Computing the set of Epsilon-efficient solutions in multiobjective space mission design

In this work, we consider multiobjective space mission design problems. We will start from the need, from a practical point of view, to consider in addition to the (Pareto) optimal solutions also nearly optimal ones. In fact, extending the set of solutions for a given mission to those nearly optimal significantly increases the number of options for the decision maker and gives a measure of the size of the launch windows corresponding to each optimal solution, i.e., a measure of its robustness. Whereas the possible loss of such approximate solutions compared to optimal—and possibly even ‘better’—ones is dispensable. For this, we will examine several typical problems in space trajectory design—a biimpulsive transfer from the Earth to the asteroid Apophis and two low-thrust multigravity assist transfers—and demonstrate the possible benefit of the novel approach. Further, we will present a multiobjective evolutionary algorithm which is designed for this purpose

Approximate solutions in space mission design

In this paper, we address multi-objective space mission design problems. From a practical point of view, it is often the case that,during the preliminary phase of the design of a space mission, the solutions that are actually considered are not 'optimal' (in the Pareto sense)but belong to the basin of attraction of optimal ones (i.e. they are nearly optimal). This choice is motivated either by additional requirements that the decision maker has to take into account or, more often, by robustness considerations. For this, we suggest a novel MOEA which is a modification of the well-known NSGA-II algorithm equipped with a recently proposed archiving strategy which aims at storing the set of approximate solutions of a given MOP. Using this algorithm we will examine some space trajectory design problems and demonstrate the benefit of the novel approach

The Dynamic Multi-objective Multi-vehicle Covering Tour Problem

This work introduces a new routing problem called the Dynamic Multi-Objective Multi-vehicle Covering Tour Problem (DMOMCTP). The DMOMCTPs is a combinatorial optimization problem that represents the problem of routing multiple vehicles to survey an area in which unpredictable target nodes may appear during execution. The formulation includes multiple objectives that include minimizing the cost of the combined tour cost, minimizing the longest tour cost, minimizing the distance to nodes to be covered and maximizing the distance to hazardous nodes. This study adapts several existing algorithms to the problem with several operator and solution encoding variations. The efficacy of this set of solvers is measured against six problem instances created from existing Traveling Salesman Problem instances which represent several real countries. The results indicate that repair operators, variable length solution encodings and variable-length operators obtain a better approximation of the true Pareto front

Multivariable controller design for the cooling system of a PEM fuel cell by considering nearly optimal solutions in a multi-objective optimization approach

