standard GA operates on a population of bitstrings (genotype) d, and each individual represents a solution coded for all the variables required according to a finite alphabet of cardinality (0 and 1 for binary representation). Each individual yields a decoded solution (phenotype) and is evaluated by a predefined fitness function f. An example of the chromosome representation is given in Fig. 2. Each individual string d is represented in the form d=g(x 1,x 2,x i ,. . .,x n )=g(X). Each bit position x i of the m tuple (length of m for each variable; m depends on the precision required) substrings is designed over a finite alphabet of cardinality k (usually two: 0 and 1). Therefore, there are k nm different strings in the solution space, and those k nm different strings represent k nm different solutions. g is the decoding function that converts the value of x i to the real value.
Fig. 2. Example of chromosome representation.
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Fig. 3. Example of crossover.
4.2. Algorithm Step 1
Step 2
Step 3
Generate random parent population. The parent population P, with N (population size) nm tuple strings, is selected at random with or without replacement from the k nm solution space. The fitness value is evaluated for each string, f( g(X)). Reproduction. The offspring population O of size N is created from P by probabilistically selecting the strings according to their fitness values with replacement. Crossover. With probability P c, each two strings of O undergo a crossover operation on the substring basis. Crossover means that a random selection of a crossover point along the substrings and the exchange of tailing subtuples between the two substrings
Step 4
Step 5
are involved. An example can be seen in Fig. 3. Mutation. With probability P m , the value of the bit position x i in O is changed at random according to the k alphabet of cardinality. This operator is called a mutation operator. Fig. 4 is an example of mutation. Replacement and termination. Replace P by O and evaluate the fitness values of the strings in O, f( g(X)). Repeat steps (2)–(5) until all strings in the population are identical, or until some other termination conditions are met.
Generally, in GA, the accumulated information is exploited by the selection mechanism and new regions of the search space are explored by performing genetic operations (i.e., crossover and mutation).
Fig. 4. Example of mutation.
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However, GA is usually good at global search but slow to converge. Therefore, a common way of overcome this defect is to combine the HAs used to conduct fine-tuning for locating local optima with GA used to perform global search to escape local optima [7]. The proposed new hybrid mechanism for construction simulation optimization is depicted in Section 5.
5. The hybrid mechanism A new mechanism for optimizing the simulation model, named heuristic GAs (HGA), which hybridizes the abovementioned HA and GA, is developed by combining the merits of both algorithms. HGA employs GA to search through the global solution space and applies HA to perform the local search of the selected solution. In addition, the widely used simulation methodology, CYCLONE, is selected to model the construction operation because of its simple modeling symbols. Table 2 indicates the basic modeling elements developed by CYCLONE. Readers may refer to Ref. [9] for details. The proposed hybrid mechanism woks as follows. At first, a CYCLONE model is set up according to the construction operation that needs to be evaluated in terms of resource utilization. The resource variation within the CYCLONE system happens at the queue. Therefore, the chromosome Table 2 CYCLONE system modeling elements [8]
Fig. 5. Chromosome structure proposed in HGA.
structure used in this new simulation mechanism is designed in such a way that the length of the chromosome is equal to the number of the queues and the value of each gene depicts the resource utilization at the queue. Fig. 5 illustrates a string that represents the chromosome structure used in this simulation mechanism. Secondly, numbers of strings P(t), which are defined based on the chromosome structure described above, are randomly generated and evaluated by simulating the CYCLONE model. HA is then employed to alter the resource combination of each string toward a better direction for reaching local optimum. These strings carry the genetic information of resource combinations for the construction operation. Genetic operators, such as crossover and mutation, are applied to those local optimal strings to produce the interim offspring C(t). The fitness value of each string within the interim offspring C(t) can be determined by again simulating the CYCLONE model. Then the new offspring P(t) is generated by selecting the strings from the interim offspring C(t) according to their
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Fig. 6. Summary of HGA.
