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This chapter presents the survey of selected linear and mixed integer programming multi-objective portfolio optimization. The definitions of selected percentile risk measures are presented. Some contrasts and similarities of the different types of portfolio formulations are drawn out. The survey of multi-criteria methods devoted to portfolio optimization such as weighting approach, lexicographic approach, and reference point method is also presented. This survey presents the nature of the multi-objective portfolio problems focuses on a compromise between the construction of objectives, constraints, and decision variables in a portfolio and the problem complexity of the implemented mathematical models. There is always a trade-off between computational time and the size of an input data, as well as the type of mathematical programming formulation with linear and/or mixed integer variables.

This chapter presents the portfolio optimization problem formulated as a multi-criteria mixed integer program. Weighting and lexicographic approach are proposed. The portfolio selection problem considered is based on a single-period model of investment. An extension of the Markowitz portfolio optimization model is considered, in which the variance has been replaced with the Value-at-Risk (VaR). The VaR is a quantile of the return distribution function. In the classical Markowitz approach, future returns are random variables controlled by such parameters as the portfolio efficiency, which is measured by the expectation, whereas risk is calculated by the standard deviation. As a result, the classical problem is formulated as a quadratic program with continuous variables and some side constraints. The objective of the problem considered in this chapter is to allocate wealth on different securities to maximize the weighted difference of the portfolio expected return and the threshold of the probability that the return is less than a required level. The auxiliary objectives are minimization of risk probability of portfolio loss and minimization of the number of security types in portfolio. The four types of decision variables are introduced in the model: a continuous wealth allocation variable that represents the percentage of wealth allocated to each asset, a continuous variable that prevents the probability that return of investment is not less than required level, a binary selection variable that prevents the choice of portfolios whose VaR is below the minimized threshold, and a binary selection variable that represents choice of stocks in which capital should be invested. The results of some computational experiments with the mixed integer programming approach modeled on a real data from the Warsaw Stock Exchange are reported.

This paper aims to illustrate the use of the augmented epsilon-constraint method implemented in general algebraic modelling system (GAMS), aimed at optimizing the geometry of a thermoacoustic regenerator. Thermoacoustic heat engines provide a practical solution to the problem of heat management where heat can be pumped or spot cooling can be produced. However, the most inhibiting characteristic of thermoacoustic cooling is their current lack of efficiencies.

Lexicographic optimization is presented as an alternative optimization technique to the common used weighting methods. This approach establishes a hierarchical order among all the optimization objectives instead of giving them a specific (and most of the time, arbitrary) weight.

A practical example is given, in a hypothetical scenario, showing how the proposed optimization technique may help thermoacoustic regenerator designers to identify Pareto optimal solutions when dealing with geometric parameters. This study highlights the fact that the geometrical parameters are interdependent, which support the use of a multi-objective approach for optimization in thermoacoustic.

The research output from this paper can be a valuable resource to support designers in building efficient thermoacoustic device. The research illustrates the use of a lexicographic optimization to provide more meaningful results describing the geometry of thermoacoustic regenerator. It applies the epsilon-constraint method (AUGMENCON) to solve a five-criteria mixed integer non-linear problem implemented in GAMS (GAM software).

This chapter presents two optimization multicriteria models (bi and triple objective) using a lexicographic approach. Solved models are formulated as assignment of workers to different jobs or services of a real hospital, taking into account the available budget and requirements of each job. Presented problems have been solved using AMPL programming language with solver CPLEX v9.1, with the use of branch and bound method for mixed integer mathematical programming.

The Middle East and North Africa (MENA) region is known for its extreme weather conditions during Summer. A major determinant of the sustainability of the design of a building is its fenestrations. The purpose of this paper is to explore the problem of designing and locating windows on building facades such that a number of relevant criteria to the MENA region are optimised, including solar heat gain, privacy, daylighting and cost of installation.

A multi-objective optimisation problem is proposed with the focus on capturing the requirements of residential dwellings in the MENA region. Since the problem contains conflicting objectives that need to be optimised, a lexicographic approach is adopted. In order to display the Pareto curve, a bi-objective analysis based on the ε-constraint method is utilised.

