Minimizing the fuel consumption and the risk in maritime transportation: A bi-objective weather routing approach

Highlights

• A time-dependent algorithm is presented for the ship weather routing problem.

• Given a maximum travel duration constraint, fuel consumption and risk are minimized.

• Improvements of the approach are proposed for faster execution but similar solutions.

• Techniques are also presented that improve the practicality of the derived solutions.

Abstract

The paper presents an improved solution to the ship weather routing problem based on an exact time-dependent bi-objective shortest path algorithm. The two objectives of the problem are the minimization of the fuel consumption and the total risk of the ship route while taking into account the time-varying sea and weather conditions and an upper bound on the total passage time of the route. Safety is also considered by applying the guidelines of the International Maritime Organization (IMO). As a case study, the proposed algorithm is applied for finding ship routes in the area of the Aegean Sea, Greece. Enhancements of the proposed algorithm are also presented which improve the efficiency of our approach.

Introduction

Maritime transportation is crucial for the economic growth of many countries as well as for the global economy, in general. During the past two decades, there has been a growing interest in methods for calculating optimal ship trajectories. The traditional economic objective was to minimize the total traveled distance while later, additional energy efficiency objectives were added such as the minimization of the fuel consumption and gas emissions. Besides energy efficiency, navigation safety is also considered since sea transportation poses a high environmental risk due to the possibility of maritime accidents, especially if hazardous materials (i.e. chemicals or oil) are transferred. Moreover, ship routing methods have to adhere to the safety guidelines specified by the International Maritime Organization (IMO, 2007).

The problem of optimal route planning in maritime transportation (or ship routing problem) takes into consideration the different objectives and constraints set by the ship owners, the national regulations, the international organizations, etc. Regardless of the specific objectives/constraints, the main factor that makes the ship routing problem difficult to solve, is the time-varying weather conditions (Padhy et al., 2008). The parameters and cost factors of the problem as well as the optimization criteria are strongly affected by the weather and sea conditions and therefore, finding an optimal ship route should take into consideration the weather forecasts and sea conditions during the course of the route. To accomplish this, a reliable model that predicts the ship’s response to the weather and sea conditions is required, while an effective solution approach for the ship routing problem should determine the heading control and ideally the optimal ship power settings according to the weather and sea conditions. Thus, broadly speaking, the ship routing problem is a dynamic, time-dependent problem which is usually referred to as the ship weather routing problem.

The optimization objectives in the ship routing problem are usually the minimization of the voyage time, fuel consumption and voyage risk. The ship routing algorithms appeared in the literature are classified into two categories, namely the exact and the heuristic approaches. The exact algorithms (Ari, Aksakalli, Aydogdu, Kum, 2013, Azaron, Kianfar, 2003, Babel, Zimmermann, 2015, Dolinskaya, 2012, Lo, McCord, 1998, Mannarini, Coppini, Oddo, Pinardi, 2013, Montes, 2005, Padhy, Sen, Bhaskaran, 2008, Shao, Zhou, Thong, 2012, Szlapczynski, 2006, Takashima, Mezaoui, Shoji, 2009, Tsatcha, Saux, Claramunt, 2014, Veneti, Konstantopoulos, Pantziou, 2015) determine the optimal solution at the expense of the execution time while heuristic approaches (Decò, Frangopol, 2015, Harries, Heimann, Hinnenthal, 2003, Kosmas, Vlachos, 2012, Marie, Courteille, et al., 2009, Szłapczynska and Smierzchalski, 2009, Tsou, 2010) run faster but search only inside a subspace of the search space for the best solution. Also, for coastal navigation and trans-oceanic seafaring, the methodology of the calculus of variations (Bijlsma, 2004) has also been employed and is based on long-term weather forecasts. Finally, a classic method for optimizing ship routes is still the isochrone method (Fang and Lin, 2015).