[EN] This paper presents a design for the multivariable control of a cooling system in a PEM (proton exchange membrane) fuel cell stack. This system is complex and challenging enough: interactions between variables, highly nonlinear dynamic behavior, etc. This design is carried out using a multiobjective optimization methodology. There are few previous works that address this problem using multiobjective techniques. Also, this work has, as a novelty, the consideration of, in addition to the optimal controllers, the nearly optimal controllers nondominated in their neighborhood (potentially useful alternatives). In the multiobjective optimization problem approach, the designer must make decisions that include design objectives; parameters of the controllers to be estimated; and the conditions and characteristics of the simulation of the system. However, to simplify the optimization and decision stages, the designer does not include all the desired scenarios in the multiobjective problem definition. Nevertheless, these aspects can be analyzed in the decision stage only for the controllers obtained with a much less computational cost. At this stage, the potentially useful alternatives can play an important role. These controllers have significantly different parameters and therefore allow the designer to make a final decision with additional valuable information. Nearly optimal controllers can obtain an improvement in some aspects not included in the multiobjective optimization problem. For example, in this paper, various aspects are analyzed regarding potentially useful solutions, such as (1) the influence of certain parameters of the simulator; (2) the sample time of the controller; (3) the effect of stack degradation; and (4) the robustness. Therefore, this paper highlights the relevance of this in-depth analysis using the methodology proposed in the design of the multivariable control of the cooling system of a PEM fuel cell. This analysis can modify the final choice of the designer.This study was supported in part by the Ministerio de Ciencia, Innovacion y Universidades (Spain) (grant no. RTI2018-096904-B-I00) and by the Generalitat Valenciana regional government through project AICO/2019/055.Pajares-Ferrando, A.; Blasco, X.; Herrero Durá, JM.; Simarro Fernández, R. (2020). Multivariable controller design for the cooling system of a PEM fuel cell by considering nearly optimal solutions in a multi-objective optimization approach. Complexity. 2020:1-17. https://doi.org/10.1155/2020/8649428S1172020Gunantara, N. (2018). A review of multi-objective optimization: Methods and its applications. Cogent Engineering, 5(1), 1502242. doi:10.1080/23311916.2018.1502242Engau, A., & Wiecek, M. M. (2007). Generating ε-efficient solutions in multiobjective programming. European Journal of Operational Research, 177(3), 1566-1579. doi:10.1016/j.ejor.2005.10.023Loridan, P. (1984). ?-solutions in vector minimization problems. Journal of Optimization Theory and Applications, 43(2), 265-276. doi:10.1007/bf00936165White, D. J. (1986). Epsilon efficiency. Journal of Optimization Theory and Applications, 49(2), 319-337. doi:10.1007/bf00940762Pajares, A., Blasco, X., Herrero, J. M., & Reynoso-Meza, G. (2018). A Multiobjective Genetic Algorithm for the Localization of Optimal and Nearly Optimal Solutions Which Are Potentially Useful: nevMOGA. Complexity, 2018, 1-22. doi:10.1155/2018/1792420Schutze, O., Vasile, M., & Coello, C. A. C. (2011). Computing the Set of Epsilon-Efficient Solutions in Multiobjective Space Mission Design. Journal of Aerospace Computing, Information, and Communication, 8(3), 53-70. doi:10.2514/1.46478Pajares, A., Blasco, X., Herrero, J. M., & Reynoso-Meza, G. (2019). A New Point of View in Multivariable Controller Tuning Under Multiobjective Optimization by Considering Nearly Optimal Solutions. IEEE Access, 7, 66435-66452. doi:10.1109/access.2019.2915556Fredriksson, A., Forsgren, A., & Hårdemark, B. (2011). Minimax optimization for handling range and setup uncertainties in proton therapy. Medical Physics, 38(3), 