A step counting hill climbing algorithm

This paper presents a new single-parameter local search heuristic named Step Counting Hill Climbing algorithm (SCHC). It is a very simple method in which the current cost serves as an acceptance bound for a number of consecutive steps. This is the only parameter in the method that should be set up by the user. Furthermore, the counting of steps can be organized in different ways; therefore the proposed method can generate a large number of variants and also extensions. In this paper, we investigate the behaviour of the three basic variants of SCHC on the university exam timetabling problem. Our experiments demonstrate that the proposed method shares the main properties with the Late Acceptance Hill Climbing method, namely its convergence time is proportional to the value of its parameter and a non-linear rescaling of a problem does not affect its search performance. However, our new method has two additional advantages: a more flexible acceptance condition and better overall performance. In this study we compare the new method with Late Acceptance Hill Climbing, Simulated Annealing and Great Deluge Algorithm. The Step Counting Hill Climbing has shown the strongest performance on the most of our benchmark problems used

How to Escape Local Optima in Black Box Optimisation: When Non-elitism Outperforms Elitism

Escaping local optima is one of the major obstacles to function optimisation. Using the metaphor of a fitness landscape, local optima correspond to hills separated by fitness valleys that have to be overcome. We define a class of fitness valleys of tunable difficulty by considering their length, representing the Hamming path between the two optima and their depth, the drop in fitness. For this function class we present a runtime comparison between stochastic search algorithms using different search strategies. The ((Formula presented.)) EA is a simple and well-studied evolutionary algorithm that has to jump across the valley to a point of higher fitness because it does not accept worsening moves (elitism). In contrast, the Metropolis algorithm and the Strong Selection Weak Mutation (SSWM) algorithm, a famous process in population genetics, are both able to cross the fitness valley by accepting worsening moves. We show that the runtime of the ((Formula presented.)) EA depends critically on the length of the valley while the runtimes of the non-elitist algorithms depend crucially on the depth of the valley. Moreover, we show that both SSWM and Metropolis can also efficiently optimise a rugged function consisting of consecutive valleys

Deconstructing the Big Valley Search Space Hypothesis

The big valley hypothesis suggests that, in combinatorial optimisation, local optima of good quality are clustered and surround the global optimum. We show here that the idea of a single valley does not always hold. Instead the big valley seems to de-construct into several valleys, also called ‘funnels’ in theoretical chemistry. We use the local optima networks model and propose an effective procedure for extracting the network data. We conduct a detailed study on four selected TSP instances of moderate size and observe that the big valley decomposes into a number of sub-valleys of different sizes and fitness distributions. Sometimes the global optimum is located in the largest valley, which suggests an easy to search landscape, but this is not generally the case. The global optimum might be located in a small valley, which offers a clear and visual explanation of the increased search difficulty in these cases. Our study opens up new possibilities for analysing and visualising combinatorial landscapes as complex networks

Local Optima Networks of the Permutation Flow-Shop Problem

International audienceThis article extracts and analyzes local optima networks for the permutation flow-shop problem. Two widely used move operators for permutation representations, namely, swap and insertion, are incorporated into the network landscape model. The performance of a heuristic search algorithm on this problem is also analyzed. In particular, we study the correlation between local optima network features and the performance of an iterated local search heuristic. Our analysis reveals that network features can explain and predict problem difficulty. The evidence confirms the superiority of the insertion operator for this problem

Fitness Landscapes And Performance Of Meta-Heuristics

We perform a statistical analysis of the structure of the search space of some planar, euclidian instances of the traveling salesman problem. We want to depict this structure from the point of view of iterated local search algorithms

Testing, Evaluation and Performance of Optimization and Learning Systems

Benchmarks and test suites are widely used to evaluate optimization and learning systems. The advantage is that these test problems provide an objective means of comparing systems. The potential disadvantage is that systems can become overfitted to work well on benchmarks and therefore that good performance on benchmarks does not generalize to real world problems. The meaning and significance of benchmarks is examined in light of theoretical results such as "No Free Lunch." The "structure" of common benchmarks is also explored

Genetic and Local Search Algorithms as Robust and Simple Optimization Tools

: One of the attractive features of recent metaheuristics is in its robustness and simplicity. To investigate this direction, the single machine scheduling problem is solved by various genetic algorithms (GA) and random multi-start local search algorithms (MLS), using rather simple definitions of neighbors, mutations and crossovers. The results indicate that: (1) the performance of GA is not sensitive about crossovers if implemented with mutations, (2) simple implementation of MLS is usually competitive with (or even better than) GA, (3) GRASP type modification of MLS improves its performance to some extent, and (4) GA combined with local search is quite effective if longer computational time is allowed. Key Words: combinatorial optimization, metaheuristics, genetic algorithm, local search, GRASP, single machine scheduling. 1. Introduction There are numerous combinatorial optimization problems, for which computing exact optimal solutions is computationally intractable, e.g., those known..