A survey of diversity-oriented optimization

The concept of diversity plays a crucial role in many optimization approaches: On the one hand, diversity can be formulated as an essential goal, such as in level set approximation or multiobjective optimization where the aim is to find a diverse set of alternative feasible or, respectively, Pareto optimal solutions. On the other hand, diversity maintenance can play an important role in algorithms that ultimately searc

A Comparison of Archiving Strategies for Characterization of Nearly Optimal Solutions under Multi-Objective Optimization

[EN] In a multi-objective optimization problem, in addition to optimal solutions, multimodal and/or nearly optimal alternatives can also provide additional useful information for the decision maker. However, obtaining all nearly optimal solutions entails an excessive number of alternatives. Therefore, to consider the nearly optimal solutions, it is convenient to obtain a reduced set, putting the focus on the potentially useful alternatives. These solutions are the alternatives that are close to the optimal solutions in objective space, but which differ significantly in the decision space. To characterize this set, it is essential to simultaneously analyze the decision and objective spaces. One of the crucial points in an evolutionary multi-objective optimization algorithm is the archiving strategy. This is in charge of keeping the solution set, called the archive, updated during the optimization process. The motivation of this work is to analyze the three existing archiving strategies proposed in the literature (ArchiveUpdateP(Q,epsilon)D(xy), Archive_nevMOGA, and targetSelect) that aim to characterize the potentially useful solutions. The archivers are evaluated on two benchmarks and in a real engineering example. The contribution clearly shows the main differences between the three archivers. This analysis is useful for the design of evolutionary algorithms that consider nearly optimal solutions.This work was supported in part by the Ministerio de Ciencia, Innovacion y Universidades (Spain) (grant number RTI2018-096904-B-I00), by the Generalitat Valenciana regional government through project AICO/2019/055 and by the Universitat Politecnica de Valencia (grant number SP20200109).Pajares-Ferrando, A.; Blasco, X.; Herrero Durá, JM.; Martínez Iranzo, MA. (2021). A Comparison of Archiving Strategies for Characterization of Nearly Optimal Solutions under Multi-Objective Optimization. Mathematics. 9(9):1-28. https://doi.org/10.3390/math9090999S1289

Methods to Support the Project Selection Problem With Non-Linear Portfolio Objectives, Time Sensitive Objectives, Time Sensitive Resource Constraints, and Modeling Inadequacies

The United States Air Force relies upon information production activities to gain insight regarding uncertainties affecting important system configuration and in-mission task execution decisions. Constrained resources that prevent the fulfillment of every information production request, multiple information requestors holding different temporal-sensitive objectives, non-constant marginal value preferences, and information-product aging factors that affect the value-of-information complicate the management of these activities. This dissertation reviews project selection research related to these issues and presents novel methods to address these complications. Quantitative experimentation results demonstrate these methods’ significance

Guiding evolutionary search towards innovative solutions

The main goal of this work is to develop a method that, operating on top of an Evolutionary Algorithm, increases its likeliness of finding innovative solutions. This likeliness is laid out to be increased with the diversity of the solutions found, provided that they are of sufficient quality. The developed method needs to be applicable in a scenario in which the search is required to be started from a single, fixed solution. Therefore, a scheme is envisioned in which the search is performed in a sequential fashion, zooming in on a locally-optimal solution, and then exploring for a new potentially high-quality region based on a memory of solutions encountered earlier in the search. Two exploration criteria, one using an archive of earlier solutions as memory and the other deriving from a surrogate model trained on earlier solutions, were established to be worthwhile for integration into quality-based search. The resulting schemes were applied to a real-world airfoil optimization task, showing both to perform better than the baseline method of multiple standard optimization runs. The model-based approach delivers the best results, in the sense that it finds more solutions, more diverse solutions, and better-quality solutions than the baseline method.Honda Research Institute Europe (HRI-EU)Algorithms and the Foundations of Software technolog

