Portfolio optimization with options

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics

Exopolysaccharide production by Enterobacter A47: optimization of cultivation conditions and study of polymer functional properties

Dissertação para obtenção do Grau de Mestre em Biotecnologia

Evaluation and optimization of a session-based middleware for data management

Dissertação para obtenção do Grau de Mestre em Engenharia Informática

Optimization of the electrodialytic phosphorus recovery from sewage sludge ash

Phosphorus (P) is becoming a scarce element due to the decreasing availability of primary sources. Therefore, recover P from secondary sources, e.g. waste streams, have become extremely important. Sewage sludge ash (SSA) is a reliable secondary source of P. The use of SSAs as a direct fertilizer has very restricted legislation due to the presence of inorganic contaminants. Furthermore, the P present in SSAs is not in a plant-available form. The electrodialytic (ED) process is one of the methods under development to recover P and simultaneously remove heavy metals. The present work aimed to optimize the P recovery through a 2 compartment electrodialytic cell. The research was divided in three independent phases. In the first phase, ED experiments were carried out for two SSAs from different seasons, varying the duration of the ED process (2, 4, 6 and 9 days). During the ED treatment the SSA was suspended in distilled water in the anolyte, which was separated from the catholyte by a cation exchange membrane. From both ashes 90% of P was successfully extracted after 6 days of treatment. Regarding the heavy metals removal, one of the SSAs had a better removal than the other. Therefore, it was possible to conclude that SSAs from different seasons can be submitted to ED process under the same parameters. In the second phase, the two SSAs were exposed to humidity and air prior to ED, in order to carbonate them. Although this procedure was not successful, ED experiments were carried out varying the duration of the treatment (2 and 6 days) and the period of air exposure that SSAs were submitted to (7, 14 and 30 days). After 6 days of treatment and 30 days of air exposure, 90% of phosphorus was successfully extracted from both ashes. No differences were identified between carbonated and non-carbonated SSAs. Thus, SSAs that were exposed to the air and humidity, e.g. SSAs stored for 30 days in an open deposit, can be treated under the same parameters as the SSAs directly collected from the incineration process. In the third phase, ED experiments were carried out during 6 days varying the stirring time (0, 1, 2 and 4 h/day) in order to investigate if energy can be saved on the stirring process. After 6 days of treatment and 4 h/day stirring, 80% and 90% of P was successfully extracted from SSA-A and SSA-B, respectively. This value is very similar to the one obtained for 6 days of treatment stirring 24 h/day.

Optimization of wastewater quality in the Sines refinery

In order to address and resolve the wastewater contamination problem of the Sines refinery with the main objective of optimizing the quality of this stream and reducing the costs charged to the refinery, a dynamic mass balance was developed nd implemented for ammonia and polar oil and grease (O&G) contamination in the wastewater circuit. The inadequate routing of sour gas from the sour water stripping unit and the kerosene caustic washing unit, were identified respectively as the major source of ammonia and polar substances present in the industrial wastewater effluent. For the O&G content, a predictive model was developed for the kerosene caustic washing unit, following the Projection to Latent Structures (PLS) approach. Comparison between analytical data for ammonia and polar O&G concentrations in refinery wastewater originating from the Dissolved Air Flotation (DAF) effluent and the model predictions of the dynamic mass balance calculations are in a very good agreement and highlights the dominant impact of the identified streams for the wastewater contamination levels. The ammonia contamination problem was solved by rerouting the sour gas through an existing clogged line with ammonia salts due to a non-insulated line section, while for the O&G a dynamic mass balance was implemented as an online tool, which allows for prevision of possible contamination situations and taking the required preventive actions, and can also serve as a basis for establishing relationships between the O&G contamination in the refinery wastewater with the properties of the refined crude oils and the process operating conditions. The PLS model developed could be of great asset in both optimizing the existing and designing new refinery wastewater treatment units or reuse schemes. In order to find a possible treatment solution for the spent caustic problem, an on-site pilot plant experiments for NaOH recovery from the refinery kerosene caustic washing unit effluent using an alkaline-resistant nanofiltration (NF) polymeric membrane were performed in order to evaluate its applicability for treating these highly alkaline and contaminated streams. For a constant operating pressure and temperature and adequate operating conditions, 99.9% of oil and grease rejection and 97.7% of chemical oxygen demand (COD) rejection were observed. No noticeable membrane fouling or flux decrease were registered until a volume concentration factor of 3. These results allow for NF permeate reuse instead of fresh caustic and for significant reduction of the wastewater contamination, which can result in savings of 1.5 M€ per year at the current prices for the largest Portuguese oil refinery. The capital investments needed for implementation of the required NF membrane system are less than 10% of those associated with the traditional wet air oxidation solution of the spent caustic problem. The operating costs are very similar, but can be less than half if reusing the NF concentrate in refinery pH control applications. The payback period was estimated to be 1.1 years. Overall, the pilot plant experimental results obtained and the process economic evaluation data indicate a very competitive solution through the proposed NF treatment process, which represents a highly promising alternative to conventional and existing spent caustic treatment units.