1672-1684. doi:10.1118/1.3556559Lee, J., & Johnson, G. E. (1993). Optimal tolerance allotment using a genetic algorithm and truncated Monte Carlo simulation. Computer-Aided Design, 25(9), 601-611. doi:10.1016/0010-4485(93)90075-yAndújar, J. M., & Segura, F. (2009). Fuel cells: History and updating. A walk along two centuries. Renewable and Sustainable Energy Reviews, 13(9), 2309-2322. doi:10.1016/j.rser.2009.03.015Mehta, V., & Cooper, J. S. (2003). Review and analysis of PEM fuel cell design and manufacturing. Journal of Power Sources, 114(1), 32-53. doi:10.1016/s0378-7753(02)00542-6De las Heras, A., Vivas, F. J., Segura, F., Redondo, M. J., & Andújar, J. M. (2018). Air-cooled fuel cells: Keys to design and build the oxidant/cooling system. Renewable Energy, 125, 1-20. doi:10.1016/j.renene.2018.02.077Kandlikar, S. G., & Lu, Z. (2009). Thermal management issues in a PEMFC stack – A brief review of current status. Applied Thermal Engineering, 29(7), 1276-1280. doi:10.1016/j.applthermaleng.2008.05.009Yan, Q., Toghiani, H., & Causey, H. (2006). Steady state and dynamic performance of proton exchange membrane fuel cells (PEMFCs) under various operating conditions and load changes. Journal of Power Sources, 161(1), 492-502. doi:10.1016/j.jpowsour.2006.03.077Maghanki, M. M., Ghobadian, B., Najafi, G., & Galogah, R. J. (2013). Micro combined heat and power (MCHP) technologies and applications. Renewable and Sustainable Energy Reviews, 28, 510-524. doi:10.1016/j.rser.2013.07.053Notter, D. A., Kouravelou, K., Karachalios, T., Daletou, M. K., & Haberland, N. T. (2015). Life cycle assessment of PEM FC applications: electric mobility and μ-CHP. Energy & Environmental Science, 8(7), 1969-1985. doi:10.1039/c5ee01082aMartinez, S., Michaux, G., Salagnac, P., & Bouvier, J.-L. (2017). Micro-combined heat and power systems (micro-CHP) based on renewable energy sources. Energy Conversion and Management, 154, 262-285. doi:10.1016/j.enconman.2017.10.035Elmer, T., Worall, M., Wu, S., & Riffat, S. B. (2015). Fuel cell technology for domestic built environment applications: State of-the-art review. Renewable and Sustainable Energy Reviews, 42, 913-931. doi:10.1016/j.rser.2014.10.080Hawkes, A., Staffell, I., Brett, D., & Brandon, N. (2009). Fuel cells for micro-combined heat and power generation. Energy & Environmental Science, 2(7), 729. doi:10.1039/b902222hEllamla, H. R., Staffell, I., Bujlo, P., Pollet, B. G., & Pasupathi, S. (2015). Current status of fuel cell based combined heat and power systems for residential sector. Journal of Power Sources, 293, 312-328. doi:10.1016/j.jpowsour.2015.05.050Strahl, S., & Costa-Castelló, R. (2017). Temperature control of open-cathode PEM fuel cells. IFAC-PapersOnLine, 50(1), 11088-11093. doi:10.1016/j.ifacol.2017.08.2492Zhang, G., & Kandlikar, S. G. (2012). A critical review of cooling techniques in proton exchange membrane fuel cell stacks. International Journal of Hydrogen Energy, 37(3), 2412-2429. doi:10.1016/j.ijhydene.2011.11.010Navarro Gimenez, S., Herrero Dura, J. M., Blasco Ferragud, F. X., & Simarro Fernandez, R. (2019). Control-Oriented Modeling of the Cooling Process of a PEMFC-Based $\mu$ -CHP System. IEEE Access, 7, 95620-95642. doi:10.1109/access.2019.2928632Herrero, J. M., García-Nieto, S., Blasco, X., Romero-García, V., Sánchez-Pérez, J. V., & Garcia-Raffi, L. M. (2008). Optimization of sonic crystal attenuation properties by ev-MOGA multiobjective evolutionary algorithm. Structural and Multidisciplinary Optimization, 39(2), 203-215. doi:10.1007/s00158-008-0323-7Bristol, E. (1966). On a new measure of interaction for multivariable process control. IEEE Transactions on Automatic Control, 11(1), 133-134. doi:10.1109/tac.1966.1098266Blasco, X., Herrero, J. M., Sanchis, J., & Martínez, M. (2008). A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization. Information Sciences, 178(20), 3908-3924. doi:10.1016/j.ins.2008.06.010Schmittinger, W., & Vahidi, A. (2008). A review of the main parameters influencing long-term performance and durability of PEM fuel cells. Journal of Power Sources, 180(1), 1-14. doi:10.1016/j.jpowsour.2008.01.07