fitness values. The better is the fitness value of the string, the higher is the chance that the string could be selected. This process is repeated until the termination condition is met. A summary of HGA is given in Fig. 6. 5.1. The computer implementation A computer implementation coded by Microsoft Visual BasicR is developed to streamline the resource optimization process of applying the abovementioned
searching mechanism to the simulation system. This computer implementation utilizes the proposed mechanism as a selection engine to screen out the resource combinations that produce bad system performances. Fig. 7 shows the input interface of the computer implementation. Users can choose the objective to be optimized. Two optimization objectives that maximize system production rate or minimize unit cost are provided by the program. In addition, population size, generation, crossover rate, and mutation rate can be defined by users. Moreover, the convergent diagram
Fig. 7. Interface of HGA parameter input.
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Fig. 8. Convergent diagram of HGA computer program.
will be displayed simultaneously along with simulation progress, as shown in Fig. 8.
6. Case verification The verification of HGA for optimizing the simulation model is described in this section. There
are three steps in the verification process. The first step is to obtain the possible optimal solutions that maximize the system production rate and minimize the unit cost without performing any optimization algorithms. This process can be accomplished by using the maximum amount of resources and minimum amount of resources to the simulation model, respectively. It is because, intuitively, the maximal
Fig. 9. Sewer pipeline installation process [9].
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Fig. 10. CYCLONE model for sewer line installation operation.
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are both used to validate this proposed new optimization mechanism.
system production rate may be obtained by using the maximum amount of resources for each work task. Likewise, the minimal unit cost may be reached by employing the minimum amount of resources for each work task. The second step is to employ both HA and GA to obtain the possible optimal solution. Finally, the results obtained from steps (1) and (2) are compared with the solution reported by running HGA in terms of accuracy and efficiency. In addition, two objectives, which are maximizing the system production rate and minimizing the system unit cost,
6.1. The test example The sewer pipeline construction case presented in Fig. 9 is adapted from Halpin and Riggs [9]. This construction operation involves the installation of a sewer line that requires six sequential processes, which are pavement breaking, excavation, pipe laying, backfilling, compaction, and paving. These
Table 3 Initial resource information for the sewer line installation model Initialized at QUEUE
Resource description
Minimum available resource unit
Maximum available resource unit
Cost ($/h or unit)
1 3 4 5 6 10 11 12 13 15
SECTION READY BREAKER IDLE READY FOR EXCAVATE TRUCK WAIT B/H IDLE READY FOR SHORING PIPE STORAGE TRENCH BOX IDEL SMALL CRANE IDLE BED READY FOR BED PREPARE TRUCK IDEL PIPE COMMAND PIPE STOCK PILED CREW IDEL PIPE BED PREPED READY FOR SEAL RDY TO REMOVE TR BOX WAIT BACKFILL B/H IDLE CREW IDEL RDY FOR SURFACE PREP ROLLER RDY SURF RDY FOR PAVEMENT TRUCKS RDY BATCH PLANT IDLE CONCR RDY RDY TO POUR CREW RDY GEN 3 TRKS RDY TO COMPACT CREW DUMMY DUMMY RDY TO PREP SURF DUMMY DUMMY
1 1 0 1 1 0 2000 1 1 0
20 5 0 10 5 0 0 20 10 0
– 2000 – 1000 875 – – – 1000 –
1 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 0 1 1 1 0 1 1
10 0 0 5 0 0 0 0 5 5 0 5 0 10 5 0 0 5 0 0 5 1 1 0 1 1
1000 – – 275 – – – – 875 275 – 275 – 1000 – – – 275 – – 275 – – – – –
16 17 20 22 24 27 29 32 33 34 36 38 40 41 42 45 47 50 54 57 58 60 62 64 60 62
T. Cheng et al. / Automation in Construction 14 (2005) 85–98 Table 4 Activity duration for the sewer line installation model Element number
Activity
2 7 8 14 18 19 21 23 25 26
BREAK PAVEMENT EXCAVATE PAVEMENT TRK BACK CYCLE INSTALL TRENCH BOX LOAD PIPE HAUL TO SITE PLACE PIPE PREPARE PIPE bed TRK TRAVEL TO STACK LEVEL AND HAND BACKFILL HBF INSTALL RUBBER SEAL REMOVED TRENCH BOX BACKFILL WETTED MATERIAL COMPACT MATERIAL LOAD T–M TRK TRAVEL TO SITE PREP FORM WORK PLACE CONCRETE RETURN TO PLANT SPREAD/FINISH DUMMY WEATHER DELAY DUMMY
