組合最佳化問題為為工業工程相關研究中一個重要的領域。此類問題通常為NP-hard問題，無法於可接受時間內求得最佳解。因此使用適當的啟發式搜尋法於有限時間內求得一個可接受之解為實務運用上最有效的方法。但就算使用啟發式搜尋法求解，當問題大小擴展至實務規模時，於有限的時間內求得高品質的解仍是一大挑戰，另如何於求解過程即時評估求解品質亦需克服。這些挑戰驅使搜尋法之設計趨向平行化提高運算效能與混合化結合不同方法特點的方向發展。
本研究首先探討傳統啟發式搜尋技術於實務上面臨之組合最佳化問題求解及應用，並以ㄧ個供應鏈設計最佳化問題，嘗試以傳統之啟發式搜尋技術求解對應之數學規劃模式，並由結果中探討傳統啟發式搜尋法應用之效益與限制。本研究接下來嘗試以平行化與混合化的概念改進傳統搜尋方法，運用合作式搜尋之概念，發展結合精確解法與啟發式搜尋法2種不同求解技術特點之平行混合搜尋法，以滿足計算初期快速改善、可評估求解品質，具備一般化之演算結構等實務運用時的需求。本研究以精確解法中的分支界限法與啟發式搜尋法中常用之塔布搜尋法為結合標的，以合作式搜尋架構，平行執行的方式結合二種不同搜尋法之優點，並運用於求解銷售員旅行問題以分析其整合架構之特性。結果顯示此平行混合化搜尋法可以達成結合二種不同結構搜尋法特點之預期目的，並因關鍵資訊的分享與交換，獲得比傳統同質平行化搜尋法更好的效能，且具備良好的線性加速性，可藉由增加從動節點的數量，來縮短運算的時間。

Obtaining optimal solutions of combinatorial optimization problems is computationally intractable. These problems are known as NP-hard and cannot be solved optimally within a reasonable amount of time. Satisfying with good solution obtained by heuristic search methods within an acceptable execution time is the efficient way in practice. Even using heuristic search, obtaining a good quality solution within a reasonable computing time for large scale and evaluating the quality of the obtained solutions have still difficulties. The hybridization and parallelism of heuristics search offer the possibility for enhancing the efficiency of the search.
In first place, a case study of heuristic search techniques for solving a real-world combinatorial optimization problem is discussed in this study. Two straightforward and efficient approaches based on simulated annealing and tabu search are implemented to solve the integer nonlinear programming model which proposed in the case study. In second place, we aim the hybridization of different methods by parallel computing. We present a parallel hybrid heuristic search that combines branch-and-bound method and tabu search algorithm by cooperative multi-search scheme to integrate the benefits of exact methods and metaheuristics. These two algorithms perform searches in parallel and cooperate by asynchronously exchanging information. We use a master-slave model to reduce the complexity of communication and enhance the performance of data exchange. A branch-and-bound process is used as the master process to control the exchange of information and the termination of computation. Several tabu search processes are executed simultaneously as the slave processes, and are cooperative by asynchronously exchanging information of the best solutions found and new initial solutions with the master process of branch-and-bound. According to the computation experiments of solving traveling salesman problems, the proposed heterogeneous parallel search algorithm outperforms a conventional parallel branch-and-bound method and a conventional parallel tabu search. The results also show the proposed heterogeneous parallel search algorithm achieves linear accelerations when we use more processors to accelerate searching time.

Aarts, E., Bont, J., and Laarhoven, P. (1986), “Parallel implementations of the statistical cooling algorithm”, Integration, Vol. 4, pp. 209-238.
Ahuja, R.K., Ergun, O., Orlin, J.B., and Punnen, A.P. (2002), “A survey of very large-scale neighborhood search techniques”, Discrete Applied Mathematics, Vol. 123, pp. 75-102.
Alabau, M., Idoumghar, L., and Schott, M. (2002), “New hybrid genetic algorithm for the frequency assignment problem”, IEEE Transactions on Broadcasting, Vol. 48, pp. 27-34.
Arora, J.S. and Huang, M.W. (1994), “Methods for optimization of nonlinear problem with discrete variables: a review”, Structural Optimization, Vol. 8, pp. 69-85.
Augerat, F., Belenguer, J.M., Benavent, E., Corber’n, A., and Naddef, D. (1998), “Separating capacity constraints in the CVRP using tabu search”, European Journal of Operational Research, Vol. 106, pp. 546-557.
