POPMUSIC as a matheuristic for the berth allocation problem

Abstract

The Berth Allocation Problem aims at assigning and scheduling incoming vessels to berthing positions along the quay of a container terminal. This problem is a well-known optimization problem within maritime shipping. In order to address it, we propose two POPMUSIC (Partial Optimization Metaheuristic Under Special Intensification Conditions) approaches that incorporate an existing mathematical programming formulation. POPMU-SIC is an efficient metaheuristic that may serve as blueprint for matheuristics approaches once hybridized with mathematical programming. In this regard, the use of exact methods for solving the sub-problems defined in the POPMUSIC template highlight an interoperation between metaheuristics and mathematical programming techniques, which provide a new type of approach for this problem. The computational experiments reveal excellent results.

Late Acceptance Hill-Climbing Matheuristic for the General Lot Sizing and Scheduling Problem with Rich Constraints

“…By means of this function, an input solution is used for extracting and fixing decision variables with the aim of generating smaller sub-problems and solving them in an exact way, producing thus a candidate solution. In a similar way as proposed in [6] through the definition of reduced sub-problems from larger and more complex ones, we are able to address them using an exact algorithm in a small and reasonable computational time. This, as discussed in the relevant section, allows improving the quality of the provided solution while reducing the overall solving time.…”

“…Within matheuristics, decomposition approaches belong to one of the most relevant algorithms (some recent examples can be consulted in, for example, [3][4][5]). For instance, the principal idea behind proposing the matheuristic version of POPMUSIC is to decompose the problems into smaller (and likely more tractable) ones and solve them by means of an exact technique [6]. As remarked by [7] to successfully apply decomposition matheuristic approaches, one may develop an iterated procedure where the information is interchanged along the process.…”

Migrating Birds Optimization for the Seaside Problems at Maritime Container Terminals

“…Their approach reports the same quality solutions as [12] in terms of objective function value; nevertheless, it requires less computational time. Finally, Lalla-Ruiz and Voß [14] propose a matheuristic based on POPMUSIC (Partial Optimization Metaheuristic Under Special Intensification Conditions). The authors tested their approach over the largest instances proposed in [5] exhibiting a high robustness in terms of the average objective values reported by their approach.…”

“…Once those Journal of Applied Mathematics 5 (1) Generate birds initial solutions in a random manner and place them on a hypothetical formation arbitrarily (2) = 0 (3) while < do (4) for ( = 0; < iter max ; ++) do (5) Try to improve the leading solution by generating and evaluating neighbours of it (6) = + (7) for all (solutions in the flock (except leader)) do (8) Try to improve the leading solution by generating and evaluating − neighbours of it and the unused best neighbours from the solution in the front. (9) = + ( − ) (10) end for (11) end for (12) Move the leader solution to the end and forward one of the solutions following it to the leader position (13) end while (14) Return best solution in the flock Algorithm 1: Migrating Birds Optimization algorithm (Duman et al [6]). iterations have been reached, the leader individual is moved to the end of one of the lines of the -formation and one of its direct follower individuals becomes the new leader of the flock.…”

Construct, Merge, Solve and Adapt Versus Large Neighborhood Search for Solving the Multi-dimensional Knapsack Problem: Which One Works Better When?

“…Thus, the destruction step defines a large neighborhood, from which a best (or nearly best) solution is determined, not by naive enumeration but by the application of a more effective alternative technique. Apart from LNS, the related literature offers algorithms that make use of alternative ways of defining large neighborhoods, such as the so-called Corridor Method [5], POPMUSIC [6], and Local Branching [7].…”