Evolutionary Multiobjective Optimization including Practically Desirable Solutions

In many practical situations the decision-maker has to pay special attention to decision space to determine the constructability of a potential solution, in addition to its optimality in objective space. Practically desirable solutions are those around preferred values in decision space and within a distance from optimality. This work investigates two methods to find simultaneously optimal and practically desirable solutions. The methods expand the objective space by adding fitness functions that favor preferred values for some variables. In addition, the methods incorporate a ranking mechanism that takes into account Pareto dominance in objective space and desirability in decision space. One method searches with one population in the expanded space, whereas the other one uses two populations to search concurrently in the original and expanded space. Our experimental results on benchmark and real world problems show that the proposed method can effectively find optimal and practically desirable solutions

Fidelity Between Unitary Operators and the Generation of Gates Robust Against Off-Resonance Perturbations

We perform a functional expansion of the fidelity between two unitary matrices in order to find the necessary conditions for the robust implementation of a target gate. Comparison of these conditions with those obtained from the Magnus expansion and Dyson series shows that they are equivalent in first order. By exploiting techniques from robust design optimization, we account for issues of experimental feasibility by introducing an additional criterion to the search for control pulses. This search is accomplished by exploring the competition between the multiple objectives in the implementation of the NOT gate by means of evolutionary multi-objective optimization

Multi-Objective Archiving

Most multi-objective optimisation algorithms maintain an archive explicitly or implicitly during their search. Such an archive can be solely used to store high-quality solutions presented to the decision maker, but in many cases may participate in the search process (e.g., as the population in evolutionary computation). Over the last two decades, archiving, the process of comparing new solutions with previous ones and deciding how to update the archive/population, stands as an important issue in evolutionary multi-objective optimisation (EMO). This is evidenced by constant efforts from the community on developing various effective archiving methods, ranging from conventional Pareto-based methods to more recent indicator-based and decomposition-based ones. However, the focus of these efforts is on empirical performance comparison in terms of specific quality indicators; there is lack of systematic study of archiving methods from a general theoretical perspective. In this paper, we attempt to conduct a systematic overview of multi-objective archiving, in the hope of paving the way to understand archiving algorithms from a holistic perspective of theory and practice, and more importantly providing a guidance on how to design theoretically desirable and practically useful archiving algorithms. In doing so, we also present that archiving algorithms based on weakly Pareto compliant indicators (e.g., epsilon-indicator), as long as designed properly, can achieve the same theoretical desirables as archivers based on Pareto compliant indicators (e.g., hypervolume indicator). Such desirables include the property limit-optimal, the limit form of the possible optimal property that a bounded archiving algorithm can have with respect to the most general form of superiority between solution sets.Comment: 21 pages, 4 figures, journa

Clustering Solutions of Multiobjective Function Inlining Problem

Hard real time-systems are often small devices operating on batteries that must react within a given deadline, so they must satisfy their timing, code size, and energy consumption requirements. Since these three objectives contradict each other, compilers for real-time systems go towards multiobjective optimizations which result in sets of trade-off solutions. A system designer can use the solution sets to choose the most suitable system configuration. Evolutionary algorithms can find trade-off solutions but the solution set might be large which complicates the task of the system designer. We propose to divide the solution set into clusters, so the system designer chooses the most suitable cluster and examines a smaller subset in detail. In contrast to other clustering techniques, our method guarantees that the sizes of all clusters are less than a predefined limit. Our method clusters a set by using any existing clustering method, divides clusters with sizes exceeding the predefined size into smaller clusters, and reduces the number of clusters by merging small clusters. The method guarantees that the final clusters satisfy the size constraint. We demonstrate our approach by considering a well-known compiler-based optimization called function inlining. It substitutes function calls by the function bodies which decreases the execution time and energy consumption of a program but increases its code size

A Simple Proposal for Including Designer Preferences in Multi-Objective Optimization Problems

[EN] Including designer preferences in every phase of the resolution of a multi-objective optimization problem is a fundamental issue to achieve a good quality in the final solution. To consider preferences, the proposal of this paper is based on the definition of what we call a preference basis that shows the preferred optimization directions in the objective space. Associated to this preference basis a new basis in the objective space-dominance basis-is computed. With this new basis the meaning of dominance is reinterpreted to include the designer's preferences. In this paper, we show the effect of changing the geometric properties of the underlying structure of the Euclidean objective space by including preferences. This way of incorporating preferences is very simple and can be used in two ways: by redefining the optimization problem and/or in the decision-making phase. The approach can be used with any multi-objective optimization algorithm. An advantage of including preferences in the optimization process is that the solutions obtained are focused on the region of interest to the designer and the number of solutions is reduced, which facilitates the interpretation and analysis of the results. The article shows an example of the use of the preference basis and its associated dominance basis in the reformulation of the optimization problem, as well as in the decision-making phase.This work has been supported by the Ministerio de Ciencia, Innovacion y Universidades, Spain, under Grant RTI2018-096904-B-I00.Blasco, X.; Reynoso Meza, G.; Sánchez Pérez, EA.; Sánchez Pérez, JV.; Jonard Pérez, N. (2021). A Simple Proposal for Including Designer Preferences in Multi-Objective Optimization Problems. Mathematics. 9(9):1-19. https://doi.org/10.3390/math90909911199

A Multi-Stage Supply Chain Network Optimization Using Genetic Algorithms

In today's global business market place, individual firms no longer compete as independent entities with unique brand names but as integral part of supply chain links. Key to success of any business is satisfying customer's demands on time which may result in cost reductions and increase in service level. In supply chain networks decisions are made with uncertainty about product's demands, costs, prices, lead times, quality in a competitive and collaborative environment. If poor decisions are made, they may lead to excess inventories that are costly or to insufficient inventory that cannot meet customer's demands. In this work we developed a bi-objective model that minimizes system wide costs of the supply chain and delays on delivery of products to distribution centers for a three echelon supply chain. Picking a set of Pareto front for multi-objective optimization problems require robust and efficient methods that can search an entire space. We used evolutionary algorithms to find the set of Pareto fronts which have proved to be effective in finding the entire set of Pareto fronts.Comment: 12 pages, 4 figure

Water network design using a multiobjective real options framework

This is the final version of the article. Available from the publisher via the DOI in this record.Water distribution networks (WDNs) are an essential element of urban infrastructure. To achieve a good level of performance, the traditional design of WDNs based on expected future conditions should be replaced by a flexible design, using real options (ROs), that accounts for uncertainty by taking a broader view of possible future options. This work proposes a multiobjective ROs framework that sets out to reduce costs, minimize hydraulic pressure deficiency, and a third objective for minimizing carbon emissions. A multiobjective simulated annealing algorithm is used to identify the Pareto-optimal solutions, thus enabling a tradeoff analysis between solutions. These trade-offs show that a low pressure deficit solution is achieved by increasing investment at a much faster rate after a certain pressure deficit threshold (60 m). Also, the pressure deficits can only be reduced by increasing carbon emissions. Finally, this work also emphasizes the importance of including carbon emissions as a specific objective by comparing the results of the proposed model and another one that did not cover the environmental objective. The results show that it is possible to reduce CO2 for the same level of capital expenditure or the same level of network pressure deficits if carbon emissions are minimized in the optimization process.This study had the support of Fundac¸ao para a Ci ˜ encia e ˆ Tecnologia (FCT), through the Strategic Project UID/MAR/ 04292/2013 granted to MARE