Complexity of Max-SAT using stochastic algorithms

2015

Evol. Intel.

The anatomy of the fitness landscape for the quadratic assignment problem is studied in this paper. We study the properties of both random problems, and realworld problems. Using auto-correlation as a measure for the landscape ruggedness, we study the landscape of the problems and show how this property is related to the problem matrices with which the problems are represented. Our main goal in this paper is to study new properties of the fitness landscape, which have not been studied before, and we believe are more capable of reflecting the problem difficulties. Using local search algorithm which exhaustively explore the plateaus and the local optima, we explore the landscape, store all the local optima we find, and study their properties. The properties we study include the time it takes for a local search algorithm to find local optima, the number of local optima, the probability of reaching the global optimum, the expected cost of the local optima around the global optimum and the basin of attraction of the global and local optima. We study the properties for problems of different sizes, and through extrapolations, we show how the properties change with the system size and why the problem becomes harder as the system size grows. In our study we show how the real-world problems are similar to, or different from the random problems. We also try to show what properties of the problem matrices make the landscape of the real problems be different from or similar to one another.

Section: Introductionmentioning

confidence: 99%

Quadratic assignment problem: a landscape analysis

Tayarani-N.

2015

Evol. Intel.

“…The number of iterations were increased with the number of variables so that BHC would be given more opportunities to find better quality solutions. With the growth of the number of variables it becomes more difficult for a local search algorithm to reach local maxima [7], although the goal was not necessarily to reach a local maximum, but only to find a good solution. The best result for the 1 000 hill-climbs averaged over all 100 problem instances is shown in the second column of table 1.…”

Section: Methodsmentioning

confidence: 99%

Improving Performance in Combinatorial Optimisation Using Averaging and Clustering

Qasem

Evolutionary Computation in Combinatorial Optimization

2009

Self Cite

Abstract. In a recent paper an algorithm for solving MAX-SAT was proposed which worked by clustering good solutions and restarting the search from the closest feasible solutions. This was shown to be an extremely effective search strategy, substantially out-performing traditional optimisation techniques. In this paper we extend those ideas to a second classic NP-Hard problem, namely Vertex Cover. Again the algorithm appears to provide an advantage over more established search algorithms, although it shows different characteristics to MAX-SAT. We argue this is due to the different large-scale landscape structure of the two problems.

“…These numbers were chosen after experimentation as they gave good quality solutions. We increased the number of iterations with the size of the problem to give more opportunities for the larger problems to find good quality solutions, since it has been shown that the time to reach a local maxima grows with the problem size [20]. However it should be stressed that it was not the goal to necessarily reach a local maximum, but only to find a good solution.…”

Section: A Experimental Setupmentioning

confidence: 99%

Learning the Large-Scale Structure of the MAX-SAT Landscape Using Populations

Qasem

IEEE Trans. Evol. Computat.

2010

Abstract-A new algorithm for solving MAX-SAT problems is introduced which clusters good solutions, and restarts the search from the closest feasible solution to the centroid of each cluster. This is shown to be highly efficient for finding good solutions of large MAX-SAT problems. We argue that this success is due to the population learning the large-scale structure of the fitness landscape. Systematic studies of the landscape are presented to support this hypothesis. In addition, a number of other strategies are tested to rule out other possible explanations of the success.Preliminary results are shown indicating that extensions of the proposed algorithm can give similar improvements on other hard optimisation problems.