Reference point approaches in Stochastic Multiobjective Programming.

A new interactive method is proposed for a class of stochastic multiobjective problems, where only the objective functions are random. Several solutions can be generated by this new method, making use of the same preferential information, using the different achievement scalarizing functions.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

On multiobjective optimization from the nonsmooth perspective

Practical applications usually have multiobjective nature rather than having only one objective to optimize. A multiobjective problem cannot be solved with a single-objective solver as such. On the other hand, optimization of only one objective may lead to an arbitrary bad solutions with respect to other objectives. Therefore, special techniques for multiobjective optimization are vital. In addition to multiobjective nature, many real-life problems have nonsmooth (i.e. not continuously differentiable) structure. Unfortunately, many smooth (i.e. continuously differentiable) methods adopt gradient-based information which cannot be used for nonsmooth problems. Since both of these characteristics are relevant for applications, we focus here on nonsmooth multiobjective optimization. As a research topic, nonsmooth multiobjective optimization has gained only limited attraction while the fields of nonsmooth single-objective and smooth multiobjective optimization distinctively have attained greater interest. This dissertation covers parts of nonsmooth multiobjective optimization in terms of theory, methodology and application. Bundle methods are widely considered as effective and reliable solvers for single-objective nonsmooth optimization. Therefore, we investigate the use of the bundle idea in the multiobjective framework with three different methods. The first one generalizes the single-objective proximal bundle method for the nonconvex multiobjective constrained problem. The second method adopts the ideas from the classical steepest descent method into the convex unconstrained multiobjective case. The third method is designed for multiobjective problems with constraints where both the objectives and constraints can be represented as a difference of convex (DC) functions. Beside the bundle idea, all three methods are descent, meaning that they produce better values for each objective at each iteration. Furthermore, all of them utilize the improvement function either directly or indirectly. A notable fact is that none of these methods use scalarization in the traditional sense. With the scalarization we refer to the techniques transforming a multiobjective problem into the single-objective one. As the scalarization plays an important role in multiobjective optimization, we present one special family of achievement scalarizing functions as a representative of this category. In general, the achievement scalarizing functions suit well in the interactive framework. Thus, we propose the interactive method using our special family of achievement scalarizing functions. In addition, this method utilizes the above mentioned descent methods as tools to illustrate the range of optimal solutions. Finally, this interactive method is used to solve the practical case studies of the scheduling the final disposal of the spent nuclear fuel in Finland.Käytännön optimointisovellukset ovat usein luonteeltaan ennemmin moni- kuin yksitavoitteisia. Erityisesti monitavoitteisille tehtäville suunnitellut menetelmät ovat tarpeen, sillä monitavoitteista optimointitehtävää ei sellaisenaan pysty ratkaisemaan yksitavoitteisilla menetelmillä eikä vain yhden tavoitteen optimointi välttämättä tuota mielekästä ratkaisua muiden tavoitteiden suhteen. Monitavoitteisuuden lisäksi useat käytännön tehtävät ovat myös epäsileitä siten, etteivät niissä esiintyvät kohde- ja rajoitefunktiot välttämättä ole kaikkialla jatkuvasti differentioituvia. Kuitenkin monet optimointimenetelmät hyödyntävät gradienttiin pohjautuvaa tietoa, jota ei epäsileille funktioille ole saatavissa. Näiden molempien ominaisuuksien ollessa keskeisiä sovelluksia ajatellen, keskitytään tässä työssä epäsileään monitavoiteoptimointiin. Tutkimusalana epäsileä monitavoiteoptimointi on saanut vain vähän huomiota osakseen, vaikka sekä sileä monitavoiteoptimointi että yksitavoitteinen epäsileä optimointi erikseen ovat aktiivisia tutkimusaloja. Tässä työssä epäsileää monitavoiteoptimointia on käsitelty niin teorian, menetelmien kuin käytännön sovelluksien kannalta. Kimppumenetelmiä pidetään yleisesti tehokkaina ja luotettavina menetelminä epäsileän optimointitehtävän ratkaisemiseen ja siksi tätä ajatusta hyödynnetään myös tässä väitöskirjassa kolmessa eri menetelmässä. Ensimmäinen näistä yleistää yksitavoitteisen proksimaalisen kimppumenetelmän epäkonveksille monitavoitteiselle rajoitteiselle tehtävälle sopivaksi. Toinen menetelmä hyödyntää klassisen nopeimman laskeutumisen menetelmän ideaa konveksille rajoitteettomalle tehtävälle. Kolmas menetelmä on suunniteltu erityisesti monitavoitteisille rajoitteisille tehtäville, joiden kohde- ja rajoitefunktiot voidaan ilmaista kahden konveksin funktion erotuksena. Kimppuajatuksen lisäksi kaikki kolme menetelmää ovat laskevia eli ne tuottavat joka kierroksella paremman arvon jokaiselle tavoitteelle. Yhteistä on myös se, että nämä kaikki hyödyntävät parannusfunktiota joko suoraan sellaisenaan tai epäsuorasti. Huomattavaa on, ettei yksikään näistä menetelmistä hyödynnä skalarisointia perinteisessä merkityksessään. Skalarisoinnilla viitataan menetelmiin, joissa usean tavoitteen tehtävä on muutettu sopivaksi yksitavoitteiseksi tehtäväksi. Monitavoiteoptimointimenetelmien joukossa skalarisoinnilla on vankka jalansija. Esimerkkinä skalarisoinnista tässä työssä esitellään yksi saavuttavien skalarisointifunktioiden perhe. Yleisesti saavuttavat skalarisointifunktiot soveltuvat hyvin interaktiivisten menetelmien rakennuspalikoiksi. Täten kuvaillaan myös esiteltyä skalarisointifunktioiden perhettä hyödyntävä interaktiivinen menetelmä, joka lisäksi hyödyntää laskevia menetelmiä optimaalisten ratkaisujen havainnollistamisen apuna. Lopuksi tätä interaktiivista menetelmää käytetään aikatauluttamaan käytetyn ydinpolttoaineen loppusijoitusta Suomessa