28 30 35 37 39 43 44 46 48 49 51 53 63 65
Duration (min) 20 45 10 20 20 5 20 5 10 20 20 20 60 6 180 6 10 60 20 10 120 0 600 0
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efforts. Therefore, the aforementioned three steps for verification are taken. Each work task within this test example is first assigned with the maximum amount of resources to obtain the possible maximal system production rate and unit cost. Then each work task is assigned with the minimum amount of resources to obtain the minimal system production rate and unit cost. In addition, this example is simulated in 200 cycles. The result shown in Table 5 indicates that the production rate of using the maximum amount of resources is 0.777 cycles/h, which is about 17 times that of 0.045 cycles/h by using the minimum amount of resources. Moreover, the unit cost of using the minimum amount of resources is $84,503 per section, which is about 42% of $203,323 per section by using the maximum amount of resources. Higher production rate could be reached by using the maximum amount of resource for each work task; however, it is not clear that the production rate obtained so far is the highest one. Similarly, lower unit cost rate could be reached by using the minimum amount of resource for each work task; however, it is also not clear that the unit cost obtained so far is the lowest one. Section 6.2 explains steps (2) and (3) of the verification. 6.2. HGA simulation analysis
processes are programmed in series with no shared resources and transportation and feedback loops. The CYCLONE model for the sewer line operation is shown in Fig. 10. The test data, which include the duration of each work task, available resources, and related cost information, are listed in Tables 3 and 4, respectively. As it can be estimated, the total number of resource combinations is 7.81251012 (=202 10458). Consequently, it is not economical to exhaustively enumerate all resource combinations to obtain the optimal solutions in terms of computational
In steps (2) and (3), the test example is also optimized by HA, GA, and HGA for allocating optimal resource combinations, respectively. In addition, two objective functions, which are maximizing the system production rate and minimizing the system unit cost, are used to verify the results of HGA in terms of accuracy and efficiency. Running GA and HGA involves setting up parameters (i.e., population size, generation number, crossover rate, and mutation rate). Based on the suggestion from the experiments of Cheng and Feng [5], the population size, generation
Table 5 Best guess of both the production rate and unit cost of the sewer line installation system Item
Guess of possible worse result
Guess of possible best result
System production rate System unit cost Resource combination [number of Q (quantity)]
0.045 (cycles/h) $203,323/section Q 1 (1), Q 3 (1), Q 5 (1), Q 6 (1), Q 12 (1), Q 13 (1), Q 16 (1), Q 22 (1), Q 33 (1), Q 34 (1), Q 38 (1), Q 41 (1), Q 42 (1), Q 50 (1), Q 58 (1)
0.777 (cycles/h) $84,503/section Q 1 (20), Q 3 (5), Q 5 (10), Q 6 (5), Q 12 (20), Q 13 (10), Q 16 (10), Q 22 (5), Q 33 (5), Q 34 (5), Q 38 (5), Q 41 (10), Q 42 (5), Q 50 (5), Q 58 (5)
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number, crossover rate, and mutation rate are set to 50, 50, 0.5, and 0.1, respectively. In addition, although generating a single pilot resource combination is sufficient for performing HA optimization, 50 pilot resource combinations are randomly generated to locate the possible optimal solutions simultaneously for the purpose of comparing GA and HGA in terms of accuracy and efficiency. Moreover, in order to fairly compare three methodologies, the termination condition for running HA is also determined by generation rather than blimited resource reaching specific boundary.Q The results are analyzed as follows. 6.2.1. Comparisons based on the object of maximizing the system production rate When the objective is defined to maximize the system production rate, the results obtained by conducting HA, GA, and HGA optimization are 0.86, 0.87, and 0.88 units per cycle, respectively. It is clear that HGA generates the best system production rate compared to the results reported by HA and GA. Moreover, as indicated in Fig. 11, HGA takes only 17 generations to find the best system production rate, which is the fastest one among the three algorithms. Furthermore, only 2500 (=50 50) resource combinations are explored. In other words,