The conflicting nature of the proposed problem is indicated via the Pareto optimal solutions yielded. Depending on the preference of criteria adopted in lexicographic optimisation, the location of the windows on the building façade tends to change. The bi-objective analysis indicates the importance of balancing out the daylight factor against each of privacy, solar heat gain and installation cost criteria. Furthermore, an analysis conducted in three major cities in the MENA region highlights the discrepancy in design alternatives generated depending on the local climatic condition.

This work proposes a novel mathematical optimisation model which focuses on producing a sustainable design and layout for windows on the facades of residential dwellings located in the MENA region. The proposed model provides designers with guidance through an automated support tool that yields optimised window designs and layout to ensure the sustainability of their designed buildings.

The purpose of this paper is to address the need for new approaches in locating items that closely match user preference criteria due to the rise in data volume of knowledge bases resulting from Open Data initiatives. Specifically, the paper focuses on evaluating SPARQL qualitative preference queries over user preferences in SPARQL.

The paper outlines a novel approach for handling SPARQL preference queries by representing preferences through symbolic weights using the possibilistic logic (PL) framework. This approach allows for the management of symbolic weights without relying on numerical values, using a partial ordering system instead. The paper compares this approach with numerous other approaches, including those based on skylines, fuzzy sets and conditional preference networks.

The paper highlights the advantages of the proposed approach, which enables the representation of preference criteria through symbolic weights and qualitative considerations. This approach offers a more intuitive way to convey preferences and manage rankings.

The paper demonstrates the usefulness and originality of the proposed SPARQL language in the PL framework. The approach extends SPARQL by incorporating symbolic weights and qualitative preferences.

Prosperity of the agricultural sector is very crucial not only for the national economy but also for the regional development. However, this prosperity has quite often a significant environmental cost in terms of water resources overexploitation or pollution. The main purpose of this paper is to create, apply and evaluate a model that aims at the simultaneous maximization of farmer's welfare and the minimization of the consequent environmental burden.

Lexicographic goal programming technique is employed. This technique is implemented on a representative farm around Mashhad in Iran to seek for a solution – in terms of area and water allocation under different crops.

Results shows that application of a multi‐criteria analysis may lead to a win‐win situation.

A lexicographic goal programming is used to satisfy both goals of farm activity in a represented area in Iran.

Specifies that the case for formal analysis of new product proposals is founded on the assumption that, to a large extent, the current high rate of failure is attributable to lack of scientific new product planning. Subscribes to this assumption and develops its analysis in the context of the planning framework suggested earlier. Concludes that the method of lexicography is not without adequate and sound theoretical support.

Operating theaters are considered as the most sensitive health department within hospital centers due to their significant cost/necessity for patients and their economic benefits for hospitals. In this paper, the authors consider patients that may require more than one surgery on the same day in the surgery scheduling problem which is a major technology enhancement in the health industry.

The surgery scheduling includes both the preoperative and the postoperative units of the operative stage. Two objectives are considered in a lexicographic way: the minimization of the makespan while prioritizing the patients having two surgeries and the total completion time to perform. An adapted tabu-search algorithm is used to tackles this NP-hard scheduling problem.

The proposed schedule is more relevant for operating theaters as it integrates all stages of the surgical procedure and considers patients with more than one operation during the same day.

This paper is original as it considers patients who need more than one operation, which responds to real challenge faced by decision-makers' in hospitals. The application of the time lags between stages of the surgical procedure generates a good utilization of the hospital resources and makes the scheduling task more flexible.

Proper planning for the response phase of humanitarian relief can significantly prevent many financial and human losses. To this aim, a multi-objective optimization model is proposed in this paper that considers different types of injured people, different vehicles with determining capacities and multi-period logistic planning. This model can be updated based on new information about resources and newly identified injured people.

The main objective function of the proposed model in this paper is minimizing the unsatisfied prioritized injured people in the network. Besides, the total transportation activities of different types of vehicles are considered as another objective function. Therefore, these objectives are optimized hierarchically in the proposed model using the Lexicographic method. This method finds the best value for the first objective function. Then, it tries to optimize transportation activities as the second objective function while maintaining the optimality of the first objective function.

The performances of the proposed model were analyzed in different cases and its robust approach for different problems was shown within the framework of a case study. Besides, the sensitivity analysis of results shows the logical behavior of the proposed model against various factors.

The proposed methodology can be applied to find the best response plan for all crises.

In this paper, we have tried to use a multi-objective optimization model to guide and correct response programs to deal with the occurred crisis. This is important because it can help emergency managers to improve their plans.