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Using river formation dynamics to design heuristic algorithms

Finding the optimal solution to NP-hard problems requires at least exponential time. Thus, heuristic methods are usually applied to obtain acceptable solutions to this kind of problems. In this paper we propose a new type of heuristic algorithms to solve this kind of complex problems. Our algorithm is based on river formation dynamics and provides some advantages over other heuristic methods, like ant colony optimization methods. We present our basic scheme and we illustrate its usefulness applying it to a concrete example: The Traveling Salesman Problem.

Finding Minimum Spanning/Distances Trees by Using River Formation Dynamics

River Formation Dynamics(RFD) is an heuristic method similar to Ant Colony Optimization(ACO). In fact, RFD can be seen as a gradient version of ACO, based on copying how water forms rivers by eroding the ground and depositing sediments. As water transforms the environment, altitudes of places are dynamically modified, and decreasing gradients are constructed. The gradients are followed by subsequent drops to create new gradients, reinforcing the best ones. By doing so, good solutionsare given in the form of decreasingaltitudes. We apply this method to solve two NP-complete problems, namely the problems of finding a minimum distances treeand finding a minimum spanning treein a variable-cost graph. We show that the gradient orientation of RFD makes it specially suitable for solving these problems, and we compare our results with those given by ACO.

Applying River Formation Dynamics to Solve NP-Complete Problems

For obvious practical reasons, NP-complete problems are typically solved by applying heuristic methods. In this regard, nature has inspired many heuristic algorithms to obtain reasonable solutions to complex problems. One of these algorithms is River Formation Dynamics (RFD). This heuristic optimization method is based on imitating how water forms rivers by eroding the ground and depositing sediments. After drops transform the landscape by increasing/decreasing the altitude of places, solutions are given in the form of paths of decreasing altitudes. Decreasing gradients are constructed, and these gradients are followed by subsequent drops to compose new gradients and reinforce the best ones. In this chapter, we apply RFD to solve three NP-complete problems, and we compare our results with those obtained by using Ant Colony Optimization (ACO).

A General Testability Theory: Classes, Properties, Complexity, and Testing Reductions

In this paper we develop a general framework to reason about testing. The difficulty of testing is assessed in terms of the amount of tests that must be applied to determine whether the system is correct or not. Based on this criterion, five testability classes are presented and related. We also explore conditions that enable and disable finite testability, and their relation to testing hypotheses is studied. We measure how far incomplete test suites are from being complete, which allows us to compare and select better incomplete test suites. The complexity of finding that measure, as well as the complexity of finding minimum complete test suites, is identified. Furthermore, we address the reduction of testing problems to each other, that is, we study how the problem of finding test suites to test systems of some kind can be reduced to the problem of finding test suites for another kind of systems. This enables to export testing methods. In order to illustrate how general notions are applied to specific cases, many typical examples from the formal testing techniques domain are presented.

Applying River Formation Dynamics to the Steiner Tree Problem

River Formation Dynamics (RFD) is a heuristic optimization algorithm based on copying how water forms rivers by eroding the ground and depositing sediments. After drops transform the landscape by increasing/decreasing the altitude of places, solutions are given in the form of paths of decreasing altitudes. Decreasing gradients are constructed, and these gradients are followed by subsequent drops to compose new gradients and reinforce the best ones. We apply this method to solve the Steiner Tree Problem (STP), a well-known NP-hard problem having applications to areas like telecommunications routing and VLSI design among many others. We show that the gradient orientation of RFD makes it specially suitable for solving this problem, and we report the results of several experiments where RFD is applied to benchmark graphs from the SteinLib Testdata Library [1].

Testing restorable systems: formal definition and heuristic solution based on river formation dynamics

Given a finite state machine denoting the specification of a system, finding some short interaction sequences capable of reaching some/all states or transitions of this machine is a typical goal in testing methods. If these sequences are applied to an implementation under test, then equivalent states or transitions would be reached and observed in the implementation—provided that the implementation were actually defined as the specification. We study the problem of finding such sequences in the case where configurations previously traversed can be saved and restored (at some cost). In general, this feature enables sequences to reach the required parts of the machine in less time, because some repetitions can be avoided. However, we show that finding optimal sequences in this case is an NP-hard problem. We propose an heuristic method to approximately solve this problem based on an evolutionary computation approach, in particular river formation dynamics (RFD). Given finite state machine specifications and sets of states/transitions to be reached, we apply RFD to construct testing plans reaching these configurations. Experimental results show that being able to load previously traversed states generally reduces the time needed to cover the target configurations.

Testing Restorable Systems by Using RFD

Given a finite state machine denoting the specification of a system, finding some short interaction sequences capable to reach some/all states or transitions of this machine is a typical goal in testing methods. We study the problem of finding such sequences in the case where configurations previously traversed can be saved and restored (at some cost). Finding optimal sequences for this case is an NP-hard problem. We propose an heuristic method to approximately solve this problem based on an evolutionary computation approach, in particular River Formation Dynamics . Some experimental results are reported.

A Formal Approach to Heuristically Test Restorable Systems

In order to test a Finite State Machine (FSM), first we typically have to identify some short interaction sequences allowing to reach those states or transitions considered as critical . If these sequences are applied to an implementation under test (IUT), then equivalent states or transitions would be reached and observed in the implementation --- provided that the implementation were actually defined as the specification. In this paper we study how to obtain such sequences in a scenario where previous configurations can be restored at any time. In general, this feature enables sequences to reach the required parts of the machine in less time, because some repetitions can be avoided. However, finding optimal sequences is NP-hard when configurations can be restored. We use an evolutionary method, River Formation Dynamics, to heuristically solve this problem.

Parallelizing Particle Swarm Optimization in a Functional Programming Environment

Many bioinspired methods are based on using several simple entities which search for a reasonable solution (somehow) independently. This is the case of Particle Swarm Optimization (PSO), where many simple particles search for the optimum solution by using both their local information and the information of the best solution found so far by any of the other particles. Particles are partially independent, and we can take advantage of this fact to parallelize PSO programs. Unfortunately, providing good parallel implementations for each specific PSO program can be tricky and time-consuming for the programmer. In this paper we introduce several parallel functional skeletons which, given a sequential PSO implementation, automatically provide the corresponding parallel implementations of it. We use these skeletons and report some experimental results. We observe that, despite the low effort required by programmers to use these skeletons, empirical results show that skeletons reach reasonable speedups.

Hybridizing river formation dynamics and ant colony optimization

River Formation Dynamics (RFD) is an evolutionary computation method based on copying how drops form rivers by eroding the ground and depositing sediments. In a rough sense, this method can be seen as a gradient-oriented version of Ant Colony Optimization (ACO). Several experiments have shown that the gradient orientation of RFD makes this method solve problems in a different way as ACO. In particular, RFD typically performs deeper searches, which in turn makes it find worse solutions than ACO in the first execution steps in general, though RFD solutions surpass ACO solutions after some more time passes. In this paper we try to get the best features of both worlds by hybridizing RFD and ACO, in particular by using a kind of ant-drop hybrid and considering both pheromone trails and altitudes in the environment.