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

A PARETO-FRONTIER ANALYSIS OF PERFORMANCE TRENDS FOR SMALL REGIONAL COVERAGE LEO CONSTELLATION SYSTEMS

As satellites become smaller, cheaper, and quicker to manufacture, constellation systems will be an increasingly attractive means of meeting mission objectives. Optimizing satellite constellation geometries is therefore a topic of considerable interest. As constellation systems become more achievable, providing coverage to specific regions of the Earth will become more common place. Small countries or companies that are currently unable to afford large and expensive constellation systems will now, or in the near future, be able to afford their own constellation systems to meet their individual requirements for small coverage regions. The focus of this thesis was to optimize constellation geometries for small coverage regions with the constellation design limited between 1-6 satellites in a Walker-delta configuration, at an altitude of 200-1500km, and to provide remote sensing coverage with a minimum ground elevation angle of 60 degrees. Few Pareto-frontiers have been developed and analyzed to show the tradeoffs among various performance metrics, especially for this type of constellation system. The performance metrics focus on geometric coverage and include revisit time, daily visibility time, constellation altitude, ground elevation angle, and the number of satellites. The objective space containing these performance metrics were characterized for 5 different regions at latitudes of 0, 22.5, 45, 67.5, and 90 degrees. In addition, the effect of minimum ground elevation angle was studied on the achievable performance of this type of constellation system. Finally, the traditional Walker-delta pattern constraint was relaxed to allow for asymmetrical designs. These designs were compared to see how the Walker-delta pattern performs compared to a more relaxed design space. The goal of this thesis was to provide both a framework as well as obtain and analyze Pareto-frontiers for constellation performance relating to small regional coverage LEO constellation systems. This work provided an in-depth analysis of the trends in both the design and objective space of the obtained Pareto-frontiers. A variation on the εNSGA-II algorithm was utilized along with a MATLAB/STK interface to produce these Pareto-frontiers. The εNSGA-II algorithm is an evolutionary algorithm that was developed by Kalyanmoy Deb to solve complex multi-objective optimization problems. The algorithm used in this study proved to be very efficient at obtaining various Pareto-frontiers. This study was also successful in characterizing the design and solution space surrounding small LEO remote sensing constellation systems providing small regional coverage

Explicit Building Block Multiobjective Evolutionary Computation: Methods and Applications

This dissertation presents principles, techniques, and performance of evolutionary computation optimization methods. Concentration is on concepts, design formulation, and prescription for multiobjective problem solving and explicit building block (BB) multiobjective evolutionary algorithms (MOEAs). Current state-of-the-art explicit BB MOEAs are addressed in the innovative design, execution, and testing of a new multiobjective explicit BB MOEA. Evolutionary computation concepts examined are algorithm convergence, population diversity and sizing, genotype and phenotype partitioning, archiving, BB concepts, parallel evolutionary algorithm (EA) models, robustness, visualization of evolutionary process, and performance in terms of effectiveness and efficiency. The main result of this research is the development of a more robust algorithm where MOEA concepts are implicitly employed. Testing shows that the new MOEA can be more effective and efficient than previous state-of-the-art explicit BB MOEAs for selected test suite multiobjective optimization problems (MOPs) and U.S. Air Force applications. Other contributions include the extension of explicit BB definitions to clarify the meanings for good single and multiobjective BBs. A new visualization technique is developed for viewing genotype, phenotype, and the evolutionary process in finding Pareto front vectors while tracking the size of the BBs. The visualization technique is the result of a BB tracing mechanism integrated into the new MOEA that enables one to determine the required BB sizes and assign an approximation epistasis level for solving a particular problem. The culmination of this research is explicit BB state-of-the-art MOEA technology based on the MOEA design, BB classifier type assessment, solution evolution visualization, and insight into MOEA test metric validation and usage as applied to test suite, deception, bioinformatics, unmanned vehicle flight pattern, and digital symbol set design MOPs

Scheduling for Space Tracking and Heterogeneous Sensor Environments

This dissertation draws on the fields of heuristic and meta-heuristic algorithm development, resource allocation problems, and scheduling to address key Air Force problems. The world runs on many schedules. People depend upon them and expect these schedules to be accurate. A process is needed where schedules can be dynamically adjusted to allow tasks to be completed efficiently. For example, the Space Surveillance Network relies on a schedule to track objects in space. The schedule must use sensor resources to track as many high-priority satellites as possible to obtain orbit paths and to warn of collision paths. Any collisions that occurred between satellites and other orbiting material could be catastrophic. To address this critical problem domain, this dissertation introduces both a single objective evolutionary tasker algorithm and a multi-objective evolutionary algorithm approach. The aim of both methods is to produce space object tracking schedules to ensure that higher priority objects are appropriately assessed for potential problems. Simulations show that these evolutionary algorithm techniques effectively create schedules to assure that higher priority space objects are tracked. These algorithms have application to a range of dynamic scheduling domains including space object tracking, disaster search and rescue, and heterogeneous sensor scheduling