In this thesis, the basic principles and concepts of single and multi-objective Genetic Algorithms (GA) are reviewed. Two algorithms, one for single objective and the other for multi-objective problems, which are believed to be more efficient are described in details. The algorithms are coded with MATLAB and applied on several test functions. The results are compared with the existing solutions in literatures and shows promising results. Obtained pareto-fronts are exactly similar to the true pareto-fronts with a good spread of solution throughout the optimal region. Constraint handling techniques are studied and applied in the two algorithms. Constrained benchmarks are optimized and the outcomes show the ability of algorithm in maintaining solutions in the entire pareto-optimal region. In the end, a hybrid method based on the combination of the two algorithms is introduced and the performance is discussed. It is concluded that no significant strength is observed within the approach and more research is required on this topic. For further investigation on the performance of the proposed techniques, implementation on real-world engineering applications are recommended.

Numerous advantages attained by integrating Distributed Generation (DG) in distribution systems. These advantages include decreasing power losses and improving voltage profiles. Such benefits can be achieved and enhanced if DGs are optimally sized and located in the systems. In this thesis, the optimal DG placement and sizing problem is investigated using two approaches. First, the optimization problem is treated as single-objective optimization problem, where the system’s active power losses are considered as the objective to be minimized. Secondly, the problem is tackled as a multi-objective one, focusing on DG installation costs. These problems are formulated as constrained nonlinear optimization problems using the Sequential Quadratic Programming method. A weighted sum method and a fuzzy decision-making method are presented to generate the Pareto optimal front and also to obtain the best compromise solution. Single and multiple DG installation cases are studied and compared to a case without DG, and a 15-bus radial distribution system and 33-bus meshed distribution system are used to demonstrate the effectiveness of the proposed methods.

Šioje disertacijoje nagrinėjamas sveikatos priežiūros įstaigos darbuotojų darbų grafikų optimizavimo uždavinys, kuris formuluojamas ir sprendžiamas, remiantis vienos didžiausių Lietuvos sveikatos priežiūros įstaigų, realiais duomenimis. Disertacijoje apžvelgiami darbų grafikų optimizavimo uždaviniai bei jų sprendimo metodai, atlikta naujausių šaltinių, tiriančių panašius uždavinius, analizė. Antrame skyriuje nagrinėjamasis darbų grafikų optimizavimo uždavinys suformuluotas matematiškai. Pateikiamos dvi formuluotės: vienakriterio ir daugiakriterio optimizavimo uždavinio. Aprašomos sąlygos, kurias turi tenkinti sudaromasis darbų grafikas. Trečiajame skyriuje nagrinėjami metodai, tiek vienakriteriams, tiek daugiakriteriams uždaviniams spręsti. Pasiūlytas naujas metodas, kuris efektyviau nei kiti nagrinėti metodai sprendžia šioje disertacijoje suformuluotą uždavinį. Ketvirtame skyriuje pateikiami pasiūlyto metodo eksperimentinio tyrimo rezultatai. Pirmoje skyriaus dalyje analizuojami rezultatai gauti, sprendžiant vienakriterį optimizavimo uždavinį, o antroje dalyje – daugiakriterį optimizavimo uždavinį. Disertacijos tyrimų rezultatai buvo pristatyti respublikinėje konferencijoje ir trijose tarptautinėse konferencijose bei publikuoti trijuose mokslo žurnaluose. / In this dissertation nurse rostering problem is investigated. The formulation of the problem is based on real-world data of one of the largest healthcare centers in Lithuania. Most recent publications that tackle the nurse rostering problem and the methods for solving the nurse rostering problem are reviewed in this dissertation. The mathematical formulation of the single objective and the multi-objective nurse rostering problem is presented and the requirements for the roster are described in the second chapter. In the third chapter, the methods for solving the single objective and the multi-objective nurse rostering problem are described. A new method for solving the single objective and the multi-objective nurse rostering problem is proposed in the third chapter. In the fourth chapter, the experimental results of our proposed method are introduced. In the first section of this chapter, the results gathered solving single-objective optimization problem are analyzed, and in the second section of this chapter, the results gathered solving multi-objective optimization problem are analyzed. Dissertation research results were presented at one national conference and three international conferences and published in three scientific journals.

Background: Multiple Objective Optimization problems(MOOPs) are common and evident in every field. Container port terminals are one of the fields in which MOOP occurs. In this research, we have taken a case in logistics management and modelled Multi-agent systems to solve the MOOP using Non-dominated Sorting Genetic Algorithm-II (NSGA-II). Objectives: The purpose of this study is to build AI-based models for solving a Multiple Objective Optimization Problem occurred in port terminals. At first, we develop a port agent with an objective function of maximizing throughput and a customer agent with an objective function of maximizing business profit. Then, we solve the problem using the single-objective optimization model and multi-objective optimization model. We then compare the results of both models to assess their performance. Methods: A literature review is conducted to choose the best algorithm among the existing algorithms, which were used previously in solving other Multiple Objective Optimization problems. An experiment is conducted to know how well the models performed to solve the problem so that all the participants are benefited simultaneously. Results: The results show that all three participants that are port, customer one and customer two have gained profits by solving the problem in multi-objective optimization model. Whereas in a single-objective optimization model, a single participant has achieved earnings at a time, leaving the rest of the participants either in loss or with minimal profits. Conclusion: We can conclude that multi-objective optimization model has performed better than the single-objective optimization model because of the impartial results among the participants.