Multi-objective Optimization and its Engineering Applications

Many practical optimization problems usually have several conflicting objectives. In those multi-objective optimization, no solution optimizing all objective functions simultaneously exists in general. Instead, Pareto optimal solutions, which are ``efficient" in terms of all objective functions, are introduced. In general we have many Pareto optimal solutions. Therefore, we need to decide a final solution among Pareto optimal solutions taking into account the balance among objective functions, which is called ``trade-off analysis". It is no exaggeration to say that the most important task in multi-objective optimization is trade-off analysis. Consequently, the methodology should be discussed in view of how it is easy and understandable for trade-off analysis. In cases with two or three objective functions, the set of Pareto optimal solutions in the objective function space (i.e., Pareto frontier) can be depicted relatively easily. Seeing Pareto frontiers, we can grasp the trade-off relation among objectives totally. Therefore, it would be the best way to depict Pareto frontiers in cases with two or three objectives. (It might be difficult to read the trade-off relation among objectives with three dimension, though). In cases with more than three objectives, however, it is impossible to depict Pareto forntier. Under this circumstance, interactive methods can help us to make local trade-off analysis showing a ``certain" Pareto optimal solution. A number of methods differing in which Pareto optimal solution is to be shown, have been developed. This paper discusses critical issues among those methods for multi-objective optimization, in particular applied to engineering design problems

Combining reference point based composite indicators with data envelopment analysis: application to the assessment of universities

In our knowledge society, where universities are key players, the assessment of higher education institutions should meet the new demands of the present complex environment. This calls for the use of techniques that are able to manage this complexity. In this paper, we propose a novel combination of methodologies, jointly using a multi-criteria reference point scheme and the data envelopment analysis (DEA) for the assessment of universities. This combination allows us to take into account all the aspects regarded as relevant to assess university performance, and use them as outputs in the efficiency analysis. Our findings highlight the convenience to assess the university performance by using both compensatory and non-compensatory schemes. This way, the information provided allows to detect the actions needed to improve the performances of the universities, rather than just giving an overall performance measure. Furthermore, combining the use of composite indicators with the DEA analysis provides a more complete picture of the institutions assessed, allowing universities to check their efficiency and to detect their weaknesses and strengths accordingly. The approach is illustrated using data of 47 Spanish public universities for the academic year, 2016–2017.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. Funding for open access charge: Universidad de Málaga / CBUA

Uncertain Multi-Criteria Optimization Problems

Most real-world search and optimization problems naturally involve multiple criteria as objectives. Generally, symmetry, asymmetry, and anti-symmetry are basic characteristics of binary relationships used when modeling optimization problems. Moreover, the notion of symmetry has appeared in many articles about uncertainty theories that are employed in multi-criteria problems. Different solutions may produce trade-offs (conflicting scenarios) among different objectives. A better solution with respect to one objective may compromise other objectives. There are various factors that need to be considered to address the problems in multidisciplinary research, which is critical for the overall sustainability of human development and activity. In this regard, in recent decades, decision-making theory has been the subject of intense research activities due to its wide applications in different areas. The decision-making theory approach has become an important means to provide real-time solutions to uncertainty problems. Theories such as probability theory, fuzzy set theory, type-2 fuzzy set theory, rough set, and uncertainty theory, available in the existing literature, deal with such uncertainties. Nevertheless, the uncertain multi-criteria characteristics in such problems have not yet been explored in depth, and there is much left to be achieved in this direction. Hence, different mathematical models of real-life multi-criteria optimization problems can be developed in various uncertain frameworks with special emphasis on optimization problems

Multicriteria Decision Making in Sustainable Tourism and Low-Carbon Tourism Research: A Systematic Literature Review

Multicriteria Decision Making (MCDM) is increasingly being utilized as an analytical research tool for sectors that require decision-making with specific objectives and constraints, such as the tourism industry. Sustainable tourism, which examines the balance of numerous aspects, including stakeholders’ interests, is the critical feature propelling the increased usage of MCDM. This paper explores the use of Multicriteria Decision Making (MCDM) methods applied in studies of sustainable tourism and its derivative term, low-carbon tourism, using a systematic literature review (SLR) search from the Scopus database. The analysis has identified 189 relevant studies published between 1987 to April 2022. After selection, screening, and synthesizing processes, we selected 135 pertinent studies, which were analysed in general descriptive data, citation impacts, geographical categorization, categorization of the methodologies’ objectives, and possible trajectories of similar research in the future. We find that highly cited authors and articles are related to sustainable tourism indicators\u27 development and case studies. Furthermore, most relevant studies are concentrated in Asia and Europe rather than other regions. We also categorize the reviewed studies into six classifications depending on each method\u27s intended usage and further suggest four contexts for the studies’ future trajectory

