An investigation of new methods for estimating parameter sensitivities

The method proposed for estimating sensitivity derivatives is based on the Recursive Quadratic Programming (RQP) method and in conjunction a differencing formula to produce estimates of the sensitivities. This method is compared to existing methods and is shown to be very competitive in terms of the number of function evaluations required. In terms of accuracy, the method is shown to be equivalent to a modified version of the Kuhn-Tucker method, where the Hessian of the Lagrangian is estimated using the BFS method employed by the RQP algorithm. Initial testing on a test set with known sensitivities demonstrates that the method can accurately calculate the parameter sensitivity

Impact of travel time uncertainties on the solution cost of a two-echelon vehicle routing problem with synchronization

Two-echelon vehicle routing problems which contain synchronization between vehicles can be deeply impacted by time uncertainty, because one vehicle's delay can propagate to other vehicles. In this paper, we evaluate the deterministic solution of such a problem based on simulated travel time scenarios. The information obtained by simulation is incorporated in the optimization procedure iteratively. Computational results show that the degree of synchronization in an instance is directly correlated with the potential improvements by reoptimization. We present findings on the number of travel time scenarios required to obtain a representative picture of the stochastic solutions. In addition, we demonstrate that time dependent travel times can be aggregated on a city-wide level and linearized as a function of free flow times without major loss of reliability

Dynamic vehicle routing problems: Three decades and counting

Since the late 70s, much research activity has taken place on the class of dynamic vehicle routing problems (DVRP), with the time period after year 2000 witnessing a real explosion in related papers. Our paper sheds more light into work in this area over more than 3 decades by developing a taxonomy of DVRP papers according to 11 criteria. These are (1) type of problem, (2) logistical context, (3) transportation mode, (4) objective function, (5) fleet size, (6) time constraints, (7) vehicle capacity constraints, (8) the ability to reject customers, (9) the nature of the dynamic element, (10) the nature of the stochasticity (if any), and (11) the solution method. We comment on technological vis-à-vis methodological advances for this class of problems and suggest directions for further research. The latter include alternative objective functions, vehicle speed as decision variable, more explicit linkages of methodology to technological advances and analysis of worst case or average case performance of heuristics.© 2015 Wiley Periodicals, Inc

A review of portfolio planning: Models and systems

In this chapter, we first provide an overview of a number of portfolio planning models which have been proposed and investigated over the last forty years. We revisit the mean-variance (M-V) model of Markowitz and the construction of the risk-return efficient frontier. A piecewise linear approximation of the problem through a reformulation involving diagonalisation of the quadratic form into a variable separable function is also considered. A few other models, such as, the Mean Absolute Deviation (MAD), the Weighted Goal Programming (WGP) and the Minimax (MM) model which use alternative metrics for risk are also introduced, compared and contrasted. Recently asymmetric measures of risk have gained in importance; we consider a generic representation and a number of alternative symmetric and asymmetric measures of risk which find use in the evaluation of portfolios. There are a number of modelling and computational considerations which have been introduced into practical portfolio planning problems. These include: (a) buy-in thresholds for assets, (b) restriction on the number of assets (cardinality constraints), (c) transaction roundlot restrictions. Practical portfolio models may also include (d) dedication of cashflow streams, and, (e) immunization which involves duration matching and convexity constraints. The modelling issues in respect of these features are discussed. Many of these features lead to discrete restrictions involving zero-one and general integer variables which make the resulting model a quadratic mixed-integer programming model (QMIP). The QMIP is a NP-hard problem; the algorithms and solution methods for this class of problems are also discussed. The issues of preparing the analytic data (financial datamarts) for this family of portfolio planning problems are examined. We finally present computational results which provide some indication of the state-of-the-art in the solution of portfolio optimisation problems

A hydrologically-driven approach to climate change adaptation for multipurpose multireservoir system

