Constraint programming methods in three-dimensional container packing

Cutting and packing problems are present in many, at first glance unconnected, areas, therefore it's beneficial to have a good understanding of their underlying structure, to select proper techniques for finding solutions. Cutting and packing problems are a class of combinatorial problems in which there are specified two classes of objects: big and small items and the task is to place the small items within big items. Even in the 1-dimensional case, bin-packing is strongly NP-hard (Garey 1978), which suggests, that exact solutions may not be found in a reasonable time for bigger instances. In the literature, there are presented many various approaches to packing problems, e.g. mixed-integer programming, approximation algorithms, heuristic solutions, and local search algorithms, including metaheuristic approaches like Tabu Search or Simulated Annealing. The main goal of this work is to review existing solutions, survey the variants arising from the industry applications, present a solution based on constraint programming and compare its performance with the results in the literature. Optimization with constraint programming is a method searching for the global optima, hence it may require a higher workload compared to the heuristic and local search approaches, which may finish in a local optimum. The performance of the presented model will be measured on test data used in the literature, which were used in many articles presenting a variety of approaches to three-dimensional container packing, which will allow us to compare the efficiency of the constraint programming model with other methods used in the operational research

Coordination of Mobile Mules via Facility Location Strategies

In this paper, we study the problem of wireless sensor network (WSN) maintenance using mobile entities called mules. The mules are deployed in the area of the WSN in such a way that would minimize the time it takes them to reach a failed sensor and fix it. The mules must constantly optimize their collective deployment to account for occupied mules. The objective is to define the optimal deployment and task allocation strategy for the mules, so that the sensors' downtime and the mules' traveling distance are minimized. Our solutions are inspired by research in the field of computational geometry and the design of our algorithms is based on state of the art approximation algorithms for the classical problem of facility location. Our empirical results demonstrate how cooperation enhances the team's performance, and indicate that a combination of k-Median based deployment with closest-available task allocation provides the best results in terms of minimizing the sensors' downtime but is inefficient in terms of the mules' travel distance. A k-Centroid based deployment produces good results in both criteria.Comment: 12 pages, 6 figures, conferenc

A bi-objective genetic algorithm approach to risk mitigation in project scheduling

A problem of risk mitigation in project scheduling is formulated as a bi-objective optimization problem, where the expected makespan and the expected total cost are both to be minimized. The expected total cost is the sum of four cost components: overhead cost, activity execution cost, cost of reducing risks and penalty cost for tardiness. Risks for activities are predefined. For each risk at an activity, various levels are defined, which correspond to the results of different preventive measures. Only those risks with a probable impact on the duration of the related activity are considered here. Impacts of risks are not only accounted for through the expected makespan but are also translated into cost and thus have an impact on the expected total cost. An MIP model and a heuristic solution approach based on genetic algorithms (GAs) is proposed. The experiments conducted indicate that GAs provide a fast and effective solution approach to the problem. For smaller problems, the results obtained by the GA are very good. For larger problems, there is room for improvement

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions