Abstract
Trip distribution is one of the important stages in transportation planning model, by which decision-makers can estimate the number of trips among zones. As a basis, the gravity model is commonly used. To cope with complicated situations, a multiple objective mathematical model was developed to attain a set of conflict goals. In this paper, a goal programming model is proposed to enhance the developed multiple objective model to optimize three objectives simultaneously, i.e. (1) maximization of the interactivity of the system, (2) minimization of the generalized costs and (3) minimization of the deviation from the observed year. A genetic algorithm (GA) is developed to solve the proposed non-linear goal programming model. As with other genetic algorithms applied to real-world problems, the GA procedure contains representation, initialization, evaluation, selection, crossover, and mutation. The modification of crossover and mutation to satisfy the doubly constraints is described. A set of Hong Kong data has been used to test the effectiveness and efficiency of the proposed mode. Results demonstrate that decision-makers can find the flexibility and robustness of the proposed model by adjusting the weighting factors with respect to the importance of each objective.
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References
Arasan VT, Wermuth M, Srinivas BS (1996) Modeling of stratified urban trip distribution. J Transp Eng 122:342–346
Bruton MJ (1985) Introduction to transportation planning. UCL Press, London
Casey HJ (1955) Applications to traffic engineering of the law of retail gravitation. Traffic Q IX:23–35
Charnes A, Cooper WW (1961) Management models and industrial applications of linear programming. Wiley, New York
Dinkel JJ, Wong D (1984) External zones in trip distribution model: characterization and solvability. Transp Sci 18:253–266
Duffus LN, Alfa AS, Soliman AH (1987) The reliability of using the gravity model for forecasting trip distribution. Transportation 14:175–192
Easa SM (1993a) Urban trip distribution in practice, I: conventional analysis. J Transp Eng 119:793–815
Easa SM (1993b) Urban trip distribution in practice, II: quick responses and special topics. J Transp Eng 119:816–834
Erlander S (1981) Entropy in linear programs. Math Program 21:137–151
Fang SC, Tsao HSJ (1995) Linearly-constrained entropy maximization problem with quadratic cost and its applications to transportation planning problems. Transp Sci 29:353–365
Fogel D (1995) Evolution computation: toward a new philosophy of machine intelligence. IEEE Press, New York
Gen M, Cheng R (1997) Genetic algorithms and engineering design. Wiley, New York
Hallefjord A, Jornsten K (1986) Gravity models with multiple objectives—theory and applications. Trans Res B 20:19–39
Hitchcock FL (1941) The distribution of a product from several sources to numerous localities. J Math Phys 20:224–230
Leung SCH, Lai KK (2002) Multiple objective decision-making in the mode choice problem: a goal-programming approach. Int J Syst Sci 33:35–43
Lin KS, Niemeier DA (1998) Temporal disaggregation of travel demand for high resolution emissions inventories. Trans Res 3D:375–387
Michalewicz Z (1994) Genetic algorithm + data structure = evolution program, 2nd edn. Springer, Berlin
Mozolin M, Thill JC, Usery EL (2000) Trip distribution forecasting with multilayer perceptron neural networks: a critical evaluation. Trans Res 34B:53–73
Ortuzar S, Willumsen LG (1994) Modelling transport. Wiley, New York
Reeves CR (1995) Genetic algorithms and combinatorial optimization. In: Rayward-Smith VJ Applications of Modern Heuristic Method. Alfred Waller, Oxon, pp 111–125
Rifai AK (1994) A note on the structure of the goal programming model: assessment and evaluation. Int J Oper Prod Manag 16:40–49
Salminen S (2000) Traffic accidents during work and work commuting. Int J Ind Ergon 26:75–85
Tamiz M, Jones D, Romero C (1998) Goal programming for decision making: an overview of the current state-of-the-art. Eur J Oper Res 111:569–581
Teodorovic D (1994) Fuzzy sets theory applications in traffic and transportation. Eur J Oper Res 74:379–390
Teodorovic D (1999) Fuzzy logic systems for transportation engineering: the state of the art. Trans Res 33A:337–364
Toth ZB, Atkins DM, Bolger D, Foster R (1990) Regional shopping center linked trip distribution. ITE J 60:41–46
Vaughan RJ (1985) A continuous analysis of the role of transportation and crowding costs in determining trip distribution and location in a linear city. Trans Res A 19:89–107
Vincke P (1992) Multicriteria decision-aid. Wiley, New York
Wilson AG (1970) Entropy in urban and regional modelling. Poin, England
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Leung, S.C.H. A non-linear goal programming model and solution method for the multi-objective trip distribution problem in transportation engineering. Optim Eng 8, 277–298 (2007). https://doi.org/10.1007/s11081-007-9019-x
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DOI: https://doi.org/10.1007/s11081-007-9019-x