Axäter, S. (1996), “Using the deterministic EOQ formula in stochastic inventory control”, Management Science, Vol. 42, pp. 830-834.
Balas, E. (1968), “A note on the branch-and-bound principle”, Operations Research, Vol. 16, pp. 442-445.
Battiti, R. and Tecchiolli, G. (1992), “Parallel based search for combinatorial optimization: genetic algorithms and TABU”, Microprocessors and Microsystems, Vol. 16, pp. 351-367.
Bent, R. and Van Hentenryck, P. (2004), “A two-stage hybrid local search for the vehicle routing problem with time windows”, Transportation Science, Vol. 38, pp. 515-530.
Blum, C. and Roli, A. (2003), “Metaheuristics in combinatorial optimization: overview and conceptual comparison”, ACM Computing Surveys, Vol. 35, pp. 268-308.
Blum, C. and Roli, A. (2008), “Hybrid Metaheuristics: an introduction”, In: Blum, C., Blesa Aguilera, M.J., Roli, A., and Sampels, M. (eds.), Hybrid Metaheuristics, pp. 1-30. Springer Berlin, Heidelberg.
Bock, S. and Rosenberg, O. (2000), “A new parallel breadth first tabu search technique for solving production planning problems”, International Transaction in Operational Research, Vol. 7, pp. 625-635.
Bożzejko, W., Pempera, J., and Smutnicki, C. (2009), “Parallel simulated annealing for the job shop scheduling problem”, Lecture Notes in Computer Science, Vol. 5544, pp. 631-640.
Cordeau, J.-F. and Masichberger, M. (2012), “A parallel iterated tabu search heuristic for vehicle routing problems”, Computers & Operations Research, Vol. 39, pp. 2033-2050.
Cotta, C., Aldana, J.F., Nebro, A.J., and Troya, J.M, (1995) “Hybridizing genetic algorithms with branch and bound techniques for the resolution of the tsp”, In: Pearson, D.W., Steele, N.C., and Albrecht, R.F. (eds.), Artificial Neural Nets and Genetic Algorithms 2, pp. 227-280, Springer-Verlag, New York.
Crainic, T.G. and Gendreau, M. (1999), “Towards an evolutionary method-cooperating multi-thread parallel tabu search hybrid”, In: Martello, S., Roucairol, C., and Osman, I.H. (eds.), Melta-Heuristics 98: Theory & Applications, pp. 331-344, Kluwer Academic Publishers, Norwell.
Crainic, T.G. and Gendreau, M. (2002), “Cooperative parallel tabu search for capacitated network design”, Journal of Heuristics, Vol. 8, 601-627.
Crainic, T.G., Le Cun, B., Roucairol, C. (2006), “Parallel branch and bound algorithm”, In: Talbi, E.-G. (ed.), Parallel Combinatorial Optimizations, pp. 1-28, John Wiley & Sons, New York.
Crainic, T.G., Toulouse, M. (2003), “Parallel strategies for meta-heuristics”, In: Glover, F. and Kochenberger, G. (eds.), Handbook of Metaheuristics, pp. 475-513, Kluwer Academic Publishers, Norwell.
Crainic, T.G., Toulouse, M. (2010), “Parallel meta-heuristics”, In: Gendreau, M. and Potvin, J.-Y. (eds.), Handbook of Metaheuristics (2nd ed.), pp. 497-541, Springer, Berlin.
Crainic, T.G., Toulouse, M., and Gendreau, M. (1996), “Parallel asynchronous tabu search for multicommodity location-allocation with balancing requirements”, Annals of operations Research, Vol. 63, pp. 277-299.
Dantzig, G.B., Fulkerson, D.R., Johnson, S.M. (1959), “On a linear-programming, combinatorial approach to the traveling-salesman problem”, Operations Research. Vol. 7, pp. 58-66.
Daskin, M.S., Coullard, C.R., and Shen, Z.-J.M. (2002), “An inventory-location model: formulation, solution algorithm and computational results”, Annals of Operations Research, Vol. 110, pp. 83-106.
Drezner, Z. and Hamacher, H.W., Eds. (2002), Facility location: Applications and theory, Springer, New York.
Eglese, R.W. (1990), “Simulated annealing: a tool for operational research”, European Journal of Operational Research, Vol. 46, pp. 271-281.
