In this paper we propose an adaptation of the GRASP metaheuristic to solve multi-objective combinatorial optimization problems. In particular we describe several alternatives to specialize the construction and improvement components of GRASP when two or more objectives are considered. GRASP has been successfully coupled with path-relinking for single-objective optimization. In this paper, we pr...

Unitary Matrices and Hermitian Matrices Recall that the conjugate of a complex number a + bi is a − bi. The conjugate of a + bi is denoted a+ bi or (a+ bi)∗. In this section, I’ll use ( ) for complex conjugation of numbers of matrices. I want to use ( )∗ to denote an operation on matrices, the conjugate transpose. Thus, 3 + 4i = 3− 4i, 5− 6i = 5 + 6i, 7i = −7i, 10 = 10. Complex conjugation sati...

The optimal design of a plate-fin recuperator of a 200-kW microturbine was studied in this paper. The exergy efficiency, pressure drop and total cost were selected as the three important objective functions of the recuperator. Genetic Algorithm (GA) and Non-dominated Sorting Genetic Algorithm (NSGA-II) were respectively employed for single-objective and multi-objective optimizations. By opt...

This thesis contains five chapters. The notations, terminologies, definitions and numbering of equations, theorems and algorithms are independent in each chapter. Chapter 1 provides a fundamental introduction and contextual discussions to provide a unified theme for the subsequent chapters into a complete work. Chapters 2, 3 and 4 are arranged for ease of reading and understanding separately. F...

Diacylglycerol (DAG) and monoacylglycerol (MAG) are two natural occurring minor components found in most edible fats and oils. These compounds have gained increasing market demand owing to their unique physicochemical properties. Enzymatic glycerolysis in solvent-free system might be a promising approach in producing DAG and MAG-enriched oil. Understanding on glycerolysis mechanism is therefore...

In this paper, we study I-fuzzy bi-matrix games with I-fuzzy goals. The indeterminacy factor in the I-fuzzy goal of each player is resolved using the Hurwicz optimism-pessimism rule. As a result, such an I-fuzzy bi-matrix game reduces to solving a fuzzy optimization problem with S-shaped membership functions. The latter problem is equivalently converted into its crisp counterpart using the conv...

The global optimization of constrained Non-Linear Bi-Objective Optimization problems (NLBOO) aims at covering their Pareto-optimal front which is in general a manifold in R. Continuation methods can help in this context as they can follow a continuous component of this front once an initial point on it is provided. They constitute somehow a generalization of the classical scalarizing framework ...

An interactive pareto optimal with advantage (IPOA) approach for bi-objective programming is proposed and applied on capacitor placement and sizing problem. Two main contradictory concerned which including cost and quality properties are considered as bi-objective programming formulation. The IPOA approach can provide a valuable trade-off pareto-optimal solution by following the intention of de...

We present a framework for biclustering and clustering where the observations are general labels. Our approach is based on the maximum likelihood estimator and its convex relaxation, and generalizes recent works in graph clustering to the biclustering setting. In addition to standard biclustering setting where one seeks to discover clustering structure simultaneously in two domain sets, we show...

In many problems from different disciplines such as engineering, physics, medicine, and biology, a series of experimental data is used in order to generate a model that can describe a system with minimum noise. The procedure for building a model provides a description of the behavior of the system under study and can be used to give a prediction for the future. Herein a novel hierarchical bi-le...