[EN] Climate change can significantly affect water systems with negative impacts on many facets of society and ecosystems. Therefore, significant attention must be devoted to the development of efficient adaptation strategies. More specifically, the reoperation of water resources systems to keep the overall performance within acceptable limits should be prioritized to avoid, or at least delay as much as possible, costly infrastructural investments. This manuscript presents a hydrologically-driven approach to support the reoperation of multipurpose multireservoir systems. The approach is organized around 1) the use of a large ensemble of GCM hydro-climate projections to drive a climate stress test; 2) the bottom-up clustering of those hydrologic projections based on hydrologic attributes that are both relevant to the region of interest and interpretable by the operators; and finally, 3) the identification of adaptation measures for each cluster after developing a one-way coupling of an optimization model with a simulation model. The climate impact assessment is illustrated with the multipurpose multireservoir system of the Lievre River basin in Quebec (Canada). Results show that cluster-specific, adapted, operating rules can improve the performance of the system and reveal its operational flexibility with respect to the different operating objectives.The work was partly supported by a project funded by MELCC (Quebecs Ministere de lEnvironnement et de la Lutte contre les changements climatiques) through two programs: PACC 2013-2020 and Fonds vert. This study does not represent the views of MELCC. Also, this work was partly supported by the NSERC Discovery Grant (Natural Sciences and Engineering Research Council of Canada) of the second author, and the intersectorial flood network of Quebec (RIISQ). This research was enabled in part by support provided by Compute Canada (www.computecanada.ca).Sant Anna, C.; Tilmant, A.; Pulido-Velazquez, M. (2022). A hydrologically-driven approach to climate change adaptation for multipurpose multireservoir system. Climate Risk Management. 36:1-16. https://doi.org/10.1016/j.crm.2022.1004271163

Design of optimal reservoir operating rules in large water resources systems combining stochastic programming, fuzzy logic and expert criteria