In this paper, we consider the bi-objective time-constrained ship weather routing problem as a time-dependent bi-objective point-to-point shortest path problem with a constraint on the total voyage time. The two objectives of the problem are the minimization of the fuel consumption and the total risk. In practice, frequent change of ship power or equivalently of nominal speed during the voyage is avoided (Szlapczynski, 2006) especially in the case of coastal navigation. Thus, in this work, the navigation speed is not a control variable; it is assumed to be constant during the whole journey and should be given as an input parameter. Notably, when the objective is the fastest route between two ports, the networks modelling the sea transportation commonly have the FIFO property.¹ However, in our problem setting, the objectives are different and leaving from a node immediately after the arrival may not be the best option, for instance, when the costs (fuel consumption and risk) along the outgoing link are decreasing in the next time interval (Orda and Rom, 1991). Although, computing shortest paths in FIFO networks is a polynomially solvable problem (Kaufman, Smith, 1993, Orda, Rom, 1990), this is not the case when optimal waiting policy should be determined for other cost objectives (Orda and Rom, 1991). On the other hand, frequent stops in the middle of the sea or alternating ship speed frequently is not a common practice in ship routing (Szlapczynski, 2006). Thus, although it is generally better to wait at a node, in our maritime setting, we assume that there is neither the option of waiting nor the option of speed decrease; by decreasing the speed, we could simulate the forbidden waiting and shift the arrival at the node later exactly at the optimal departure time.

To sum up, in this work, we address the time-dependent bi-objective shortest path problem on a network with objectives other than the travel time, with fixed departure time, no waiting at nodes, constant nominal speed and a constraint on the total travel time. Also, since the problem is time-dependent, it is assumed that all arc costs are deterministic functions of the time. However, considering the low execution time of the proposed techniques, dynamic situations where the weather changes unpredictably during the journey can be handled by running the algorithms afresh.

We first give a non linear integer programming formulation of the problem, and in the sequel we present a new exact algorithm for solving it. To the best of our knowledge, only a few algorithmic approaches for the multi-objective time-dependent shortest path problem have been proposed in the literature (Getachew, Kostreva, Lancaster, 2000, Hamacher, Ruzika, Tjandra, 2006, Kostreva, Wiecek, 1993) are not efficient when waiting at nodes is forbidden. We employ a forward label-setting approach to efficiently tackle the aforementioned time-dependent bi-objective shortest path problem. The number of the labels being processed during the algorithm execution is kept at a reasonable level, reducing the computational overhead. The algorithms is compared against the backward algorithm of Hamacher et al.’s (2006), the best so far algorithm in the literature that solves the problem at hand, and the experimental results confirm the faster execution time of the proposed algorithms. A preliminary version of the algorithm appears in Veneti et al. (2015a).

Furthermore, we present critical modelling issues that directly affect the performance of our problem solution approach. We introduce a novel grid structure that is used as a base layer for solving the ship weather routing problem and significantly improves the efficiency of the proposed algorithm. We also proposed a number of methods to further improve the efficiency of our approach, namely: (i) a dynamically partitioned grid for reduced graph size as well as an alternative reduction technique where grid is pruned along a given voyage plan, (ii) a heuristic function used to transform the initial algorithm into a bi-objective A* algorithm thereby reducing the search space and (iii) a technique for deriving loopless ship routes, thus making the solutions conformable to the usual practice in this industry. In order to test and validate our approach in a realistic setting, we applied the proposed algorithm as well as the speeding up techniques and improvements on the algorithm for the optimal ship route planning in the Aegean Sea, Greece. The experimental results confirm the efficiency of the approach and its applicability in a realistic scenario. Preliminary results for some of the aforementioned techniques appear in Makrygiorgos et al. (2015).

The rest of the paper is organized as follows. Section 2 overviews the related work. Section 3 presents a non-linear integer programming formulation of the ship weather routing problem which is considered as a time-dependent bi-objective point-to-point shortest path problem, and gives an efficient exact algorithm for solving the problem. Section 4 presents critical modeling issues while Section 5 includes the speeding up techniques and improvements on the proposed algorithm. Section 6 presents the empirical evaluation of the proposed algorithm and its enhancements. Finally, Section 7 concludes our work.