Eppen, G. (1979), “Effect of centralization on expected costs in multi-location newsboy problem”, Management Science, Vol. 25, pp. 498-501.
Fiechter, C.,-N. (1994), “A parallel tabu search algorithm for large travelling salesman problems”, Discrete Applied Mathematics, Vol. 51, pp. 243-267.
French, A.P., Robinson, A.C., and Wilson, J.M. (2001), “Using a hybrid genetic-algorithm/branch and bound approach to solve feasibility and optimization integer programming problems”, Journal of Heuristics, Vol. 7, pp. 551-564.
Gendreau, M., Laporte, G., and Semet, F. (2001), “A dynamic model and parallel tabu search heuristic for real-time ambulance relocation”, Parallel Computing, Vol. 27, pp. 1641-1653.
Gendreau, M. and Potvin, J.-Y. (2010), “Tabu search”, In: Gendreau, M. and Potvin, J.-Y. (eds.), Handbook of Metaheuristics (2nd ed.), pp. 41-59, Springer, Berlin.
Gill, S. (1958), “Parallel programming”, The Computer Journal, Vol.1, pp.2-10.
Glover, F. (1989), “Tabu search –part I”, ORSA Journal of Computing, Vol. 1, pp. 190-206.
Glover, F. and Laguna, M. (1997), Tabu search, Kluwer Academic Publishers, Norwell.
Groër, C., Golden, B., and Wasil, E. (2011), “A parallel algorithm for the vehicle routing problem”, INFORMS Journal on Computing, Vol. 23, pp. 315-330.
Grossmann, I.E. (2002), “Review of nonlinear mixed-integer and disjunctive programming techniques”, Optimization and Engineering, Vol. 3, pp. 227-252.
Huang, W., Romeijm, H.E., and Geunes, J. (2005), “The continuous-time single-sourcing problem with capacity expansion opportunities”, Naval Research Logistics, Vol. 52, pp. 193-211.
Hung, Y.-F., Chen, C.-P., and Shih, C.-C. (2003), “Using Tabu Search with Ranking Candidate List to Solve Production Planning Problems with Setups”, Computer and Industrial Engineering, Vol. 45, pp.615-634.
Jahuria, C.A.R. (2003), “Hybrid genetic algorithm with exact technique applied to tsp”, in: Second International Workshop on Intelligent System Design and Application, Dynamic Publishers, pp.119-124.
James, T., Rego, C., and Glover, F. (2009), “A cooperative parallel tabu search algorithm for the quadratic assignment problem”, European Journal of Operational Research, Vol. 195, pp. 810-826.
Jourdan, L., Basseur, M., and Talbi, E.-G. (2009), “Hybridizing exact methods and meatheuristics: A taxonomy”, European Journal of Operational Research, Vol. 199, pp 620-629.
Kirkpatick, S.T., Gelett, Jr.C.D., and Vechhi, M.P. (1983), “Optimization by simulated annealing”, Science, Vol. 220, pp. 671-680.
Klepeis, J.L., Pieja, M.J. and Floudas, C.A. (2003), “Hybrid global optimization algorithms for protein structure prediction: alternating hybrids”, Biophysical Journal, Vol. 4, pp 869-882.
Knysh, D.S. and Kureichik, V.M. (2010), “Parallel genetic algorithms: a survey and problem state of the art”, Journal of Computer and Systems Sciences International, Vol. 49, pp. 579-589.
Lawler, E.L. (1985), The traveling salesman problem: a guided tour of combinatorial optimization, John Wiley & Sons, Hoboken.
Lawler, E.L. and Wood, D.E. (1966), “Branch-and-bound methods: a survey”, Operations Research, Vol. 14, pp. 699-719.
Le Bouthillier, A. and Crainic, T.G. (2005), “A cooperative parallel meta-heuristic for the vehicle routing problem with time windows”, Computers & Operations Research, Vol. 32, pp. 1685-1708.
Lundy, M. and Mess, A. (1986), “Convergence of an annealing algorithm”, Mathematical Programming, Vol. 34, pp. 111-124.
Message Passing Interface Forum (1995), MPI: A message-passing interface standard.
Metropolis, N., Rosenbluth, A.W., and Teller, A.H. (1953), “Equation of state calculations by first computing machines”, Journal of Chemistry Physics, Vol. 21, pp. 1087-1092.
