Boosting the performance of metaheuristics for the MinLA problem using a more discriminating evaluation function

U radu se ispituje uloga funkcije evaluacije u metaheuristici kod rješavanja kombinatornih problema optimizacije. Evaluacijska funkcija (EF) je ključna sastavnica svakog metaheurističkog algoritma i njezin dizajn direktno utječe na performansu takvog algoritma. Međutim, u literaturi je dizajn kritičnijih EF-a donekle zanemaren. U ovom radu dajemo prvu temeljnu analizu standardne EF za problem Minimum Linear Arrangement (MinLA). Dobiveni rezultati su ukazali na moguće nedostatke i dali koristan uvid i informacije potrebne za dizajniranje kritičnije EF. Njezina se praktična korisnost procijenila u tri različita algoritma: parameter-free Steepest Descent, Iterated Local Search i Tabu Search. Analiza dobivenih podataka pokazala je da bi se performansa ta tri primijenjena pristupa mogla poboljšati primjenom predloženih kritičnijih EF.This paper investigates the role of evaluation function used by metaheuristics for solving combinatorial optimization problems. Evaluation function (EF) is a key component of any metaheuristic algorithm and its design directly influences the performance of such an algorithm. However, the design of more discriminating EFs is somewhat overlooked in the literature. We present in this work the first in-depth analysis of the conventional EF for the Minimum Linear Arrangement (MinLA) problem. The results from this study highlighted its potential drawbacks and led to useful insight and information which guided us to design a new more discerning EF. Its practical usefulness was assessed within three different algorithms: a parameter-free Steepest Descent, an Iterated Local Search and a Tabu Search. The analysis of the data produced by these comparisons showed that the performance of the three adopted approaches could be boosted by using the proposed more discriminating EF

Optimization by quantum annealing for the graph colouring problem

Quantum annealing is the quantum equivalent of the well known classical simulated annealing algorithm for combinatorial optimization problems. Despite the appeal of the approach, quantum annealing algorithms competitive with the state of the art for specific problems hardly exist in the literature. Graph colouring is a difficult problem of practical significance that can be formulated as combinatorial optimization. By introducing a symmetry-breaking problem representation, and finding fast incremental techniques to calculate energy changes, a competitive graph colouring algorithm based on quantum annealing is derived. This algorithm is further enhanced by tuning simplification techniques; replica spacing techniques to increase robustness; and a messaging protocol, which enables quantum annealing to efficiently take advantage of multiprocessor environments. Additionally, observations of some patterns in the tuning for random graphs led to a more effective algorithm able to find new upper bounds for several widely-used benchmark graphs, some of which had resisted improvement in the last two decades

A study of evaluation functions for the graph K-coloring problem.

International audienceAbstract. The evaluation or fitness function is a key component of any heuristic search algorithm. This paper introduces a new evaluation function for the well-known graph K-coloring problem. This function takes into account not only the number of conflicting vertices, but also inherent information related to the structure of the graph. To assess the effectiveness of this new evaluation function, we carry out a number of experiments using a set of DIMACS benchmark graphs. Based on statistic data obtained with a parameter free steepest descent, we show an improvement of the new evaluation function over the classical one