Preference driven multi-objective optimization design procedure for industrial controller tuning

Multi-objective optimization design procedures have shown to be a valuable tool for con- trol engineers. These procedures could be used by designers when (1) it is difficult to find a reasonable trade-off for a controller tuning fulfilling several requirements; and (2) if it is worthwhile to analyze design objectives exchange among design alternatives. Despite the usefulness of such methods for describing trade-offs among design alterna- tives (tuning proposals) with the so called Pareto front, for some control problems finding a pertinent set of solutions could be a challenge. That is, some control problems are com- plex in the sense of finding the required trade-off among design objectives. In order to improve the performance of MOOD procedures for such situations, preference handling mechanisms could be used to improve pertinency of solutions in the approximated Pareto front. In this paper an overall MOOD procedure focusing in controller tuning applications using designer s preferences is proposed. In order to validate such procedure, a bench- mark control problem is used and reformulated into a multi-objective problem statement, where different preference handling mechanisms in the optimization process are evalu- ated and compared. The obtained results validate the overall proposal as a potential tool for industrial controller tuning.This work was partially supported by projects TIN2011-28082, ENE2011-25900 from the Spanish Ministry of Economy and Competitiveness. First author gratefully acknowledges the partial support provided by the postdoctoral fellowship BJT-304804/2014-2 from the National Council of Scientific and Technologic Development of Brazil (CNPq) for the development of this work.Reynoso Meza, G.; Sanchís Saez, J.; Blasco Ferragud, FX.; Martínez Iranzo, MA. (2016). Preference driven multi-objective optimization design procedure for industrial controller tuning. Information Sciences. 339:108-131. doi:10.1016/j.ins.2015.12.002S10813133

A study of evolutionary multiobjective algorithms and their application to knapsack and nurse scheduling problems

Evolutionary algorithms (EAs) based on the concept of Pareto dominance seem the most suitable technique for multiobjective optimisation. In multiobjective optimisation, several criteria (usually conflicting) need to be taken into consideration simultaneously to assess a quality of a solution. Instead of finding a single solution, a set of trade-off or compromise solutions that represents a good approximation to the Pareto optimal set is often required. This thesis presents an investigation on evolutionary algorithms within the framework of multiobjective optimisation. This addresses a number of key issues in evolutionary multiobjective optimisation. Also, a new evolutionary multiobjective (EMO) algorithm is proposed. Firstly, this new EMO algorithm is applied to solve the multiple 0/1 knapsack problem (a wellknown benchmark multiobjective combinatorial optimisation problem) producing competitive results when compared to other state-of-the-art MOEAs. Secondly, this thesis also investigates the application of general EMO algorithms to solve real-world nurse scheduling problems. One of the challenges in solving real-world nurse scheduling problems is that these problems are highly constrained and specific-problem heuristics are normally required to handle these constraints. These heuristics have considerable influence on the search which could override the effect that general EMO algorithms could have in the solution process when applied to this type of problems. This thesis outlines a proposal for a general approach to model the nurse scheduling problems without the requirement of problem-specific heuristics so that general EMO algorithms could be applied. This would also help to assess the problems and the performance of general EMO algorithms more fairly

Hypervolume based metaheuristics for multiobjective optimization

The purpose of multiobjective optimization is to find solutions that are optimal regarding several goals. In the branch of vector or Pareto optimization all these goals are considered to be of equal importance, so that compromise solutions that cannot be improved regarding one goal without deteriorating in another are Paretooptimal. A variety of quality measures exist to evaluate approximations of the Paretooptimal set generated by optimizers, wherein the hypervolume is the most significant one, making the hypervolume calculation a core problem of multiobjective optimization. This thesis tackles that challenge by providing a new hypervolume algorithm from computational geometry and analyzing the problem’s computational complexity. Evolutionary multiobjective optimization algorithms (EMOA) are state-of-the-art methods for Pareto optimization, wherein the hypervolume-based algorithms belong to the most powerful ones, among them the popular SMS-EMOA. After its promising capabilities have already been demonstrated in first studies, this thesis is dedicated to deeper understand the underlying optimization process of the SMS-EMOA and similar algorithms, in order to specify their performance characteristics. Theoretical analyses are accomplished as far as possible with established and newly developed tools. Beyond the limitations of rigorous scrutiny, insights are gained via thorough experimental investigation. All considered problems are continuous, whereas the algorithms are as well applicable to discrete problems. More precisely, the following topics are concerned. The process of approaching the Pareto-optimal set of points is characterized by the convergence speed, which is analyzed for a general framework of EA with hypervolume selection on several classes of bi-objective problems. The results are achieved by a newly developed concept of linking single and multiobjective optimization. The optimization on the Pareto front, that is turning the population into a set with maximal hypervolume, is considered separately, focusing on the question under which circumstances the steady-state selection of exchanging only one population member suffices to reach a global optimum. We answer this question for different bi-objective problem classes. In a benchmarking on so-called many-objective problems of more than three objectives, the qualification of the SMS-EMOA is demonstrated in comparison to other EMOA, while also studying their cause of failure. Within the mentioned examinations, the choice of the hypervolume’s reference point receives special consideration by exposing its influence. Beyond the study of the SMS-EMOA with default setup, it is analyzed to what extent the performance can be improved by parameter tuning of the EMOA anent to certain problems, focusing on the influence of variation operators. Lastly, an optimization algorithm based on the gradient of the hypervolume is developed and hybridized with the SMS-EMOA

