It is a known fact that the performance of optimization algorithms for NP-Hard problems vary from instance to instance. We observed the same trend when we comprehensively studied multi-objective evolutionary algorithms (MOEAs) on a six benchmark instances of discrete time-cost trade-off problem (DTCTP) in a construction project. In this paper, instead of using a single algorithm to solve DTCTP, we use a portfolio approach that takes multiple algorithms as its constituent. We proposed portfolio comprising of four MOEAs, Non-dominated Sorting Genetic Algorithm II (NSGA-II), the strength Pareto Evolutionary Algorithm II (SPEA-II), Pareto archive evolutionary strategy (PAES) and Niched Pareto Genetic Algorithm II (NPGA-II) to solve DTCTP. The result shows that the portfolio approach is computationally fast and qualitatively superior to its constituent algorithms for all benchmark instances. Moreover, portfolio approach provides an insight in selecting the best algorithm for all benchmark instances of DTCTP.
The content ranking problem in a social news website is typically a function that maximizes a scalar metric like dwell-time. However, in most real-world applications we are interested in more than one metric — for instance, simultaneously maximizing click-through rate, monetization metrics, and dwell-time — while also satisfying the constraints from traffic requirements promised to different publishers. The solution needs to be an online algorithm since the data arrives serially. Additionally, the objective function and the constraints can dynamically change. In this paper, we formulate this problem as a constrained, dynamic, multi-objective optimization problem. We propose a novel framework that extends a successful genetic optimization algorithm, NSGA-II, to solve our ranking problem. We evaluate optimization performance using the Hypervolume metric. We demonstrate the application of our framework on a real-world article ranking problem from the Yahoo! News page. We observe that our proposed solution makes considerable improvements in both time and performance over a brute-force baseline technique that is currently in production.
Bayesian Networks have been widely used in the last decades in many fields, to describe statistical dependencies among random variables. In general, learning the structure of such models is a problem with considerable theoretical interest that still poses many challenges. On the one hand, this is a well-known NP-complete problem, which is practically hardened by the huge search space of possible solutions. On the other hand, the phenomenon of I-equivalence, i.e., different graphical structures underpinning the same set of statistical dependencies, may lead to multimodal fitness landscapes further hindering maximum likelihood approaches to solve the task. Despite all these difficulties, greedy search methods based on a likelihood score coupled with a regularization term to account for model complexity, have been shown to be surprisingly effective in practice. In this paper, we consider the formulation of the task of learning the structure of Bayesian Networks as an optimization problem based on a likelihood score. Nevertheless, our approach do not adjust this score by means of any of the complexity terms proposed in the literature; instead, it accounts directly for the complexity of the discovered solutions by exploiting a multi-objective optimization procedure. To this extent, we adopt NSGA-II and define the first objective function to be the likelihood of a solution and the second to be the number of selected arcs. We thoroughly analyze the behavior of our method on a wide set of simulated data, and we discuss the performance considering the goodness of the inferred solutions both in terms of their objective functions and with respect to the retrieved structure. Our results show that NSGA-II can converge to solutions characterized by better likelihood and less arcs than classic approaches, although paradoxically frequently characterized by a lower similarity to the target network.
Rosales-Pérez, Alejandro (Instituto Nacional de Astrofísica, Óptica y Electrónica) | Escalante, Hugo Jair (Instituto Nacional de Astrofísica, Óptica y Electrónica) | Gonzalez, Jesus A. (Instituto Nacional de Astrofísica, Óptica y Electrónica) | Reyes-Garcia, Carlos A. (Instituto Nacional de Astrofísica, Óptica y Electrónica)
Support vector machines (SVMs) are among the most used methods for pattern recognition. Acceptable results have been obtained with such methods in many domains and applications. However, as most learning algorithms, SVMs have hyperparameters that influence the effectiveness of the generated model. Thus, choosing adequate values for such hyperparameters is critical in order to obtain satisfactory results for a given classification task, a problem known as model selection. This paper introduces a novel model selection approach for SVMs based on multi-objective optimization and on the bias and variance definition. We propose an evolutionary algorithm that aims to select the configuration of hyperparameters that optimizes a trade-off between estimates of bias and variance; two factors that are closely related to the model accuracy and complexity. The proposed technique is evaluated using a suite of benchmark data sets for classification. Experimental results show the validity of our approach. We found that the model selection criteria resulted very helpful for selecting highly effective classification models.
In spite of the recent quick growth of the Evolutionary Multi-objective Optimization (EMO) research field, there has been few trials to adapt the general variation operators to the particular context of the quest for the Pareto-optimal set. The only exceptions are some mating restrictions that take in account the distance between the potential mates - but contradictory conclusions have been reported. This paper introduces a particular mating restriction for Evolutionary Multi-objective Algorithms, based on the Pareto dominance relation: the partner of a non-dominated individual will be preferably chosen among the individuals of the population that it dominates. Coupled with the BLX crossover operator, two different ways of generating offspring are proposed. This recombination scheme is validated within the well-known NSGA-II framework on three bi-objective benchmark problems and one real-world bi-objective constrained optimization problem. An acceleration of the progress of the population toward the Pareto set is observed on all problems.