Evolutionary Algorithms in Engineering Design Optimization

Evolutionary algorithms (EAs) are population-based global optimizers, which, due to their characteristics, have allowed us to solve, in a straightforward way, many real world optimization problems in the last three decades, particularly in engineering fields. Their main advantages are the following: they do not require any requisite to the objective/fitness evaluation function (continuity, derivability, convexity, etc.); they are not limited by the appearance of discrete and/or mixed variables or by the requirement of uncertainty quantification in the search. Moreover, they can deal with more than one objective function simultaneously through the use of evolutionary multi-objective optimization algorithms. This set of advantages, and the continuously increased computing capability of modern computers, has enhanced their application in research and industry. From the application point of view, in this Special Issue, all engineering fields are welcomed, such as aerospace and aeronautical, biomedical, civil, chemical and materials science, electronic and telecommunications, energy and electrical, manufacturing, logistics and transportation, mechanical, naval architecture, reliability, robotics, structural, etc. Within the EA field, the integration of innovative and improvement aspects in the algorithms for solving real world engineering design problems, in the abovementioned application fields, are welcomed and encouraged, such as the following: parallel EAs, surrogate modelling, hybridization with other optimization techniques, multi-objective and many-objective optimization, etc

Improving evolutionary algorithms by MEANS of an adaptive parameter control approach

Evolutionary algorithms (EA) constitute a class of optimization methods that is widely used to solve complex scientific problems. However, EA often converge prematurely over suboptimal solutions, the evolution process is computational expensive, and setting the required EA parameters is quite difficult. We believe that the best way to address these problems is to begin by improving the parameter setting strategy, which will in turn improve the search path of the optimizer, and, we hope, ultimately help prevent premature convergence and relieve the computational burden. The strategy that will achieve this outcome, and the one we adopt in this research, is to ensure that the parameter setting approach takes into account the search path and attempts to drive it in the most advantageous direction. Our objective is therefore to develop an adaptive parameter setting approach capable of controlling all the EA parameters at once. To interpret the search path, we propose to incorporate the concept of exploration and exploitation into the feedback indicator. The first step is to review and study the available genotypic diversity measurements used to characterize the exploration of the optimizer over the search space. We do this by implementing a specifically designed benchmark, and propose three diversity requirements for evaluating the meaningfulness of those measures as population diversity estimators. Results show that none of the published formulations is, in fact, a qualified diversity descriptor. To remedy this, we introduce a new genotypic formulation here, the performance analysis of which shows that it produces better results overall, notwithstanding some serious defects. We initiate a similar study aimed at describing the role of exploitation in the search process, which is to indicate promising regions. However, since exploitation is mainly driven by the individuals’ fitness, we turn our attention toward phenotypic convergence measures. Again, the in-depth analysis reveals that none of the published phenotypic descriptors is capable of portraying the fitness distribution of a population. Consequently, a new phenotypic formulation is developed here, which shows perfect agreement with the expected population behavior. On the strength of these achievements, we devise an optimizer diagnostic tool based on the new genotypic and phenotypic formulations, and illustrate its value by comparing the impacts of various EA parameters. Although the main purpose of this development is to explore the relevance of using both a genotypic and a phenotypic measure to characterize the search process, our diagnostic tool proves to be one of the few tools available to practitioners for interpreting and customizing the way in which optimizers work over real-world problems. With the knowledge gained in our research, the objective of this thesis is finally met, with the proposal of a new adaptive parameter control approach. The system is based on a Bayesian network that enables all the EA parameters to be considered at once. To the authors’ knowledge, this is the first parameter setting proposal devised to do so. The genotypic and phenotypic measures developed are combined in the form of a credit assignment scheme for rewarding parameters by, among other things, promoting maximization of both exploration and exploitation. The proposed adaptive system is evaluated over a recognized benchmark (CEC’05) through the use of a steady-state genetic algorithm (SSGA), and then compared with seven other approaches, like FAUC-RMAB and G-CMA-ES, which are state-of-the-art adaptive methods. Overall, the results demonstrate statistically that the new proposal not only performs as well as G-CMA-ES, but outperforms almost all the other adaptive systems. Nonetheless, this investigation revealed that none of the methods tested is able to locate global optimum over complex multimodal problems. This led us to conclude that synergy and complementarity among the parameters involved is probably missing. Consequently, more research on these topics is advised, with a view to devising enhanced optimizers. We provide numerous recommendations for such research at the end of this thesis