only 3.21010 (=2500/(7.81251012)) of the total solution space is explored by running HGA. As the results indicate, HGA can find the better solution with less computational efforts. 6.2.2. Comparisons based on the object of minimizing system unit cost In addition, HA, GA, and HGA are employed to minimize the system unit cost of the test example. The results of the unit cost of the test example generated by HA, GA, and HGA are $38,555, $28,657, and $28,103 per section, respectively. Again, HGA reports the minimal unit cost among the three algorithms. HGA also takes the least number of generations to converge to the optimal solution, as shown in Fig. 12. 6.3. Sensitivity analysis Since running HA, GA, and HGA all requires the random selection of initial resource combinations, it is necessary to see whether the random selection will affect the final optimum solution. Table 6 lists 10 different independent simulation results when the population size and the number of generation are, respectively, set to 50 and 50 for running all three methods. In addition, the crossover rate and the
Fig. 11. Convergent curve for maximizing system production rate.
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Fig. 12. Convergent curve for minimizing system unit cost.
combinations could result in the same system production rate. Furthermore, the average solutions of running HA, GA, and HGA for minimizing the system unit cost are 33,667, 30,367, and 29,488 ($/ unit), respectively. The optimal solution (i.e., 26,484) is gained by the fourth run in running HGA. In these tests, HGA decreases the system unit cost by 12.4% ([33,667–29,488]/33,667) and 2.9% ([30,367– 29,488]/30,367) compared with HA and GA, respectively. The sensitivity analysis results indicate that HGA outperforms HA and GA in optimizing both the production rate and the system unit cost.
mutation rate for running GA and HGA are set to 0.5 and 0.1, respectively. When the objective is to maximize the production rate, the average solutions of 10 runs for HA, GA, and HGA are 0.861, 0.869, and 0.881 (cycle/h), respectively. The maximum value of 0.91 is obtained in the sixth run in running HGA. In those 10 runs, none of the production rates obtained by HGA was below 0.87, which indicates that HGA can keep a good performance. It is also interesting to note that, in these tests, the system production rate is usually dominated by the resource that has the lowest output rate. It is possible that different resource Table 6 Sensitivity analysis for running HA, GA, and HGA Run
Objective and method Maximize production rate (cycles/h)
1 2 3 4 5 6 7 8 9 10 Average
Minimize unit cost ($/unit)
HA
GA
HGA
HA
GA
HGA
0.86 0.84 0.88 0.87 0.87 0.84 0.87 0.87 0.84 0.87 0.861
0.87 0.87 0.88 0.87 0.87 0.81 0.88 0.88 0.88 0.88 0.869
0.88 0.88 0.88 0.88 0.88 0.91 0.88 0.87 0.87 0.88 0.881
38,555 32,562 33,547 34,040 27,636 38,392 31,305 28,443 37,853 34,340 33,667
28,657 30,658 31,988 28,412 28,197 30,369 34,157 27,235 31,099 32,893 30,367
28,103 26,437 33,083 26,484 30,514 28,657 29,228 31,775 26,501 34,107 29,488
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7. Conclusions Computer simulation techniques have been applied to the field of construction engineering and management for predicting the performance of the construction operation with predefined resource combination. Conventionally, the sensitivity analysis is conducted to find the optimal resource combination, in which all possible resource combinations are exhaustively enumerated to find the suitable resource combination that produces the optimal system performance. If the potential resource combinations are small in size, the sensitivity analysis would not cost too much computational efforts. However, when a large size of resource combinations is presented in the simulation model, such a sensitivity analysis process is no longer appropriate. This paper proposes a hybrid optimization mechanism that integrates HAs and GAs, named as HGA, to efficiently generate the resource combination that produces the optimal system performance. Case study shows that this new hybrid mechanism, along with the implemented computer program, can efficiently and accurately generate the optimal solution to help construction engineers streamline the planning process of construction operations.
