A genetic algorithm for the partial binary constraint satisfaction problem: an application to a frequency assignment problem

We describe a genetic algorithm for the partial constraint satisfaction problem. The typical elements of a genetic algorithm, selection, mutation and cross-over, are filled in with combinatorial ideas. For instance, cross-over of two solutions is performed by taking the one or two domain elements in the solutions of each of the variables as the complete domain of the variable. Then a branch-and-bound method is used for solving this small instance. When tested on a class of frequency assignment problems this genetic algorithm produced the best known solutions for all test problems. This feeds the idea that combinatorial ideas may well be useful in genetic algorithms.Economics ;

Parental Influences and the Relationship to their Children’s Physical Activity Levels

International Journal of Exercise Science 10(2): 205-212, 2017 Engaging in a physically active lifestyle relates positively to current health and reduces chances of chronic diseases in the future. Given escalating health care costs, it is paramount to reduce illnesses associated with a lack of physical activity and thus critical to identify factors that influence physical activity - especially in children, with the opportunity for a lifetime impact. One of these influencing factors may be parents/guardians. The intent of this study was to examine the relationship between children’s physical activity levels and parental factors including parental physical activity, support/encouragement, restrictiveness, and self-reported participation. Data was collected from 15 child-parent pairs with children ranging in age from 7 to 10 years. Daily physical activity levels were determined from pedometer data using a Piezo SC-Step Pedometer. Number of steps and moderate and vigorous physical activity were extracted from the pedometers and levels of support/encouragement, restrictiveness, and participation were quantified from parents’ self-reported responses to a questionnaire created for this study. Pearson Product correlation analyses were carried out between: the children’s and parent steps (r = -0.069; p = 0.597); children’s steps and parent’s self-reported encouragement/support (r = 0.045, p = 0.563); children’s steps and parents’ self-reported restrictiveness (r = -.0254, p = 0.820); and children’s steps and parents’ self-reported participation (r = -0.002, p = 0.503). The lack of significant relationships among these variables implies that more complex interactions occur between children and their parents regarding physical activity with children’s participation influenced by other factors

On the computational complexity of (maximum) shift class scheduling

In this paper we consider a generalization of the Fixed Job Scheduling Problem (FSP) which appears in a natural way in the aircraft maintenance process at an airport. A number of jobs has to be carried out, where the main attributes of a job are: a fixed start time, a fixed finish time and a value representing the priority of the job. For carrying out these jobs a number of machines is available. These machines are available in specific time intervals (shifts) only. A job can be carried out by a machine only if the interval between the start time and the finish time of the job is a subinterval of the shift of the machine. Furthermore, the jobs must be carried out in a non-preemptive way and each machine can be carrying out at most one job at the same time

On the computational complexity of (maximum) class scheduling

In this paper we consider several generalizations of the Fixed Job Scheduling Problem (FSP) which appear in a natural way in the aircraft maintenance process at an airport: A number of jobs have to be carried out, where the main attributes of a job are: a fixed start time, a fixed finish time, a value representing the job's priority and a job class. For carrying out these jobs a number of machines are available. These machines can be split up into a number of disjoint machine classes. For each combination of a job class and a machine class it is known whether or not it is allowed to assign a job in the job class to a machine in the machine class. Furthermore the jobs must be carried out in a non-preemptive way and each machine can be carrying out at most one job at the same time. Within this setting one can ask for a feasible schedule for all jobs or, if such a schedule does not exist, for a feasible schedule for a subset of the jobs of maximum total value. In this paper we present a complete classification of the computational complexity of two classes of combinatorial problems related this operational job scheduling problem

License class design: complexity and algorithms

In this paper a generalization of the Fixed Job Scheduling Problem (FSP) is considered, which appears in the aircraft maintenance process at an airport. A number of jobs have to be carried out, where the main attributes of a job are a fixed start time, a fixed finish time and an aircraft type. For carrying out these jobs a number of engineers are available. An engineer is allowed to carry out a specific job only if he has a license for the corresponding aircraft type. Furthermore, the jobs must be carried out in a non-preemptive way and each engineer can be carrying out at most one job at the same time. Within this setting natural questions to be answered ask for the minimum number of engineers required for carrying out all jobs or, more generally, for the minimum total costs for hiring engineers. In this paper a complete classification of the computational complexity of two classes of mathematical problems related to these practical questions is given. Furthermore, it is shown that the polynomially solvable cases of these problems can be solved by a combination of Linear Programming and Network Flow algorithms

A general framework for shortest path algorithms

In this paper we present a general framework for shortest path algorithms, including amongst others Dijkstra's algorithm and the A* algorithm. By showing that all algorithms are special cases of one algorithm in which some of the nondeterministic choices are made deterministic, termination and correctness can be proved by proving termination and correctness of the root algorithm. Furthermore, several invariants of the algorithms are derived which improve the insight with respect to the operations of the algorithms