Rigorous Runtime Analysis of Diversity Optimization with GSEMO on OneMinMax

The evolutionary diversity optimization aims at finding a diverse set of solutions which satisfy some constraint on their fitness. In the context of multi-objective optimization this constraint can require solutions to be Pareto-optimal. In this paper we study how the GSEMO algorithm with additional diversity-enhancing heuristic optimizes a diversity of its population on a bi-objective benchmark problem OneMinMax, for which all solutions are Pareto-optimal. We provide a rigorous runtime analysis of the last step of the optimization, when the algorithm starts with a population with a second-best diversity, and prove that it finds a population with optimal diversity in expected time $O(n^2)$, when the problem size $n$ is odd. For reaching our goal, we analyse the random walk of the population, which reflects the frequency of changes in the population and their outcomes.Comment: The full version of the paper accepted to FOGA 2023 conferenc

An Interactive Simple Indicator-Based Evolutionary Algorithm (I-SIBEA) for Multiobjective Optimization Problems

This paper presents a new preference based interactive evolutionary algorithm (I-SIBEA) for solving multiobjective optimization problems using weighted hypervolume. Here the decision maker iteratively provides her/his preference information in the form of identifying preferred and/or non-preferred solutions from a set of nondominated solutions. This preference information provided by the decision maker is used to assign weights of the weighted hypervolume calculation to solutions in subsequent generations. In any generation, the weighted hypervolume is calculated and solutions are selected to the next generation based on their contribution to the weighted hypervolume. The algorithm is compared with a recently developed interactive evolutionary algorithm, W-Hype on some benchmark multiobjective optimization problems. The results show significant promise in the use of the I-SIBEA algorithm. In addition, the performance of the algorithm is demonstrated using a human decision maker to show its flexibility towards changes in the preference information. The I-SIBEA algorithm is found to flexibly exploit the preference information from the decision maker and generate solutions in the regions preferable to her/him.peerReviewe

Handling expensive multiobjective optimization problems with evolutionary algorithms

Multiobjective optimization problems (MOPs) with a large number of conflicting objectives are often encountered in industry. Moreover, these problem typically involve expensive evaluations (e.g. time consuming simulations or costly experiments), which pose an extra challenge in solving them. In this thesis, we first present a survey of different methods proposed in the literature to handle MOPs with expensive evaluations. We observed that most of the existing methods cannot be easily applied to problems with more than three objectives. Therefore, we propose a Kriging-assisted reference vector guided evolutionary algorithm (K-RVEA) for problems with at least three expensive objectives. The algorithm dynamically balances between convergence and diversity by using reference vectors and uncertainty information from the Kriging models. We demonstrate the practicality of K-RVEA with an air intake ventilation system in a tractor. The problem has three expensive objectives based on time consuming computational fluid dynamics simulations. We also emphasize the challenges of formulating a meaningful optimization problem reflecting the needs of the decision maker (DM) and connecting different pieces of simulation tools. Furthermore, we extend K-RVEA to handle constrained MOPs. We found out that infeasible solutions can play a vital role in the performance of the algorithm. In many real-world MOPs, the DM is usually interested in one or a small set of Pareto optimal solutions based on her/his preferences. Additionally, it has been noticed in practice that sometimes it is easier for the DM to identify non- preferable solutions instead of preferable ones. Therefore, we finally propose an interactive simple indicator-based evolutionary algorithm (I-SIBEA) to incorporate the DM’s preferences in the form of preferable and/or non-preferable solutions. Inspired by the involvement of the DM, we briefly introduce a version of K-RVEA to incorporate the DM’s preferences when using surrogates. By providing efficient algorithms and studies, this thesis will be helpful to practitioners in industry and increases their ability of solving complex real-world MOPs