Combinatorial Fitness Landscapes Research Articles

Problem features vs. algorithm performance on rugged multi-objective combinatorial fitness landscapes

In this paper, we attempt to understand and to contrast the impact of performance of randomized search heuristics for black-box multiobjective combinatorial optimization problems. At first, we measure the performance of two conventional dominance-based approaches with unbounded archive on a benchmark of enumerable binary optimization problems with tunable ruggedness, objective space dimension, and objective correlation (ρMNK-landscapes). Precisely, we investigate the expected runtime required by a global evolutionary optimization algorithm with an ergodic variation operator (GSEMO) and by a neighborhood-based local search heuristic (PLS), to identify a -approximation of the Pareto set. Then, we define a number of problem features characterizing the fitness landscape, and we study their intercorrelation and their association with algorithm runtime on the benchmark instances. At last, with a mixed-effects multi-linear regression we assess the individual and joint effect of problem features on the performance of both algorithms, within and across the instance classes defined by benchmark parameters. Our analysis reveals further insights into the importance of ruggedness and multi-modality to characterize instance hardness for this family of multi-objective optimization problems and algorithms.

Climbing combinatorial fitness landscapes

Hill-climbing constitutes one of the simplest way to produce approximate solutions of a combinatorial optimization problem, and is a central component of most advanced metaheuristics. This paper focuses on evaluating climbing techniques in a context where deteriorating moves are not allowed, in order to isolate the intensification aspect of metaheuristics. We aim at providing guidelines to choose the most adequate method for climbing efficiently fitness landscapes with respect to their size and some ruggedness and neutrality measures. To achieve this, we compare best and first improvement strategies, as well as different neutral move policies, on a large set of combinatorial fitness landscapes derived from academic optimization problems, including NK landscapes. The conclusions highlight that first-improvement is globally more efficient to explore most landscapes, while best-improvement superiority is observed only on smooth landscapes and on some particular structured landscapes. The empirical analysis realized on neutral move policies shows that a stochastic hill-climbing reaches in average better configurations and requires fewer evaluations than other climbing techniques. Results indicate that accepting neutral moves at each step of the search should be useful on all landscapes, especially those having a significant rate of neutrality. Last, we point out that reducing adequately the precision of a fitness function makes the climbing more efficient and helps to solve combinatorial optimization problems.

Complex-network analysis of combinatorial spaces: TheNKlandscape case

We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces. We use the well-known family of NK landscapes as an example. In our case the inherent network is the graph whose vertices represent the local maxima in the landscape, and the edges account for the transition probabilities between their corresponding basins of attraction. We exhaustively extracted such networks on representative NK landscape instances, and performed a statistical characterization of their properties. We found that most of these network properties are related to the search difficulty on the underlying NK landscapes with varying values of K .