# Efficient solutions to a class of generalized time-dependent combinatorial optimization problems

#### Abstract

As a branch of operations research, combinatorial optimization plays important role in obtaining efficient solutions to NP-hard problems common in science, engineering, and management domains. In 2001, Michael L. Gargano and William Edelson described a model of time-dependent combinatorial optimization problems, and outlined several important applications of the model in terms of the genetic algorithm meta-heuristic. The model assumes a set of unit-time tasks to be completed sequentially, a set of workers bidding on completing the tasks with time-dependent costs, and seeks an optimized ordering for completing the tasks with an optimized assignment of the tasks to the workers. The model can be subdivided into sub-models depending on whether a worker can bid on multiple tasks, or whether a worker can be assigned to completing more than one task. ^ In 2002, Joseph DeCicco used genetic algorithm to solve a sub-model of the above problems in which a worker can only bid on one task and be assigned at most one task. In 2003, Rigoberto Diaz established the mathematical model for the same sub-model of problems that Joseph DeCicco worked on, simplified the problems in the sub-model with a novel problem transformation algorithm, and claimed significantly reduced solution costs and algorithm time-complexity with his algorithm based on simulated annealing meta-heuristic. In 2004, Maheswara Kasinadhuni proposed a new genetic algorithm heuristic to solve the same sub-mode of problems with multiple genome coding. ^ This research focuses on the efficient solutions to the most difficult sub-model variant of the time-dependent combinatorial optimization problems in which a worker can bid on multiple tasks but can be assigned at most one task. Since the task assignment for a worker now depends on all previous such assignments, Diaz's problem transformation cannot be applied to simplify the problems. In addition to its own value in solving more difficult real-world problems, this sub-model of problems also provides a platform for more objective comparison of solution quality and time-complexity of different solution approaches. ^ Efficient solution algorithms based on exhaustive search, repeated random solutions, genetic algorithm, and simulated annealing were designed and implemented in Java. Except for the exhaust search algorithm that can find optimal solutions to problem instances of size less than 10, the others are all heuristic algorithms that can provide efficient solutions for problem instances of size larger than 200. Extensive experimental study shows that the simulated annealing algorithm outperforms all of the other approaches in terms of both solution quality and algorithm time-complexity. ^

#### Subject Area

Computer Science

#### Recommended Citation

Todd W Kolb,
"Efficient solutions to a class of generalized time-dependent combinatorial optimization problems"
(January 1, 2005).
*ETD Collection for Pace University.*
Paper AAI3172923.

http://digitalcommons.pace.edu/dissertations/AAI3172923

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