Given the high degree of development of hydraulic infrastructure in the developed countries, and with the increasing opposition to constructing new facilities in developing countries, the focus of water resource system analysis has turned into defining adequate operation strategies. Better management is necessary to cope with the challenge of supplying increasing demands and conflicts on water allocation while facing climate change impacts. To do so, a large set of mathematical simulation and optimization tools have been developed. However, the real application of these techniques is still limited. One of the main lines of research to fix this issue regards to the involvement of experts' knowledge in the definition of mathematical algorithms. To define operating rules in a way in which system operators could rely, their expert knowledge should be fully accounted and merged with the results from mathematical algorithms. This thesis develops a methodological framework and the required tools to improve the operation of large-scale water resource systems. In such systems, decision-making processes are complex and supported, at least partially, by the expert knowledge of decision-makers. This importance of expert judgment in the operation strategies requires mathematical tools able to embed and combine it with optimization algorithms. The methods and tools developed in this thesis rely on stochastic programming, fuzzy logic and the involvement of system operators during the whole rule-defining process. An extended stochastic programming algorithm, able to be used in large-scale water resource systems including stream-aquifer interactions, has been developed (the CSG-SDDP). The methodological framework proposed uses fuzzy logic to capture the expert knowledge in the definition of optimal operating rules. Once the current decision-making process is fairly reproduced using fuzzy logic and expert knowledge, stochastic programming results are introduced and thus the performance of the rules is improved. The framework proposed in this thesis has been applied to the Jucar river system (Eastern Spain), in which scarce resources are allocated following complex decision-making processes. We present two applications. In the first one, the CSG-SDDP algorithm has been used to define economically-optimal conjunctive use strategies for a joint operation of reservoirs andaquifers. In the second one, we implement a collaborative framework to couple historical records with expert knowledge and criteria to define a decision support system (DSS) for the seasonal operation of the reservoirs of the Jucar River system. The co-developed DSS tool explicitly reproduces the decision-making processes and criteria considered by the system operators. Two fuzzy logic systems have been developed and linked with this purpose, as well as with fuzzy regressions to preview future inflows. The DSS developed was validated against historical records. The developed framework offers managers a simple way to define a priori suitable decisions, as well as to explore the consequences of any of them. The resulting representation has been then combined with the CSG-SDDP algorithm in order to improve the rules following the current decision-making process. Results show that reducing pumping from the Mancha Oriental aquifer would lead to higher systemwide benefits due to increased flows by stream-aquifer interaction. The operating rules developed successfully combined fuzzy logic, expert judgment and stochastic programming, increasing water allocations to the demands by changing the way in which Alarcon, Contreras and Tous are balanced. These rules follow the same decision-making processes currently done in the system, so system operators would feel familiar with them. In addition, they can be contrasted with the current operating rules to determine what operation options can be coherent with the current management and, at the same time, achieve an optimal operationDado el alto número de infraestructuras construidas en los países desarrollados, y con una oposición creciente a la construcción de nuevas infraestructuras en los países en vías de desarrollo, la atención del análisis de sistemas de recursos hídricos ha pasado a la definición de reglas de operación adecuadas. Una gestión más eficiente del recurso hídrico es necesaria para poder afrontar los impactos del cambio climático y de la creciente demanda de agua. Para lograrlo, un amplio abanico de herramientas y modelos matemáticos de optimización se han desarrollado. Sin embargo, su aplicación práctica en la gestión hídrica sigue siendo limitada. Una de las más importantes líneas de investigación para solucionarlo busca la involucración de los expertos en la definición de dichos modelos matemáticos. Para definir reglas de operación en las cuales los gestores confíen, es necesario tener en cuenta su criterio experto y combinarlo con algoritmos de optimización. La presente tesis desarrolla una metodología, y las herramientas necesarias para aplicarla, con el fin de mejorar la operación de sistemas complejos de recursos hídricos. En éstos, los procesos de toma de decisiones son complicados y se sustentan, al menos en parte, en el juicio experto de los gestores. Esta importancia del criterio de experto en las reglas de operación requiere herramientas matemáticas capaces de incorporarlo en su estructura y de unirlo con algoritmos de optimización. Las herramientas y métodos desarrollados se basan en la optimización estocástica, en la lógica difusa y en la involucración de los expertos durante todo el proceso. Un algoritmo estocástico extendido, capaz de ser usado en sistemas complejos con interacciones río-acuífero se ha desarrollado (el CSG-SDDP). La metodología definida usa lógica difusa para capturar el criterio de experto en la definición de reglas óptimas. En primer lugar se reproducen los procesos de toma de decisiones actuales y, tras ello, el algoritmo de optimización estocástica se emplea para