Nature is characterized by its chaotic behavior. Mathematics is considered one of the appropriate tools to achieve the best definition of possible its chaos variables and process. Classical mathematics deals with the numbers as static and meaningless, but chaos mathematics deals with it as dynamic evolutionary, and value- added. This paper attempts to introduce the transportation problem re...

The firefighter problem (FFP) is used as a model to simulate how a fire breaks out and spreads to its surroundings over a discrete time period. The goal is to deploy a given number of firefighters on strategic points at each time step to contain the fire in a most efficient way, so that as many areas are saved from the fire as possible. In this paper we introduce a new solution representation f...

In the study a developed solution for VRP (Vehicle Routing Problem) and its algorithms were analysed in order to find explanations for their success and evaluate their results. Another exciting question at the combinatorial optimization is the solution space which is often referred in the literature despite we do not have tools for its representation, although the distinction of solutions seems...

Decision diagrams are a family of data structures that can compactly encode many functions on discrete structured domains, that is, domains that are the cross-product of finite sets. We present some important classes of decision diagrams and show how they can be effectively employed to derive “symbolic” algorithms for the analysis of large discrete-state models. In particular, we discuss both e...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3

exit states Abstract State Both techniques eliminate distinctions within unconstrained regions of the solution space by abstracting these regions into a single state within the search tree. (The gure above is a generalized representation of the search space explored during simulation.) By identifying the boundaries of the unconstrained region, both algorithms are able to generate an abstract st...