An evolutionary multi-objective optimization system for earthworks

Earthworks involve the levelling or shaping of a target area through the moving or processing of the ground surface. Most construction projects require earthworks, which are heavily dependent on mechanical equipment (e.g., excavators, trucks and compactors). Often, earthworks are the most costly and time-consuming component of infrastructure constructions (e.g., road, railway and airports) and current pressure for higher productivity and safety highlights the need to optimize earthworks, which is a nontrivial task. Most previous attempts at tackling this problem focus on single-objective optimization of partial processes or aspects of earthworks, overlooking the advantages of a multi-objective and global optimization. This work describes a novel optimization system based on an evolutionary multi-objective approach, capable of globally optimizing several objectives simultaneously and dynamically. The proposed system views an earthwork construction as a production line, where the goal is to optimize resources under two crucial criteria (costs and duration) and focus the evolutionary search (non-dominated sorting genetic algorithm-II) on compaction allocation, using linear programming to distribute the remaining equipment (e.g., excavators). Several experiments were held using real-world data from a Portuguese construction site, showing that the proposed system is quite competitive when compared with current manual earthwork equipment allocation.

Global vs. local nonlinear optimization techniques for human-like movement of an anthropomorphic robot

In this paper a comparison between using global and local optimization techniques for solving the problem of generating human-like arm and hand movements for an anthropomorphic dual arm robot is made. Although the objective function involved in each optimization problem is convex, there is no evidence that the admissible regions of these problems are convex sets. For the sequence of movements for which the numerical tests were done there were no significant differences between the optimal solutions obtained using the global and the local techniques. This suggests that the optimal solution obtained using the local solver is indeed a global solution.

Development of procedures for the design, optimization and manufacturing of customized orthopaedic and trauma implants: Geometrical/anatomical modelling from 3D medical imaging

Tese de Doutoramento (Programa Doutoral em Engenharia Biomédica)

Development of an intelligent earthwork optimization system

Tese de Doutoramento em Engenharia Civil.

A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization.

The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa.

Generic optimality conditions for semi-algebraic convex programs

We consider linear optimization over a nonempty convex semi-algebraic feasible region F. Semidefinite programming is an example. If F is compact, then for almost every linear objective there is a unique optimal solution, lying on a unique \active" manifold, around which F is \partly smooth", and the second-order sufficient conditions hold. Perturbing the objective results in smooth variation of the optimal solution. The active manifold consists, locally, of these perturbed optimal solutions; it is independent of the representation of F, and is eventually identified by a variety of iterative algorithms such as proximal and projected gradient schemes. These results extend to unbounded sets F.

A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex conguration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases.

On the stability of the optimal value and the optimal set in optimization problems

The paper develops a stability theory for the optimal value and the optimal set mapping of optimization problems posed in a Banach space. The problems considered in this paper have an arbitrary number of inequality constraints involving lower semicontinuous (not necessarily convex) functions and one closed abstract constraint set. The considered perturbations lead to problems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the abstract constraint set can also be perturbed. The spaces of functions involved in the problems (objective and constraints) are equipped with the metric of the uniform convergence on the bounded sets, meanwhile in the space of closed sets we consider, coherently, the Attouch-Wets topology. The paper examines, in a unified way, the lower and upper semicontinuity of the optimal value function, and the closedness, lower and upper semicontinuity (in the sense of Berge) of the optimal set mapping. This paper can be seen as a second part of the stability theory presented in [17], where we studied the stability of the feasible set mapping (completed here with the analysis of the Lipschitz-like property).

Optimization of multiclass queueing networks with changeover times via the achievable region approach: Part I, the single-station case

We address the performance optimization problem in a single-stationmulticlass queueing network with changeover times by means of theachievable region approach. This approach seeks to obtainperformance bounds and scheduling policies from the solution of amathematical program over a relaxation of the system's performanceregion. Relaxed formulations (including linear, convex, nonconvexand positive semidefinite constraints) of this region are developedby formulating equilibrium relations satisfied by the system, withthe help of Palm calculus. Our contributions include: (1) newconstraints formulating equilibrium relations on server dynamics;(2) a flow conservation interpretation of the constraintspreviously derived by the potential function method; (3) newpositive semidefinite constraints; (4) new work decomposition lawsfor single-station multiclass queueing networks, which yield newconvex constraints; (5) a unified buffer occupancy method ofperformance analysis obtained from the constraints; (6) heuristicscheduling policies from the solution of the relaxations.

Optimization of multiclass queueing networks with changeover times via the achievable region method: Part II, the multi-station case

We address the problem of scheduling a multi-station multiclassqueueing network (MQNET) with server changeover times to minimizesteady-state mean job holding costs. We present new lower boundson the best achievable cost that emerge as the values ofmathematical programming problems (linear, semidefinite, andconvex) over relaxed formulations of the system's achievableperformance region. The constraints on achievable performancedefining these formulations are obtained by formulatingsystem's equilibrium relations. Our contributions include: (1) aflow conservation interpretation and closed formulae for theconstraints previously derived by the potential function method;(2) new work decomposition laws for MQNETs; (3) new constraints(linear, convex, and semidefinite) on the performance region offirst and second moments of queue lengths for MQNETs; (4) a fastbound for a MQNET with N customer classes computed in N steps; (5)two heuristic scheduling policies: a priority-index policy, anda policy extracted from the solution of a linear programmingrelaxation.