mejorar las reglas previamente obtenidas. La metodología propuesta en esta tesis se ha aplicado al sistema Júcar (Este de España), en el que los recursos hídricos son gestionados de acuerdo a complejos procesos de toma de decisiones. La aplicación se ha realizado de dos formas. En la primera, el algoritmo CSG-SDDP se ha utilizado para definir una estrategia óptima para el uso conjunto de embalses y acuíferos. En la segunda, la metodología se ha usado para reproducir las reglas de operación actuales en base a criterio de expertos. La herramienta desarrollada reproduce de forma explícita los procesos de toma de decisiones seguidos por los operadores del sistema. Dos sistemas lógicos difusos se han empleado e interconectado con este fin, así como regresiones difusas para predecir aportaciones. El Sistema de Ayuda a la Decisión (SAD) creado se ha validado comparándolo con los datos históricos. La metodología desarrollada ofrece a los gestores una forma sencilla de definir decisiones a priori adecuadas, así como explorar las consecuencias de una decisión concreta. La representación matemática resultante se ha combinado entonces con el CSG-SDDP para definir reglas óptimas que respetan los procesos actuales. Los resultados obtenidos indican que reducir el bombeo del acuífero de la Mancha Oriental conlleva una mejora en los beneficios del sistema debido al incremento de caudal por relación río-acuífero. Las reglas de operación han sido adecuadamente desarrolladas combinando lógica difusa, juicio experto y optimización estocástica, aumentando los suministros a las demandas mediante modificaciones el balance de Alarcón, Contreras y Tous. Estas reglas siguen los procesos de toma de decisiones actuales en el Júcar, por lo que pueden resultar familiares a los gestores. Además, pueden compararse con las reglas de operación actuales para establecer qué decisiones entreDonat l'alt nombre d'infraestructures construïdes en els països desenrotllats, i amb una oposició creixent a la construcció de noves infraestructures en els països en vies de desenrotllament, l'atenció de l'anàlisi de sistemes de recursos hídrics ha passat a la definició de regles d'operació adequades. Una gestió més eficient del recurs hídric és necessària per a poder afrontar els impactes del canvi climàtic i de la creixent demanda d'aigua. Per a aconseguir-ho, una amplia selecció de ferramentes i models matemàtics d'optimització s'han desenrotllat. No obstant això, la seua aplicació pràctica en la gestió hídrica continua sent limitada. Una de les més importants línies d'investigació per a solucionar-ho busca la col·laboració activa dels experts en la definició dels models matemàtics. Per a definir regles d'operació en les quals els gestors confien, és necessari tindre en compte el seu criteri expert i combinar-ho amb algoritmes d'optimització. La present tesi desenrotlla una metodologia, i les ferramentes necessàries per a aplicar-la, amb la finalitat de millorar l'operació de sistemes complexos de recursos hídrics. En estos, els processos de presa de decisions són complicats i se sustenten, almenys en part, en el juí expert dels gestors. Esta importància del criteri d'expert en les regles d'operació requereix ferramentes matemàtiques capaces d'incorporar-lo en la seua estructura i d'unir-lo amb algoritmes d'optimització. Les ferramentes i mètodes desenrotllats es basen en l'optimització estocàstica, en la lògica difusa i en la col·laboració activa dels experts durant tot el procés. Un algoritme estocàstic avançat, capaç de ser usat en sistemes complexos amb interaccions riu-aqüífer, s'ha desenrotllat (el CSG-SDDP) . La metodologia definida utilitza lògica difusa per a capturar el criteri d'expert en la definició de regles òptimes. En primer lloc es reprodueixen els processos de presa de decisions actuals i, després d'això, l'algoritme d'optimització estocàstica s'empra per a millorar les regles prèviament obtingudes. La metodologia proposada en esta tesi s'ha aplicat al sistema Xúquer (Est d'Espanya), en el que els recursos hídrics són gestionats d'acord amb complexos processos de presa de decisions. L'aplicació s'ha realitzat de dos formes. En la primera, l'algoritme CSG-SDDP s'ha utilitzat per a definir una estratègia òptima per a l'ús conjunt d'embassaments i aqüífers. En la segona, la metodologia s'ha usat per a reproduir les regles d'operació actuals basant-se en criteri d'experts. La ferramenta desenvolupada reprodueix de forma explícita els processos de presa de decisions seguits pels operadors del sistema. Dos sistemes lògics difusos s'han empleat i interconnectat amb este fi, al igual què regressions difuses per preveure cabdals. El Sistema d'Ajuda a la Decisió (SAD) creat s'ha validat comparant-lo amb les dades històriques. La metodologia desenvolupada ofereix als gestors una manera senzilla de definir decisions a priori adequades, així com per explorar les conseqüències d'una decisió concreta. La representació matemàtica resultant s'ha combinat amb el CSG-SDDP per a definir regles òptimes que respecten els processos actuals. Els resultats obtinguts indiquen que reduir el bombament de l'aqüífer de la Mancha Oriental comporta una millora en els beneficis del sistema a causa de l'increment de l'aigua per relació riu-aqüífer. Les regles d'operació han sigut adequadament desenrotllades combinant lògica difusa, juí expert i optimització estocàstica, augmentant els subministres a les demandes per mitjà de modificacions del balanç d'Alarcón, Contreras i Tous. Estes regles segueixen els processos de presa de decisions actuals en el Xúquer, per la qual cosa poden resultar familiars als gestors. A més, poden comparar-se amb les regles d'operació actuals per a establir quines decisions entre les possibles serien coherentsMacián Sorribes, H. (2017). Design of optimal reservoir operating rules in large water resources systems combining stochastic programming, fuzzy logic and expert criteria [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/82554TESI