Natural Environment Management and Applied Systems Analysis

This volume contains papers from the NEMASA Konan-IIASA Joint Workshop on Natural Environment Management and Applied Systems Analysis, which took place at IIASA September 6-8, 2000. The workshop was an activity of the research project "Modeling by Computational Intelligence and its Application to Natural Environment Management." The project is being supported by the Hirao Taro Foundation of the Konan University Association for Academic Research, Kobe, Japan. The management of the natural environment -- in particular, the use of advanced agricultural practices -- poses a major challenge to modern society, but perhaps applied systems analysis can help. The workshop set was about to: present new concepts and methodologies for managing the environment, and offer an open forum for the exchange of ideas among research disciplines, especially between agro-environmental and applied systems analysis research and between researchers and practitioners. The paper deal with a range of topics. The editors have arranged them into the following categories: (1) modeling methodologies, (2) data analysis, (3) land use, (4) water management, and (5) applications

Managing radiotherapy treatment trade-offs using multi-criteria optimisation and data envelopment analysis

Techniques for managing trade-offs between tumour control and normal tissue sparing in radiotherapy treatment planning are reviewed and developed. Firstly, a quality control method based on data envelopment analysis is proposed. The method measures the improvement potential of a plan by comparing the plan to other reference plans. The method considers multiple criteria, including one that represents anatomical variations between patients. An application to prostate cases demonstrates the capability of the method in identifying plans with further improvement potential. A multi-criteria based planning technique that considers treatment delivery is then proposed. The method integrates column generation in the revised normal boundary intersection method, which projects a set of equidistant reference points onto the non-dominated set to form a representative set of non-dominated points. The delivery constraints are considered in the column generation process. Essentially, the method generates a set of deliverable plans featuring a range of treatment trade-offs. Demonstrated by a prostate case, the method generates near-optimal plans that can be delivered with dramatically lower total fluence than the optimal ones post-processed for treatment delivery constraints. Finally, a navigation method based on solving interactive multi-objective optimisation for a discrete set of plans is developed. The method sets the aspiration values for criteria as soft constraints, thus allowing the planner to freely express his/her preferences without causing infeasibility. Navigation is conducted on planner-defined clinical criteria, including the non-convex dose-volume criteria and treatment delivery time. Navigation steps on a prostate case are demonstrated with a prototype implementation. The prostate case shows that optimisation criteria may not correctly reflect plan quality and can mislead a planner to select a “sub-optimal” plan. Instead, using clinical criteria provides the most relevant measure of plan quality, hence allowing the planner to quickly identify the most preferable plan from a representative set

Multiple criteria assessment of sustainability programs in the textile industry

To survive in the long term, business needs to profit, controlling environmental impacts with social responsibility. Sustainability programs involve the integration of social and environmental issues in business models and organizational processes. The assessment of sustainability programs is a problem of multiple criteria decision analysis (MCDA). This work presents applications of MCDA for the assessment of sustainability programs in the textile industry. Applied methods for MCDA are analytic hierarchy process (AHP) and the technique for the order of preference by similarity to ideal solution (TOPSIS). The reasons to apply AHP and TOPSIS include providing an assessment index, ranging from 0 to 1, and that the MCDA model is expected to have more criteria than alternatives. Therefore, an application of other methods, such as data envelopment analysis, could be prejudiced. Concepts from the triple bottom line, economic, social as well as environmental criteria were inserted in the proposed model. Sustainability programs of six leading companies from the Brazilian textile industry were evaluated. The main finding of the research is that AHP and TOPSIS resulted in similar evaluations for sustainability programs. Both methods resulted in the same rank of alternatives. However, with TOPSIS, companies’ sustainability indices were more disperse, varying from 0.10 to 0.92 against a range from 0.23 to 0.69 with AHP

Practical common weights scalarizing function approach for efficiency analysis

A characteristic of Data Envelopment Analysis (DEA) is to allow individual decision making units (DMUs) to select the factor weights which are the most advantageous for them in calculating their efficiency scores. This flexibility in selecting the weights, on the other hand, deters the comparison among DMUs on a common base. For dealing with this difficulty and assessing all the DMUs on the same scale, this paper proposes using a multiple objective linear programming (MOLP) approach based on scalarizing function for generating common set of weights under the DEA framework. This is an advantageous of the proposed approach against general approaches in the literature which are based on multiple objective nonlinear programming