Many concrete problems, ranging from Portfolio selection to Water resource management, may be cast into a multiobjective programming framework. The simplistic way of superseding blindly conflictual goals by one objective function let no chance to the model but to churn out meaningless outcomes. Hence interest of discussing ways for tackling Multiobjective Programming Problems. More than this, in many real-life situations, uncertainty and imprecision are in the state of affairs. In this dissertation we discuss ways for solving Multiobjective Programming Problems with fixed and fuzzy coefficients. No preference, a priori, a posteriori, interactive and metaheuristic methods are discussed for the deterministic case. As far as the fuzzy case is concerned, two approaches based respectively on possibility measures and on Embedding Theorem for fuzzy numbers are described. A case study is also carried out for the sake of illustration. We end up with some concluding remarks along with lines for further development, in this field. / Operations Research / M. Sc. (Operations Research)

Many concrete problems, ranging from Portfolio selection to Water resource management, may be cast into a multiobjective programming framework. The simplistic way of superseding blindly conflictual goals by one objective function let no chance to the model but to churn out meaningless outcomes. Hence interest of discussing ways for tackling Multiobjective Programming Problems. More than this, in many real-life situations, uncertainty and imprecision are in the state of affairs. In this dissertation we discuss ways for solving Multiobjective Programming Problems with fixed and fuzzy coefficients. No preference, a priori, a posteriori, interactive and metaheuristic methods are discussed for the deterministic case. As far as the fuzzy case is concerned, two approaches based respectively on possibility measures and on Embedding Theorem for fuzzy numbers are described. A case study is also carried out for the sake of illustration. We end up with some concluding remarks along with lines for further development, in this field. / Operations Research / M. Sc. (Operations Research)

In the recent years there has been a great deal of attention on the optimal demand and supply side strategy. The increase in renewable energy sources and the expansion in demand response programmes has shown the need for a robust power system. These changes in power system require the control of the uncertain generation and load at the same time. Therefore, it is important to provide an optimal scheduling strategy that can meet an adequate energy mix under demand response without affecting the system reliability and economic performance. This thesis addresses the following four aspects to these changes. First, a renewable obligation model is proposed to maintain an adequate energy mix in the economic dispatch model while minimising the operational costs of the allocated spinning reserves. This method considers a minimum renewable penetration that must be achieved daily in the energy mix. If the renewable quota is not achieved, the generation companies are penalised by the system operator. The uncertainty of renewable energy sources are modelled using the probability density functions and these functions are used for scheduling output power from these generators. The overall problem is formulated as a security constrained economic dispatch problem. Second, a combined economic and demand response optimisation model under a renewable obligation is presented. Real data from a large-scale demand response programme are used in the model. The model finds an optimal power dispatch strategy which takes advantage of demand response to minimise generation cost and maximise renewable penetration. The optimisation model is applied to a South African large-scale demand response programme in which the system operator can directly control the participation of the electrical water heaters at a substation level. Actual load profile before and after demand reduction are used to assist the system operator in making optimal decisions on whether a substation should participate in the demand response programme. The application of these real demand response data avoids traditional approaches which assume arbitrary controllability of flexible loads. Third, a stochastic multi-objective economic dispatch model is presented under a renewable obligation. This approach minimises the total operating costs of generators and spinning reserves under renewable obligation while maximising renewable penetration. The intermittency nature of the renewable energy sources is modelled using dynamic scenarios and the proposed model shows the effectiveness of the renewable obligation policy framework. Due to the computational complexity of all possible scenarios, a scenario reduction method is applied to reduce the number of scenarios and solve the model. A Pareto optimal solution is presented for a renewable obligation and further decision making is conducted to assess the trade-offs associated with the Pareto front. Four, a combined risk constrained stochastic economic dispatch and demand response model is presented under renewable obligation. An incentive based optimal power dispatch strategy is implemented to minimise generation costs and maximise renewable penetration. In addition, a risk-constrained approach is used to control the financial risks of the generation company under demand response programme. The coordination strategy for the generation companies to dispatch power using thermal generators and renewable energy sources while maintaining an adequate spinning reserve is presented. The proposed model is robust and can achieve significant demand reduction while increasing renewable penetration and decreasing the financial risks for generation companies. / Thesis (PhD (Electrical Engineering))--University of Pretoria, 2020. / Electrical, Electronic and Computer Engineering / PhD (Electrical Engineering) / Unrestricted

Yes / Investigation of the environmental/economic optimal operation management of a microgrid (MG) as a case study for applying a novel modified multi-objective grey wolf optimizer (MMOGWO) algorithm is presented in this paper. MGs can be considered as a fundamental solution in order for distributed generators’ (DGs) management in future smart grids. In the multi-objective problems, since the objective functions are conflict, the best compromised solution should be extracted through an efficient approach. Accordingly, a proper method is applied for exploring the best compromised solution. Additionally, a novel distance-based method is proposed to control the size of the repository within an aimed limit which leads to a fast and precise convergence along with a well-distributed Pareto optimal front. The proposed method is implemented in a typical grid-connected MG with non-dispatchable units including renewable energy sources (RESs), along with a hybrid power source (micro-turbine, fuel-cell and battery) as dispatchable units, to accumulate excess energy or to equalize power mismatch, by optimal scheduling of DGs and the power exchange between the utility grid and storage system. The efficiency of the suggested algorithm in satisfying the load and optimizing the objective functions is validated through comparison with different methods, including PSO and the original GWO. / Supported in part by Royal Academy of Engineering Distinguished Visiting Fellowship under Grant DVF1617\6\45

Σε αυτήν την εργασία, παρουσιάζουμε τις βασικότερες κλασικές προσεγγίσεις επίλυσης Πολυ-αντικειμενικών Προβλημάτων Βελτιστοποίησης(ΠΠΒ)καθώς και ένα από τα πιο δημοφιλή λογισμικά για επίλυση ΠΠΒ, το NIMBUS. Συγκεκριμένα, δίνουμε τον ορισμό ενός ΠΠΒ, το θεωρητικό υπόβαθρο -- για την καλύτερη κατανόηση των μεθόδων που θα ακολουθήσουν - και τις διαφορές των ΠΠΒ με τα κλασσικά Μονο-αντικειμενικά προβλήματα Βελτιστοποίησης. Επιπλέον, παρουσιάζουμε τις τρεις κύριες κατηγορίες προσέγγισης των ΠΠΒ (μη-αλληλεπιδραστικές, αλληλεπιδραστικές, εξελικτικές) ο διαχωρισμός των οποίων γίνεται ανάλογα με την άμεση ή έμμεση εμπλοκή του Λήπτη Απόφασης. Η μελέτη μας εστιάζεται κυρίως στην κατηγορία των μη-αλληλεπιδραστικών προσεγγίσεων, στην οποία ο ΛΑ εμπλέκεται έμμεσα. Τέλος, ολοκληρώνουμε την μελέτη μας με την αναλυτική παρουσίαση της επίλυσης ενός ΠΠB με την χρήση του λογισμικού NIMBUS. / In this contribution, we study the classical approaches for solving Multi-objective Optimization Problems (MOOP) as well as one of the most popular software that solves MOOP, namely NIMBUS. More specifically, we present the definition and the theoretical background around MOOP and we discuss the differences between MOOP and the classical single-objective optimization problems. We also present the three main categories of approaches of solving MOOP (non-interactive, interactive, evolutionary) that are characterized by the way the Decision Maker participates in the solution. We focus on the first category by analyzing each of the non-interactive approaches. Finally, we conclude by presenting an analytic illustration of an example that solves a MOOP using the NIMBUS software.