Miranda, P.A., and Garrido, R.A. (2004), “Incorporating inventory control decisions into a strategic distribution network design model with stochastic demand”, Transportation Research Part E, Logistics and Transportation Review, Vol. 40, pp. 183-207.
Mirchandani. P.B. and Francis, R.L. (1990), Discrete location theory, Wiley, New York.
Ng, C.T., Wang, J.-B., Cheng, T.C.E, and Liu, L.L. (2010), “A branch-and-bound algorithm for solving a two-machine flow shop problem with deteriorating jobs”, Computers & Operations Research, Vol. 37, pp. 83-90.
Nikolaew, A.G. and Jacobson, S.H. (2010), “Simulated annealing”, In: Gendreau, M. and Potvin, J.-Y. (eds.), Handbook of Metaheuristics (2nd ed.), pp. 1-40, Springer, Berlin.
Nwana, V., Darby-Dowman, K., and Mitra, G. (2005), “A co-operative parallel heuristic for mixed zero-one linear programming: combing simulated annealing with branch and bound”, European Journal of Operational Research, Vol. 164, pp. 12-23.
Oh, I.-S., Lee, J -S., and Moon, B.-R. (2004), “Hybrid genetic algorithm for freature selection”, IEEE transactions on pattern analysis and machine intelligence, Vol. 26, pp. 1424-1437.
Ozsen, L., Coullard, C.R., and Daskin, M.S. (2008), “Capacitated warehouse location model with risk pooling”, Naval Research Logistics, Vol. 55, pp. 295-312.
Papadimitriou, C. H. and Steiglitz, K. (1982), Combinatorial optimization–algorithms and complexity, Dover Publications, Inc., New York.
Park, S., Lee, T.E., and Sun, C.S. (2010), “A three-level supply chain network design model with risk pooling and lead times”, Transportation Research Part E, Vol. 46, pp. 563-581.
Shen, Z.-J.M., Coulard, C.R., and Daskin, M.S. (2003), “A joint location-inventory model”, Transportation Science, Vol. 37, pp. 40-55.
Shen, Z.-J.M. and Qi, L. (2006), “Incorporating inventory and routing costs in strategic location models”, European Journal of Operational Research, Vol. 179, pp. 372-389.
Shu, J. and Sun, J. (2006), “Designing the distribution network for an integrated supply chain”, Journal of Industrial and Management Optimization, Vol. 2, pp. 339-349.
Shu, J., Teo, C.P., and Shen, Z.-J.M. (2005), “Stochastic transportation-inventory network design problem”, Operations Research, Vol. 53, pp. 48-60.
Simchi-Levi, D., Kamiinsky, P., and Simchi-Levi, E. (2006), Designing & managing the supply chain: concepts, strategies, and case study, MaGraw-Hill/Irwin, Boston.
Snyder L.V., Daskin, M.S., and Teo C.P. (2007), “The stochastic location model with risk pooling”, European Journal of Operational Research, Vol. 179. pp. 1221-1238.
Sourd, F. and Kedad-Sidhoum, S. (2008), “A faster branch-and-bound algorithm for earliness-tardiness scheduling problem”, Journal of Scheduling, Vol. 11, pp. 49-58.
Tabli, E.-G. (2002), “A taxonomy of hybrid of metaheuristics”, Journal of Heuristics, Vol. 8, 541-544.
Taillard, Ѐ.D. (1993), “Parallel iterative search methods for vehicle routing problem”, Networks, Vol. 23, pp. 661-673.
Taillard, Ѐ.D. (1994), “Parallel taboo search techniques for the job shop scheduling problem”, ORSA journal on Computing, Vol.6, pp.108-117.
Tsubakitani, S. (1998), “An empirical study of a new metaheuristic for the traveling salesman problem”, European Journal of Operations Research, Vol. 104, pp. 113-128.
Wodecki, M. and Bożzejko, W. (2006), “Solving the flow shop problem by parallel simulated annealing”, Lecture Notes in Computer Science, Vol. 2328, pp. 236-247.
You, F. and Grossmann, I.E. (2008), “Mixed-integer nonlinear programming models and algorithms for large-scale supply chain design with stochastic inventory management”, Industrial and Engineering Chemistry Research, Vol. 47, pp. 7802-7817.
Zipkin, P.H. (2000), Foundations of inventory management, McGraw-Hill, Boston.