A Computational Intelligence Approach to System-of-Systems Architecting Incorporating Multi-Objective Optimization

A computational intelligence approach to system-of-systems architecting is developed using multi-objective optimization. Such an approach yields a set of optimal solutions (the Pareto set) which has both advantages and disadvantages. The primary benefit is that a set of solutions provides a picture of the optimal solution space that a single solution cannot. The primary difficulty is making use of a potentially infinite set of solutions. Therefore, a significant part of this approach is the development of a method to model the solution set with a finite number of points allowing the architect to intelligently choose a subset of optimal solutions based on criteria outside of the given objectives. The approach developed incorporates a meta-architecture, multi-objective genetic algorithm, and a corner search to identify points useful for modeling the solution space. This approach is then applied to a network centric warfare problem seeking the optimum selection of twenty systems. Finally, using the same problem, it is compared to a hybrid approach using single-objective optimization with a fuzzy logic assessor to demonstrate the advantage of multi-objective optimization

Metaheuristic Approaches to Solve a Complex Aircraft Performance Optimization Problem

The increasing demands for travelling comfort and reduction of carbon dioxide emissions have been considered substantially in the stage of conceptual aircraft design. However, the design of a modern aircraft is a multidisciplinary process, which requires the coordination of information from several specific disciplines, such as structures, aerodynamics, control, etc. To address this problem with adequate accuracy, the multidisciplinary analysis and optimization (MAO) method is usually applied as a systematic and robust approach to solve such complex design issues arising from industries. Since MAO method is tedious and computationally expensive, genetic programming (GP)-based metamodeling techniques incorporating MAO are proposed as an effective approach to minimize the wing stiffness of a large aircraft subject to aerodynamic, aeroelastic and stability constraints in the conceptual design phase. Based on the linear small-disturbance theory, the state-space equation is employed for stability analysis. In the process of multidisciplinary analysis, aeroelastic response simulations are performed using Nastran. To construct metamodels representing the responses of the interests with high accuracy as well as less computational burden, optimal Latin hypercube design of experiments (DoE) is applied to determine the optimized distribution of sampling points. Following that, parametric optimization is carried out on metamodels to obtain the optimal wing geometry shape, elastic axis positions and stiffness distribution, and then the solution is verified by finite element simulations. Finally, the superiority of the GP-based metamodel technique over genetic algorithm is demonstrated by multidisciplinary design optimization of a representative beam-frame wing structure in terms of accuracy and efficiency. The results also show that GP metamodel-based strategy for solving MAO problems can provide valuable insights to tailoring parameters for the effective design of a large aircraft in the conceptual phase

Advances and applications in high-dimensional heuristic optimization

“Applicable to most real-world decision scenarios, multiobjective optimization is an area of multicriteria decision-making that seeks to simultaneously optimize two or more conflicting objectives. In contrast to single-objective scenarios, nontrivial multiobjective optimization problems are characterized by a set of Pareto optimal solutions wherein no solution unanimously optimizes all objectives. Evolutionary algorithms have emerged as a standard approach to determine a set of these Pareto optimal solutions, from which a decision-maker can select a vetted alternative. While easy to implement and having demonstrated great efficacy, these evolutionary approaches have been criticized for their runtime complexity when dealing with many alternatives or a high number of objectives, effectively limiting the range of scenarios to which they may be applied. This research introduces mechanisms to improve the runtime complexity of many multiobjective evolutionary algorithms, achieving state-of-the-art performance, as compared to many prominent methods from the literature. Further, the investigations here presented demonstrate the capability of multiobjective evolutionary algorithms in a complex, large-scale optimization scenario. Showcasing the approach’s ability to intelligently generate well-performing solutions to a meaningful optimization problem. These investigations advance the concept of multiobjective evolutionary algorithms by addressing a key limitation and demonstrating their efficacy in a challenging real-world scenario. Through enhanced computational efficiency and exhibited specialized application, the utility of this powerful heuristic strategy is made more robust and evident”--Abstract, page iv

