Heuristics in permutation GOMEA for solving the permutation flowshop scheduling problem

The recently introduced permutation Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) has shown to be an effective Model Based Evolutionary Algorithm (MBEA) for permutation problems. So far, permutation GOMEA has only been used in the context of Black-Box Optimization (BBO). This paper first shows that permutation GOMEA can be improved by incorporating a constructive heuristic to seed the initial population. Secondly, the paper shows that hybridizing with job swapping neighborhood search does not lead to consistent improvement. The seeded permutation GOMEA is compared to a state-of-the-art algorithm (VNS4) for solving the Permutation Flowshop Scheduling Problem (PFSP). Both unstructured and structured instances are used in the benchmarks. The results show that permutation GOMEA often outperforms the VNS4 algorithm for the PFSP with the total flowtime criterion

On the impact of linkage learning, gene-pool optimal mixing, and non-redundant encoding on permutation optimization

Gene-pool Optimal Mixing Evolutionary Algorithms (GOMEAs) have been shown to achieve state-of-the-art results on various types of optimization problems with various types of problem variables. Recently, a GOMEA for permutation spaces was introduced by leveraging the random keys encoding, obtaining promising first results on permutation flow shop instances. A key cited strength of GOMEAs is linkage learning, i.e., the ability to determine and leverage, during optimization, key dependencies between problem variables. However, the added value of linkage learning was not tested in depth for permutation GOMEA. Here, we introduce a new version of permutation GOMEA, called qGOMEA, that works directly in permutation space, removing the redundancy of using random keys. We additionally consider various linkage information sources, including random noise, in both GOMEA variants, and compare performance with various classic genetic algorithms on a wider range of problems than considered before. We find that, although the benefits of linkage learning are clearly visible for various artificial benchmark problems, this is far less the case for various real-world inspired problems. Finally, we find that qGOMEA performs best, and is more applicable to a wider range of permutation problems

Hybrid linkage learning for permutation optimization with Gene-pool optimal mixing evolutionary algorithms

Linkage learning techniques are employed to discover dependencies between problem variables. This knowledge can then be leveraged in an Evolutionary Algorithm (EA) to improve the optimization process. Of particular interest is the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) family, which has been shown to exploit linkage effectively. Recently, Empirical Linkage Learning (ELL) techniques were proposed for binary-encoded problems. While these techniques are computationally expensive, they have the benefit of never reporting spurious dependencies (false linkages), i.e., marking two independent variables as being dependent. However, previous research shows that despite this property, for some problems, it is more suitable to employ more commonly-used Statistical-based Linkage Learning (SLL) techniques. Therefore, we propose to use both ELL and SLL in the form of Hybrid Linkage Learning (HLL). We also propose (for the first time) a variant of ELL for permutation problems. Using a wide range of problems and different GOMEA variants, we find that also for permutation problems, in some cases, ELL is more advantageous to use while SLL is more advantageous in other cases. However, we also find that employing the proposed HLL leads to results that are better or equal than the results obtained with SLL for all the considered problems

Effective and efficient estimation of distribution algorithms for permutation and scheduling problems.

Estimation of Distribution Algorithm (EDA) is a branch of evolutionary computation that learn a probabilistic model of good solutions. Probabilistic models are used to represent relationships between solution variables which may give useful, human-understandable insights into real-world problems. Also, developing an effective PM has been shown to significantly reduce function evaluations needed to reach good solutions. This is also useful for real-world problems because their representations are often complex needing more computation to arrive at good solutions. In particular, many real-world problems are naturally represented as permutations and have expensive evaluation functions. EDAs can, however, be computationally expensive when models are too complex. There has therefore been much recent work on developing suitable EDAs for permutation representation. EDAs can now produce state-of-the-art performance on some permutation benchmark problems. However, models are still complex and computationally expensive making them hard to apply to real-world problems. This study investigates some limitations of EDAs in solving permutation and scheduling problems. The focus of this thesis is on addressing redundancies in the Random Key representation, preserving diversity in EDA, simplifying the complexity attributed to the use of multiple local improvement procedures and transferring knowledge from solving a benchmark project scheduling problem to a similar real-world problem. In this thesis, we achieve state-of-the-art performance on the Permutation Flowshop Scheduling Problem benchmarks as well as significantly reducing both the computational effort required to build the probabilistic model and the number of function evaluations. We also achieve competitive results on project scheduling benchmarks. Methods adapted for solving a real-world project scheduling problem presents significant improvements

Preventing premature convergence and proving the optimality in evolutionary algorithms

http://ea2013.inria.fr//proceedings.pdfInternational audienceEvolutionary Algorithms (EA) usually carry out an efficient exploration of the search-space, but get often trapped in local minima and do not prove the optimality of the solution. Interval-based techniques, on the other hand, yield a numerical proof of optimality of the solution. However, they may fail to converge within a reasonable time due to their inability to quickly compute a good approximation of the global minimum and their exponential complexity. The contribution of this paper is a hybrid algorithm called Charibde in which a particular EA, Differential Evolution, cooperates with a Branch and Bound algorithm endowed with interval propagation techniques. It prevents premature convergence toward local optima and outperforms both deterministic and stochastic existing approaches. We demonstrate its efficiency on a benchmark of highly multimodal problems, for which we provide previously unknown global minima and certification of optimality

Parameter-less Late Acceptance Hill-climbing: Foundations & Applications.

PhD Theses.Stochastic Local Search (SLS) methods have been used to solve complex hard combinatorial problems in a number of elds. Their judicious use of randomization, arguably, simpli es their design to achieve robust algorithm behaviour in domains where little is known. This feature makes them a general purpose approach for tackling complex problems. However, their performance, usually, depends on a number of parameters that should be speci ed by the user. Most of these parameters are search-algorithm related and have little to do with the user's problem. This thesis presents search techniques for combinatorial problems that have fewer parameters while delivering good anytime performance. Their parameters are set automatically by the algorithm itself in an intelligent way, while making sure that they use the entire given time budget to explore the search space with a high probability of avoiding the stagnation in a single basin of attraction. These algorithms are suitable for general practitioners in industry that do not have deep insight into search methodologies and their parameter tuning. Note that, to all intents and purposes, in realworld search problems the aim is to nd a good enough quality solution in a pre-de ned time. In order to achieve this, we use a technique that was originally introduced for automating population sizing in evolutionary algorithms. In an intelligent way, we adapted it to a particular one-point stochastic local search algorithm, namely Late Acceptance Hill-Climbing (LAHC), to eliminate the need to manually specify the value of the sole parameter of this algorithm. We then develop a mathematically sound dynamic cuto time strategy that is able to reliably detect the stagnation point for these search algorithms. We evaluated the suitability and scalability of the proposed methods on a range of classical combinatorial optimization problems as well as a real-world software engineering proble