Imai et al. (2001) and Nishimura et al. (200128 NISHIMURA E, IMAI A & PAPADIMITRIOU S. 2001. Berth allocation planning in the public berth system by genetic algorithms. European Journal of Operational Research, 131: 282-292.) |
Lagrangian Relaxation (LR) and Genetic Algorithm (GA) applied to DBAP. |
The calculations obtained with GA indicated the efficient use of 5 berths instead of 7 berths used in a Japanese public port. The tests (fictitious data) demonstrated that the quality of the solution obtained by the (GA) was the same/similar to the one obtained by the (LR). |
Minimize the total waiting and handling times for every vessel. |
Kim & Moon (200315 KIM KH & MOON KC. 2003. Berth scheduling by simulated annealing. Transport Res. B, 37: 541-560.) |
Simulated Annealing applied to CBAP. |
The unfeasibility of the mixed-integer program (MIP) technique with 7 vessels was demonstrated, and the Simulated Annealing algorithm was suggested. |
Minimize the penalty cost resulting from delay and the additional handling costs resulting from non-optimal locations. |
Cordeau et al. (20056 CORDEAU JF, LAPORTE G & MERCIER A. 2001. A unified tabu search heuristic for vehicle routing problems with time windows. Journal of the Operational Research Society, 52(8): 928-936.) |
The Tabu search algorithm applied to DBAP. |
It was demonstrated that the Tabu search algorithm outperformed both the first-come first-served rule and CPLEX. |
Minimize the sum for each vessel of the service time. |
Imai et al. (2008) |
Genetic Algorithm applied to DBAP. |
The number of rejected vessels owing to lack of service within the maximum time limit was minimized. The study is useful for the efficient management of extremely busy container terminals in underdeveloped countries. |
Minimize the total service time. |
Theofanis et al. (200735 THEOFANIS S, BOILE M & GOLIAS M. 2007. An optimization based genetic algorithm heuristic for the Berth Allocation Problem. IEEE Congress on Evolutionary Computation. p. 4439-4445.) |
Optimization based GA heuristic (OBGA) and GA for DBAP. |
Sensitivity analysis for the parameters of the OBGA and GA heuristics was performed. Both heuristics proved to be efficient, with small changes in the value of the objective function. |
Minimize the total weighted service time of all the vessels. |
Mauri et al. (2008b21 MAURI GR, OLIVEIRA ACM & LORENA LAN. 2008. Heurística baseada no Simulated Annealing aplicada ao problema de alocação de berços. GEPROS - Gestão da Produção, Operações e Sistemas, 1(1): 113-127.) |
Minimization of the number of rejected vessels due to the lack of service within the maximum time limit established. |
Population Training Algorithm (PAT) in combination with Linear Programming (LP) for Column Generation for DBAP. |
Minimization of the number of rejected vessels due to the lack of service within the maximum time limit established. |
The results demonstrated the potential of the proposed approach, where high quality solutions were obtained for relatively large problems, in significantly short processing time. |
Buhrkal et al. (20114 BUHRKAL K, ZUGLIAN S, ROPKE S, LARSEN J & LUSBY R. 2011. Models for the discrete berth allocation problem: a computational comparison. Transportation Research Part E, Logistics and Transportation Review, 47(4): 461-473. http://dx.doi.org/10.1016/j.tre.2010.11.016. http://dx.doi.org/10.1016/j.tre.2010.11....
) |
Generalized set-partitioning (GSPP) applied to DBAP. |
The performance of five formulations of DBAPs was compared. It was claimed that the model proposed by Cordeau et al. (20057 CORDEAU JF, LAPORTE G, LEGATO P & MOCCIA L. 2005. Models and tabu search heuristics for the berth allocation problem. Transportation Science, 39(4): 526-538. http://dx.doi.org/10.1287/trsc.1050.0120. http://dx.doi.org/10.1287/trsc.1050.0120...
) is computationally advantageous. The results obtained with GSPP were superior to those obtained by (Cordeau et al. 2005). |
Minimize the total waiting and handling times of every ship. |
Hu (201511 HU Z-H. 2015. Multi-objective genetic algorithm for berth allocation problem considering daytime preference. Comput. Indust. Eng., 89: 2-14.) |
The multi-objective GA (moGA) for the bi-objective DBAP. |
The importance of the preference for daytime operations was demonstrated. Owing to the lack of research on the optimization of daytime shift allocation, the optimal performance of the algorithm should be studied in future work. |
Minimize the work of cargo operated at nighttime. |
Lalla-Ruiz et al. (201417 LALLA-RUIZ E, GONZALEZ-VERLARDE JL, MELIAN-BATISTA B & MORENO-VEGA JM. 2014. Biased random key genetic algorithm for the tactical berth allocation problem. Applied Soft Computing, 22: 60-76.) |
Biased Random Key Genetic Algorithm (BRKGA) for DBAP. |
The required computational time showed that, even in small-scale instances, the problem is difficult to solve by CPLEX. The use of BRKGA was justified for the solution of the tactical berth Allocation problem in realworld contexts; particularly, in those integrated designs where this problem frequently appears as a sub-problem. Therefore, the use of efficient procedures that provide nearoptimal solutions within short computational time is preferable. |
Maximize the sum of the values of the chosen quay crane profiles and minimize the yard-related housekeeping cost. |
Lalla-Ruiz et al. (2016b18 LALLA-RUIZ E, SHI X & VOß S. 2016. The waterway ship scheduling problem. Transport. Res. Part D: Transport Environment, 60: 191-209.) |
Simulated Annealing for the Waterway Ship Scheduling Problem (WSSP) for (BAP). |
Computational experiments showed that the problem is difficult to solve, even in smallscale instances, using a general-purpose solver. Nevertheless, the proposed S approaches may provide high-quality solutions in short computational time. Moreover, the tests showed that the SA approachesare suitable for contemporary problems. |
Minimize the total time required for the vessels to pass through the waterways. |
Hsu (201610 HSU H-P. 2016. A HPSO for solving dynamic and discrete berth allocation problem and dynamic quay crane assignment problem simultaneously. Swarm Evol. Comput., 27: 156-168.) |
Hybrid Particle Swarm Optimization (HPSO) for BAP. |
The proposed HPSO was compared with the two GA-based approaches. Among the three approaches, HPSO required the longest, albeit reasonable, computational time. Thus, it remains acceptable. |
Minimize the total cost consisting of the sub-costs of waiting, delay and operation. |
Mauri et al. (201622 MAURI GR, OLIVEIRA ACM & LORENA LAN. 2008-b. A hybrid column generation approach for the berth allocation problem. In: VAN HEMERT J & COTTA C. (Eds.). 8th European Conference on Evolutionary Computation in Combinatorial Optimisation - EvoCOP 2008. Lecture Notes in Computer Science, 4972: 110-122. Berlin: Springer.) |
Adaptive Large Neighborhood Search (ALNS) DBAP and CBAP. |
The computational tests indicated the relative superiority of the ALNS heuristic for solving DBAP and CBAP. It determined all known optimal solutions for DBAP within shorter computational time. Better solutions were obtained for CBAP. |
Minimize the sum of the service times while the vessels stay into the port. |
Venturini (201737 VENTURINI G, IRIS Ç, KONTOVAS CA & LARSEN A. 2017. The multi-port berth allocation problem with speed optimization and emission considerations. Transportation Research Part D, 54: 142- 159.) |
CPLEX |
A novel formulation was presented by integrating the BAP with vessel speed optimization for multiple ports under environmental considerations, in particular ship air emissions. |
Minimize the cost of idleness, delay, handling and the fuel consumption. |