A Random Forest Assisted Evolutionary Algorithm for Data-Driven Constrained Multi-Objective Combinatorial Optimization of Trauma Systems for publication

Many real-world optimization problems can be solved by using the data-driven approach only, simply because no analytic objective functions are available for evaluating candidate solutions. In this work, we address a class of expensive datadriven constrained multi-objective combinatorial optimization problems, where the objectives and constraints can be calculated only on the basis of large amount of data. To solve this class of problems, we propose to use random forests and radial basis function networks as surrogates to approximate both objective and constraint functions. In addition, logistic regression models are introduced to rectify the surrogate-assisted fitness evaluations and a stochastic ranking selection is adopted to further reduce the influences of the approximated constraint functions. Three variants of the proposed algorithm are empirically evaluated on multi-objective knapsack benchmark problems and two realworld trauma system design problems. Experimental results demonstrate that the variant using random forest models as the surrogates are effective and efficient in solving data-driven constrained multi-objective combinatorial optimization problems

Diversity assessment in many-objective optimization

Maintaining diversity is one important aim of multiobjective optimization. However, diversity for many-objective optimization problems is less straightforward to define than for multi-objective optimization problems. Inspired by measures for biodiversity, we propose a new diversity metric for manyobjective optimization, which is an accumulation of the dissimilarity in the population, where an Lp-norm-based (p < 1) distance is adopted to measure the dissimilarity of solutions. Empirical results demonstrate our proposed metric can more accurately assess the diversity of solutions in various situations. We compare the diversity of the solutions obtained by four popular many-objective evolutionary algorithms using the proposed diversity metric on a large number of benchmark problems with two to ten objectives. The behaviors of different diversity maintenance methodologies in those algorithms are discussed in depth based on the experimental results. Finally, we show that the proposed diversity measure can also be employed for enhancing diversity maintenance or reference set generation in many-objective optimization

Corner sort for pareto-based many-objective optimization

Nondominated sorting plays an important role in Pareto-based multiobjective evolutionary algorithms (MOEAs). When faced with many-objective optimization problems multiobjective optimization problems (MOPs) with more than three objectives, the number of comparisons needed in nondominated sorting becomes very large. In view of this, a new corner sort is proposed in this paper. Corner sort first adopts a fast and simple method to obtain a nondominated solution from the corner solutions, and then uses the nondominated solution to ignore the solutions dominated by it to save comparisons. Obtaining the nondominated solutions requires much fewer objective comparisons in corner sort. In order to evaluate its performance, several state-of-the-art nondominated sorts are compared with our corner sort on three kinds of artificial solution sets of MOPs and the solution sets generated from MOEAs on benchmark problems. On one hand, the experiments on artificial solution sets show the performance on the solution sets with different distributions. On the other hand, the experiments on the solution sets generated from MOEAs show the influence that different sorts bring to MOEAs. The results show that corner sort performs well, especially on many-objective optimization problems. Corner sort uses fewer comparisons than others. © 2013 IEEE

Corner Sort for Pareto-Based Many-Objective Optimization

Nondominated sorting plays an important role in Pareto-based multiobjective evolutionary algorithms (MOEAs). When faced with many-objective optimization problems multiobjective optimization problems (MOPs) with more than three objectives, the number of comparisons needed in nondominated sorting becomes very large. In view of this, a new corner sort is proposed in this paper. Corner sort first adopts a fast and simple method to obtain a nondominated solution from the corner solutions, and then uses the nondominated solution to ignore the solutions dominated by it to save comparisons. Obtaining the nondominated solutions requires much fewer objective comparisons in corner sort. In order to evaluate its performance, several state-of-the-art nondominated sorts are compared with our corner sort on three kinds of artificial solution sets of MOPs and the solution sets generated from MOEAs on benchmark problems. On one hand, the experiments on artificial solution sets show the performance on the solution sets with different distributions. On the other hand, the experiments on the solution sets generated from MOEAs show the influence that different sorts bring to MOEAs. The results show that corner sort performs well, especially on many-objective optimization problems. Corner sort uses fewer comparisons than others. © 2013 IEEE