Contributions to Methodology and Techniques of Decision Analysis (First Stage)

This collaborative volume reports on the results of a contracted study agreement between the System and Decision Analysis Program and its project on the Methodology of Decision Analysis at IIASA and a group of Polish institutes working in this area. The study includes research in four directions: mathematical programming techniques for decision support; applications of decision support systems new methodological developments in decision support; dissemination of results; and educational activities

Qualitative Characteristics and Quantitative Measures of Solution's Reliability in Discrete Optimization: Traditional Analytical Approaches, Innovative Computational Methods and Applicability

The purpose of this thesis is twofold. The first and major part is devoted to sensitivity analysis of various discrete optimization problems while the second part addresses methods applied for calculating measures of solution stability and solving multicriteria discrete optimization problems. Despite numerous approaches to stability analysis of discrete optimization problems two major directions can be single out: quantitative and qualitative. Qualitative sensitivity analysis is conducted for multicriteria discrete optimization problems with minisum, minimax and minimin partial criteria. The main results obtained here are necessary and sufficient conditions for different stability types of optimal solutions (or a set of optimal solutions) of the considered problems. Within the framework of quantitative direction various measures of solution stability are investigated. A formula for a quantitative characteristic called stability radius is obtained for the generalized equilibrium situation invariant to changes of game parameters in the case of the H¨older metric. Quality of the problem solution can also be described in terms of robustness analysis. In this work the concepts of accuracy and robustness tolerances are presented for a strategic game with a finite number of players where initial coefficients (costs) of linear payoff functions are subject to perturbations. Investigation of stability radius also aims to devise methods for its calculation. A new metaheuristic approach is derived for calculation of stability radius of an optimal solution to the shortest path problem. The main advantage of the developed method is that it can be potentially applicable for calculating stability radii of NP-hard problems. The last chapter of the thesis focuses on deriving innovative methods based on interactive optimization approach for solving multicriteria combinatorial optimization problems. The key idea of the proposed approach is to utilize a parameterized achievement scalarizing function for solution calculation and to direct interactive procedure by changing weighting coefficients of this function. In order to illustrate the introduced ideas a decision making process is simulated for three objective median location problem. The concepts, models, and ideas collected and analyzed in this thesis create a good and relevant grounds for developing more complicated and integrated models of postoptimal analysis and solving the most computationally challenging problems related to it.Siirretty Doriast

Multi-Criteria Performance Evaluation and Control in Power and Energy Systems

The role of intuition and human preferences are often overlooked in autonomous control of power and energy systems. However, the growing operational diversity of many systems such as microgrids, electric/hybrid-electric vehicles and maritime vessels has created a need for more flexible control and optimization methods. In order to develop such flexible control methods, the role of human decision makers and their desired performance metrics must be studied in power and energy systems. This dissertation investigates the concept of multi-criteria decision making as a gateway to integrate human decision makers and their opinions into complex mathematical control laws. There are two major steps this research takes to algorithmically integrate human preferences into control environments: MetaMetric (MM) performance benchmark: considering the interrelations of mathematical and psychological convergence, and the potential conflict of opinion between the control designer and end-user, a novel holistic performance benchmark, denoted as MM, is developed to evaluate control performance in real-time. MM uses sensor measurements and implicit human opinions to construct a unique criterion that benchmarks the system\u27s performance characteristics. MM decision support system (DSS): the concept of MM is incorporated into multi-objective evolutionary optimization algorithms as their DSS. The DSS\u27s role is to guide and sort the optimization decisions such that they reflect the best outcome desired by the human decision-maker and mathematical considerations. A diverse set of case studies including a ship power system, a terrestrial power system, and a vehicular traction system are used to validate the approaches proposed in this work. Additionally, the MM DSS is designed in a modular way such that it is not specific to any underlying evolutionary optimization algorithm

