Toward an estimation of nadir objective vector using a hybrid of evolutionary and local search approaches

A nadir objective vector is constructed from the worst Pareto-optimal objective values in a multiobjective optimization problem and is an important entity to compute because of its significance in estimating the range of objective values in the Pareto-optimal front and also in executing a number of interactive multiobjective optimization techniques. Along with the ideal objective vector, it is also needed for the purpose of normalizing different objectives, so as to facilitate a comparison and agglomeration of the objectives. However, the task of estimating the nadir objective vector necessitates information about the complete Pareto-optimal front and has been reported to be a difficult task, and importantly an unsolved and open research issue. In this paper, we propose certain modifications to an existing evolutionary multiobjective optimization procedure to focus its search toward the extreme objective values and combine it with a reference-point based local search approach to constitute a couple of hybrid procedures for a reliable estimation of the nadir objective vector. With up to 20-objective optimization test problems and on a three-objective engineering design optimization problem, one of the proposed procedures is found to be capable of finding the nadir objective vector reliably. The study clearly shows the significance of an evolutionary computing based search procedure in assisting to solve an age-old important task in the field of multiobjective optimization

A solution to bi/tri-level programming problems using particle swarm optimization

© 2016 Elsevier Inc. Multilevel (including bi-level and tri-level) programming aims to solve decentralized decision-making problems that feature interactive decision entities distributed throughout a hierarchical organization. Since the multilevel programming problem is strongly NP-hard and traditional exact algorithmic approaches lack efficiency, heuristics-based particle swarm optimization (PSO) algorithms have been used to generate an alternative for solving such problems. However, the existing PSO algorithms are limited to solving linear or small-scale bi-level programming problems. This paper first develops a novel bi-level PSO algorithm to solve general bi-level programs involving nonlinear and large-scale problems. It then proposes a tri-level PSO algorithm for handling tri-level programming problems that are more challenging than bi-level programs and have not been well solved by existing algorithms. For the sake of exploring the algorithms' performance, the proposed bi/tri-level PSO algorithms are applied to solve 62 benchmark problems and 810 large-scale problems which are randomly constructed. The computational results and comparison with other algorithms clearly illustrate the effectiveness of the proposed PSO algorithms in solving bi-level and tri-level programming problems

Evolutionary neural architecture search for deep learning

Deep neural networks (DNNs) have produced state-of-the-art results in many benchmarks and problem domains. However, the success of DNNs depends on the proper configuration of its architecture and hyperparameters. DNNs are often not used to their full potential because it is difficult to determine what architectures and hyperparameters should be used. While several approaches have been proposed, computational complexity of searching large design spaces makes them impractical for large modern DNNs. This dissertation introduces an efficient evolutionary algorithm (EA) for simultaneous optimization of DNN architecture and hyperparameters. It builds upon extensive past research of evolutionary optimization of neural network structure. Various improvements to the core algorithm are introduced, including: (1) discovering DNN architectures of arbitrary complexity; (1) generating modular, repetitive modules commonly seen in state-of-the-art DNNs; (3) extending to the multitask learning and multiobjective optimization domains; (4) maximizing performance and reducing wasted computation through asynchronous evaluations. Experimental results in image classification, image captioning, and multialphabet character recognition show that the approach is able to evolve networks that are competitive with or even exceed hand-designed networks. Thus, the method enables an automated and streamlined process to optimize DNN architectures for a given problem and can be widely applied to solve harder tasks.Computer Science

Canonical duality theory and algorithm for solving bilevel knapsack problems with applications

A novel canonical duality theory (CDT) is presented for solving general bilevel mixed integer nonlinear optimization governed by linear and quadratic knapsack problems. It shows that the challenging knapsack problems can be solved analytically in term of their canonical dual solutions. The existence and uniqueness of these analytical solutions are proved. NP-hardness of the knapsack problems is discussed. A powerful CDT algorithm combined with an alternative iteration and a volume reduction method is proposed for solving the NP-hard bilevel knapsack problems. Application is illustrated by benchmark problems in optimal topology design. The performance and novelty of the proposed method are compared with the popular commercial codes. © 2013 IEEE