Acknowledgements This work was partially supported by the National Science Council, Taiwan (grant no. NSC91-2211-E324-021).
References [1] S. AbouRizk, J. Shi, Automated construction–simulation optimization, Journal of Construction Engineering and Management, ASCE 120 (2) (1994) 374 – 385. [2] S.S. Bruzzone, Simulation and genetic algorithms for ship planning and shipyard layout, Simulation 71 (2) (1998) 74 – 83.
[3] D. Chang, RESQUE, PhD thesis, University of Michigan, Ann Arbor, MI, 1987. [4] T.-M. Cheng, S.-T. Wu, COST User’s Manual, Department of Construction Engineering, Chaoyang University of Technology, Taiwan, 2001. [5] T.-M. Cheng, C.-W. Feng, An effective simulation mechanism for construction operations, Automation in Construction 12 (3) (2003) 227 – 244. [6] C.-W. Feng, T.-M. Cheng, H.-T. Wu, Optimizing the schedule of dispatching RMC trucks through genetic algorithms, Automation in Construction 13 (3) (2004) 327 – 340. [7] M. Gen, R. Cheng, Genetic Algorithms and Engineering Optimization, Wiley, New York, 2002. [8] D.W. Halpin, CYCLONE-method for modeling job site processes, Journal of the Construction Division, ASCE CO3 (1977) 489 – 499. [9] D.W. Halpin, L.S. Riggs, Planning and Analysis of Construction Operations, Wiley, New York, 1992. [10] T. Hegazy, M. Kassab, Resource optimization using combined simulation and genetic algorithms, Journal of Construction Engineering and Management, ASCE 129 (6) (2003) 698 – 705. [11] J. Holland, Adaptation in Natural and Artificial System, University of Michigan Press, Ann Arbor, MI, 1975. [12] P.G. Ioannou, UM-CYCLONE User’s Guide, Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, MI, 1989. [13] L.Y. Liu, P.G. Ioannou, Graphical object-oriented discrete-event simulation system, Proceedings of the 1992 Winter Simulation Conference, Association for Computing Machinery, Arlington, VA, December, 1992, pp. 1285 – 1291. [14] J.C. Martinez, P.G. Ioannou, General-purpose systems for effective construction simulation, Journal of Construction Engineering and Management, ASCE 125 (4) (1999) 265 – 276. [15] R. McHaney, Integration of the genetic algorithm and discreteevent computer simulation for decision support, Simulation 72 (6) (1999) 401 – 411. [16] R.S. Parmar, R.W. McClendon, W.D. Potter, Farm machinery selection using simulation and genetic algorithms, Transactions of the American Society of Mechanical Engineers 39 (5) (1996) 1905 – 1909. [17] L.S. Riggs, Sensitivity analysis of construction operations, PhD thesis, Georgia Institute of Technology, Atlanta, GA, 1979.[18] [18] Z.Y. Zhao, R. de Souza, Genetic production line-balancing for the hard disk drive industry, International Journal of Advanced Manufacturing Technology 16 (2000) 297 – 302.