Evolutionary Algorithms for

Many real-world problems involve two types of problem difficulty: i) multiple, conflicting objectives and ii) a highly complex search space. On the one hand, instead of a single optimal solution competing goals give rise to a set of compromise solutions, generally denoted as Pareto-optimal. In the absence of preference information, none of the corresponding trade-offs can be said to be better than the others. On the other hand, the search space can be too large and too complex to be solved by exact methods. Thus, efficient optimization strategies are required that are able to deal with both difficulties. Evolutionary algorithms possess several characteristics that are desirable for this kind of problem and make them preferable to classical optimization methods. In fact, various evolutionary approaches to multiobjective optimization have been proposed since 1985, capable of searching for multiple Paretooptimal solutions concurrently in a single simulation run. However, in spite of this variety, there is a lack of extensive comparative studies in the literature. Therefore, it has remained open up to now

Multiobjective Optimization Using Goal Programming for Industrial Water Network Design

The multiobjective optimization (MOO) of industrial water networks through goal programming is studied using a mixed-integer linear programming (MILP) formulation. First, the efficiency of goal programming for solving MOO problems is demonstrated with an introductive mathematical example and then with industrial water and energy networks design problems, formerly tackled in literature with other MOO methods. The first industrial water network case study is composed of 10 processes, 1 contaminant, and 1 water regeneration unit. The second, a more complex real industrial case study, is made of 12 processes, 1 contaminant, 4 water regeneration units, and the addition of temperature requirements for each process, which implies the introduction of energy networks alongside water networks. For MOO purposes, several antagonist objective functions are considered according to the case, such as total freshwater flow rate, number of connections, and total energy consumption. The MOO methodology proposed is demonstrated to be very reliable as an a priori method, by providing Pareto-optimal compromise solutions in significant less time compared to other traditional methods for MOO

Research Agenda on Multiple-Criteria Decision-Making: New Academic Debates in Business and Management

[EN] Systemic disruptions are becoming more continuous, intense, and persistent. Their effects have a severe impact on the economy in volatile, uncertain, complex, and ambiguous (VUCA) environments that are increasingly transversal to productive sectors and activities. Researchers have intensified their academic production of multiple-criteria decision-making (MCDM) in recent years. This article analyzes the research agenda through a systematic review of scientific articles in the Web of Science Core Collection according to the Journal Citation Report (JCR), both in the Social Sciences Citation Index (SSCI) and in the Science Citation Index Expanded (SCIE). According to the selected search criteria, 909 articles on MCDM published between 1979 and 2022 in Web of Science journals in the business and management categories were located. A bibliometric analysis of the main thematic clusters, the international collaboration networks, and the bibliographic coupling of articles was carried out. In addition, the analysis period is divided into two subperiods (1979¿2008 and 2009¿2022), establishing 2008 as the threshold, the year of the Global Financial Crisis (GFC), to assess the evolution of the research agenda at the beginning of systemic disruptions. The bibliometric analysis allows the identification of the motor, basic, specialized, and emerging themes of each subperiod. The results show the similarities and differences between the academic debate before and after the GFC. The evidence found allows academics to be guided in their high-impact research in business and management using MCDM methodologies to address contemporary challenges. An important contribution of this study is to detect gaps in the literature, highlighting unclosed gaps and emerging trends in the field of study for journal editors.Castello-Sirvent, F.; Meneses-Eraso, C. (2022). Research Agenda on Multiple-Criteria Decision-Making: New Academic Debates in Business and Management. Axioms. 11(10):1-37. https://doi.org/10.3390/axioms11100515137111

A multi-objective optimisation approach applied to offshore wind farm location selection

This paper compares the three state-of-the-art algorithms when applied to a real-world case of the wind energy sector. Optimum locations are suggested for a wind farm by considering only Round 3 zones around the UK. The problem comprises of some of the most important techno-economic life cycle cost-related factors, which are modelled using the physical aspects of each wind farm location (i.e., the wind speed, distance from the ports, and water depth), the wind turbine size, and the number of turbines. The model is linked to NSGA II, NSGA III, and SPEA 2 algorithms, to conduct an optimisation search. The performance of these three algorithms is demonstrated and analysed, so as to assess their effectiveness in the investment decision-making process in the wind sector, more importantly, for Round 3 zones. The results are subject to the specifics of the underlying life cycle cost model