Real-World Airline Crew Pairing Optimization: Customized Genetic Algorithm versus Column Generation Method

Airline crew cost is the second-largest operating cost component and its marginal improvement may translate to millions of dollars annually. Further, it's highly constrained-combinatorial nature brings-in high impact research and commercial value. The airline crew pairing optimization problem (CPOP) is aimed at generating a set of crew pairings, covering all flights from its timetable, with minimum cost, while satisfying multiple legality constraints laid by federations, etc. Depending upon CPOP's scale, several Genetic Algorithm and Column Generation based approaches have been proposed in the literature. However, these approaches have been validated either on small-scale flight datasets (a handful of pairings) or for smaller airlines (operating-in low-demand regions) such as Turkish Airlines, etc. Their search-efficiency gets impaired drastically when scaled to the networks of bigger airlines. The contributions of this paper relate to the proposition of a customized genetic algorithm, with improved initialization and genetic operators, developed by exploiting the domain-knowledge; and its comparison with a column generation based large-scale optimizer (developed by authors). To demonstrate the utility of the above-cited contributions, a real-world test-case (839 flights), provided by GE Aviation, is used which has been extracted from the networks of larger airlines (operating up to 33000 monthly flights in the US).Comment: 7 pages, 3 figure

Objective reduction in many-objective optimization: linear and nonlinear algorithms

The difficulties faced by existing Multi-objective Evolutionary Algorithms (MOEAs) in handling many-objective problems relate to the inefficiency of selection operators, high computational cost and difficulty in visualization of objective space. While many approaches aim to counter these difficulties by increasing the fidelity of the standard selection operators, the objective reduction approach attempts to eliminate objectives that are not essential to describe the Pareto-optimal Front (POF). If the number of essential objectives are found to be two or three, the problem could be solved by the existing MOEAs. It implies that objective reduction could make an otherwise unsolvable (many-objective) problem solvable. Even when the essential objectives are four or more, the reduced representation of the problem will have favorable impact on the search efficiency, computational cost and decision-making. Hence, development of generic and robust objective reduction approaches becomes important. This paper presents a Principal Component Analysis and Maximum Variance Unfolding based framework for linear and nonlinear objective reduction algorithms, respectively. The major contribution of this paper includes: (a) the enhancements in the core components of the framework for higher robustness in terms of-applicability to a range of problems with disparate degree of redundancy; mechanisms to handle an input data that is mis-representative of the true POF; and dependence on fewer parameters to minimize the variability in performance, (b) proposition of an error measure to assess the quality of results, (c) sensitivity analysis of the proposed algorithms for the parameters involved and on the quality of the input data, and (d) study of the performance of the proposed algorithms vis-à-vis dominance relation preservation based algorithms, on a wide range of test problems (scaled up to 50 objectives) and two real-world problems

Non-linear dimensionality reduction procedures for certain large-dimensional multi-objective optimization problems: employing correntropy and a novel maximum variance unfolding

In our recent publication [1], we began with an understanding that many real-world applications of multi-objective optimization involve a large number (10 or more) of objectives but then, existing evolutionary multi-objective optimization (EMO) methods have primarily been applied to problems having smaller number of objectives (5 or less). After highlighting the major impediments in handling large number of objectives, we proposed a principal component analysis (PCA) based EMO procedure, for dimensionality reduction, whose efficacy was demonstrated by solving upto 50-objective optimization problems. Here, we are addressing the fact that, when the data points live on a non-linear manifold or that the data structure is non-gaussian, PCA which yields a smaller dimensional 'linear' subspace may be ineffective in revealing the underlying dimensionality. To overcome this, we propose two new non-linear dimensionality reduction algorithms for evolutionary multi-objective optimization, namely C-PCA-NSGA-II and MVU-PCA-NSGA-II. While the former is based on the newly introduced correntropy PCA [2], the later implements maximum variance unfolding principle [3,4,5] in a novel way. We also establish the superiority of these new EMO procedures over the earlier PCA-based procedure, both in terms of accuracy and computational time, by solving upto 50-objective optimization problems

Machine learning based decision support for many-objective optimization problems

Multiple Criteria Decision-Making (MCDM) based Multi-objective Evolutionary Algorithms (MOEAs) are increasingly becoming popular for dealing with optimization problems with more than three objectives, commonly termed as many-objective optimization problems (MaOPs). These algorithms elicit preferences from a single or multiple Decision Makers (DMs), a priori or interactively, to guide the search towards the solutions most preferred by the DM(s), as against the whole Pareto-optimal Front (POF). Despite its promise for dealing with MaOPs, the utility of this approach is impaired by the lack of- objectivity; repeatability; consistency; and coherence in DM's preferences. This paper proposes a machine learning based framework to counter the above limitations. Towards it, the preference-structure of the different objectives embedded in the problem model is learnt in terms of: a smallest set of conflicting objectives which can generate the same POF as the original problem; the smallest objective sets corresponding to pre-specified errors; and the objective sets of pre-specified sizes that correspond to minimum error. While the focus is on demonstrating how the proposed framework could serve as a decision support for the DM, its performance is also studied vis-à-vis an alternative approach (based on dominance relation preservation), for a wide range of test problems and a real-world problem. The results mark a new direction for MCDM based MOEAs for MaOPs. © 2014 Elsevier B.V

Entropy-Based Termination Criterion for Multiobjective Evolutionary Algorithms

Multiobjective evolutionary algorithms evolve a population of solutions through successive generations toward the Pareto-optimal front (POF). One of the most critical questions faced by the researchers and practitioners in this domain relates to the number of generations that may be sufficient for an algorithm to offer a good approximation of the POF for a given problem. Ironically, to date, this question largely remains unanswered and the number of generations are arbitrarily fixed a priori, with potentially punitive implications. If the a priori fixed generations are insufficient, then the algorithm reports suboptimal solutions. In contrast, if the a priori fixed generations are far too many, it implies waste of computational resources. This paper proposes a novel entropy-based dissimilarity measure that helps identify on the fly the number of generations beyond which an algorithm stabilizes, implying that either a good approximation has been obtained or that it cannot be obtained due to the stagnation of the algorithm in the search space. Given that in either case no further improvement in the approximation can be obtained, despite additional computational expense, the proposed dissimilarity measure provides a termination criterion and facilitates a termination detection algorithm. The generality, on-the-fly implementation, low-computational complexity, and the demonstrated efficacy of the proposed termination detection algorithm, on a wide range of multiobjective and many-objective test problems, define the novel contribution of this paper