During the course of the project, the work has diverted slightly from the original plan described in the project description in that the work has focussed solely on the tug fleet optimisation problem and not included any research related to the offshore industry. The reason for this is that the scope of the TFO problem was larger than expected and also led to new research questions which we had not thought about initially. For this reason, the research results exceed reaching the subgoals listed in the original project description and also divert slightly. Note however, that with small modifications, the algorithms we have developed can be transferred to other domains where dynamic resource allocation is needed, e.g., for optimising a fleet of PSVs.

Goal Achievements

The main goal has been achieved by means of completing subgoals M1–M4.

M1 — further develop and improve RHGA

The original RHGA was further developed and greatly improved as documented in Bye and Schaathun (2014):

  • the entire algorithm and its simulator framework was recoded into the functional programming language Haskell, which has a number of advantages, including
    • modularity and easier extensions and modifications;
    • code maintenance, readibility, conciseness, and easier debugging; and
    • suitability for parallelisation.
  • more than fifty-fold increase in number of simulation scenarios, making results much more reliable.
  • genetic algorithm component extended with more options and easier to adapt to new problems.
  • 1D model of problem formulation more concise and mathematically stringent.

M2 — develop new methods

A total of 14 different cost functions were developed and evaluated as documented in Bye and Schaathun (2014, 2015a,b). Configuring the RHGA with each of these cost functions essentially is equivalent to using 14 different TFO algorithms. In addition, a 2D nonlinear mixed integer programming (MIP) formulation was developed, in which the problem formulation is redefined as a 2D model, and the GA component of the RHGA is replaced by MIP to form a RHMIP algorithm. This work also included two linearisation methods and employed real, historical traffic data. A manuscript detailing this work is nearly finished and will be submitted to a level 1 or 2 journal (Assimizele et al., 2015).

M3 — develop exact solutions and benchmarks

An exact optimal solution to the original cost function by means of MIP and used with the RHGA was developed in Assimizele et al. (2013). For the 2D nonlinear MIP model in Assimizele et al. (2015), two linearisation methods with proven upper and lower solution bounds were developed, hence the level of accuracy can be chosen by the user, with higher accuracy at the cost of longer computational times.

Thorough investigation of theoretical or practical algorithmic speed was not undertaken but some quantitative results regarding computational time was done by Assimizele et al. (2015).

In order to compare the merit of different TFO algorithms, two evaluation
heuristic were developed and tested by means of a computational simulation
study (Bye and Schaathun, 2015a,b).

M4 — conferences and publications

Please see Sections “Conferences and Seminars” and “Publications” below.

Other Results

GAs lend themselves naturally to parallelisation, which can greatly improve the computational speed of an algorithm. However, parallelisation of code in the functional programming language Haskell used in the DRAMA project imposes strict demands on pseudo-random number generation (PRNG), which lies at the core of many optimisation algorithms, including GAs. Hence, a decision was made to investigate these challenges further, which resulted in a conference presentation and level 1 publication (Schaathun,2014).

Furthermore, a more in-dept study of so-called splittable PRNGs followed and the resulting level 1 journal paper is currently under review (Schaathun, 2015).

Conferences and Seminars

Research results from the project have been presented at, and published in the proceedings of, the following conferences:

  • the 27th European Conference on Modelling and Simulation (ECMS’13)
    (Assimizele et al., 2013);
  • the 28th European Conference on Modelling and Simulation (ECMS’14)
    (Bye and Schaathun, 2014);
  • Norsk Informatikkonferanse (NIK’14) (Norwegian Conference on In-
    formatics) (Schaathun, 2014); and
  • the 4th International Conference on Operations Research and Enterprise Systems (ICORES’15) (Bye and Schaathun, 2015a).

Abstracts were also submitted and accepted for presentation at the INFORMS Annual Meeting in 2013 (Brice Assimizele presentation) and Operation Days 2014 (Johan Oppen presentation). Finally, a number of internal seminars have been held at Aalesund University College and Molde University College.


A list of the publications is found here.

The DRAMA project was a continuation of earlier work by the project head and colleagues and tat was published as a conference paper (Bye et al., 2010) and a publication in a book series (Bye, 2012). In the period following the grant award by the Research Council of Norway but before the official start of the project in September 2013, the DRAMA research group managed to give the project a head start by partly completing subgoal M3, and had the results published in a conference paper (Assimizele et al., 2013). After the project startup, the publications that are a direct result of the DRAMA project’s research include three published conference papers (Bye and Schaathun, 2014, 2015a; Schaathun, 2014), one publication that has been accepted for publication in a book series and will appear during 2015 (Bye and Schaathun, 2015b), one journal paper (Schaathun, 2015) that has been submitted and is currently under review, and one journal paper that is under preparation (Assimizele et al., 2015).

In summary, excluding the two pre-project papers, the project has resulted in a total of seven publications that all qualify for publication points as recognised by the Norwegian Register for Scientific Journals, Series, and Publishers, with scientific levels as indicated in parentheses:

  • 4 conference papers (level 1);
  • 1 book series papers (level 1);
  • 1 journal paper currently under review (level 1); and
  • 1 journal paper currently under preparation (level 1 or 2).

Subgoal M4 of the project was to present the work at international conferences and publish two papers on level 1 or 2. With five accepted publications and two journal papers awaiting, the project has thus exceeded its publication goal by far. Publications can be found under the Publications tab.

Networking and Future Collaboration

The project has strengthened the cooperation with the NCA, for example by means of a field trip to the Vardø VTS. This has been important to ensure that the research is relevant and realistic. Many academics and professionals at conferences have expressed great interest in the project, including a researcher at the company Liquid Robotics and an academic at Bergen Uni-
versity College, who both are interested in collaboration and application of the project algorithms on aquatic swarm robots. Most important has been a field trip by the PhD candidate Brice Assimizele to the USA and the strong cooperation with Johannes Royset, who is the Associate Chair of Research and Associate Professor of Operations Research at the Naval Postgraduate School in Monterey, California. This cooperation has led to Royset now
actively co-supervising the PhD candidate.

New Research and Education Activities Spawned by DRAMA

After the completion of the DRAMA project, Bye and Schaathun together with colleagues have co-founded the research group Software and Intelligent Control Engineering (SoftICE) Laboratory at AAUC. The SoftICE lab will continue working with some of the core components of the DRAMA project, namely functional programming, parallel computing, and genetic algorithms. Among other things, this work has led to research funding for intelligent virtual prototyping of offshore cranes using artificial intelligence and has already resulted in a publication (Bye et al., 2015).

In addition, further delving into functional programming and GAs, the same two people have developed two new courses on artificial intelligence in AAUC’s new master programme in simulation and visualisation, as well as using the TFO problem as part of the research-based teaching component of a third year bachelor elective in intelligent systems.

Research on the TFO problem is also continuing with the work of PhD candidate Brice Assimizele, who will expand on his previous work (Assimizele et al., 2013, 2015) and develop new methods, for example using superquantile risk (also known as conditional value-at-risk (CVaR)).


The DRAMA project has been a success in that the desired goals were reached, most notably by the number of publications (seven) greatly exceeding the target number of publications (two). Part of the reason for this was the unforeseen need to explore and solve challenges related to parallelisa tion and pseudo-random number generation. Knowledge gained and the new methods developed have been transferrable to and useful in other domains in research and education (see above). In addition, research on the particular TFO problem of the DRAMA project is being continued by a PhD candidate at AAUC who is expected to complete his work late 2016.


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