Multiple Criteria Decision Analysis: State of the Art Surveys

This chapter aims at providing concrete reflections about the use of the Multiple Criteria Decision Analysis (MCDAs) in urban and territorial decision processes. The reflections provided by this chapter come from a critical analysis of different case studies faced by the Turin research group (Politecnico di Torino, InterUniversity Department DIST) composed by the authors, in some case in collaboration with other academics. Over the last decade in fact, the authors applied a number of MCDA to case studies of different nature in order to provide answers to decision-making problems in urban and territorial planning realms, towards a sustainable development. Specifically, the case studies analysed in this chapter refer to seven contexts: (i) infrastructural transport planning strategies; (ii) location of undesirable facilities; (iii) strategic urban planning; (iv) urban energy retrofitting; (v) real estate investments; (vi) cultural adaptive reuse of abandoned buildings; and (vii) environmental systems. The aforementioned case studies cover different geographical scales of intervention (local, national and transnational) offering here the opportunity to reflect around the use of MCDA as Analytic Network Process (ANP), ANP and Spatial Decision Support Systems (SDSS), Dominance Based Rough-Sets Approach (DRSA), Measuring Attractiveness by a Categorical Based Evaluation Technique (MACBETH), Preference Ranking Organization METHod for Enrichment of Evaluations (PROMETHEE), CATegorization by Similarity-Dissimilarity (CAT-SD) and Elimination Et Choix Traduisant La Realité (ELECTRE). The applications presented show that the MCDA can be a useful support to the decision-makers in order to structure the decision process in exam, characterized by a plurality of stakeholders with different interests, powers and goals. In particular, starting from the case studies, the authors highlight the applicability and the decision-making relevance of the different MCDA.

Various Multi-Criteria Decision Making (MCDM) methods have been developed to support decision making process. The main aim of all MCDM methods is to obtain ranking of the alternatives and select the best one under conflicting criteria. In this paper, a combined MCDM approach is proposed based on MACBETH (Measuring Attractiveness by a Categorical Based Evaluation TecHnique) and MULTI-MOORA (Multi Objective Optimization on the basis of Ratio Analysis) methods. In this combined approach, the weights of the criteria are determined with MACBETH method and then MULTI-MOORA method is used to obtain the final ranking of the alternatives. At the end of the paper, to illustrate the applicability of the proposed approach an application of the automobile selection of a marble company is also given.

A hybrid MCDM methodology for ERP selection problem with interacting criteria

There have been many developments in multiple criteria decision‐making (MCDM) during the last 50 years. Researchers from different areas have also recognized the multiple‐criteria nature of problems in their application areas and tried to address these issues. Unfortunately, there has not always been sufficient information flow between the researchers in the MCDM area and the researchers applying MCDM to their problems. More recently, multiobjective combinatorial optimization (MOCO) and multiobjective metaheuristic areas have been enjoying substantial developments. These problems are hard to solve. Many researchers addressed the problem of finding all nondominated solutions. This is a difficult task for MOCO problems. This difficulty limits many of the studies to concentrate on bicriteria problems. In this paper, I review some MCDM approaches that aim to find only the preferred solutions of the decision maker (DM). I argue that this is especially important for MOCO problems. I discuss several of our approaches that incorporate DM's preferences into the solution process of MOCO problems and argue that there is a need for more work to be done in this area. Copyright © 2009 John Wiley & Sons, Ltd.

In its current state, evolutionary multiobjective optimization (EMO) is an established field of research and application with more than 150 PhD theses, more than ten dedicated texts and edited books, commercial softwares and numerous freely downloadable codes, a biannual conference series running successfully since 2001, special sessions and workshops held at all major evolutionary computing conferences, and full-time researchers from universities and industries from all around the globe. In this chapter, we provide a brief introduction to EMO principles, illustrate some EMO algorithms with simulated results, and outline the current research and application potential of EMO. For solving multiobjective optimization problems, EMO procedures attempt to find a set of well-distributed Pareto-optimal points, so that an idea of the extent and shape of the Pareto-optimal front can be obtained. Although this task was the early motivation of EMO research, EMO principles are now being found to be useful in various other problem solving tasks, enabling one to treat problems naturally as they are. One of the major current research thrusts is to combine EMO procedures with other multiple criterion decision making (MCDM) () tools so as to develop hybrid and interactive multiobjective optimization algorithms for finding a set of trade-off optimal solutions and then choose a preferred solution for implementation. This chapter provides the background of EMO principles and their potential to launch such collaborative studies with MCDM researchers in the coming years.

Many optimization problems are multiobjective in nature in the sense that multiple, conflicting criteria need to be optimized simultaneously. Due to the conflict between objectives, usually, no single optimal solution exists. Instead, the optimum corresponds to a set of so-called Pareto-optimal solutions for which no other solution has better function values in all objectives. Evolutionary Multiobjective Optimization (EMO) algorithms are widely used in practice for solving multiobjective optimization problems due to several reasons. As randomized blackbox algorithms, EMO approaches allow to tackle problems with nonlinear, nondifferentiable, or noisy objective functions. As set-based algorithms, they allow to compute or approximate the full set of Pareto-optimal solutions in one algorithm run - opposed to classical solution-based techniques from the multicriteria decision making (MCDM) field. Using EMO approaches in practice has two other advantages: they allow to learn about a problem formulation, for example, by automatically revealing common design principles among (Pareto-optimal) solutions (innovization) and it has been shown that certain single-objective problems become easier to solve with randomized search heuristics if the problem is reformulated as a multiobjective one (multiobjectivization). This tutorial aims at giving a broad introduction to the EMO field and at presenting some of its recent research results in more detail. More specifically, we are going to (i) introduce the basic principles of EMO algorithms in comparison to classical solution-based approaches, (ii) show a few practical examples which motivate the use of EMO in terms of the mentioned innovization and multiobjectivization principles, and (iii) present a general overview of state-of-the-art algorithms and techniques. Moreover, we will present some of the most important research results in areas such as indicator-based EMO, preference articulation, surrogate-assisted EMO, and performance assessment. Though classified as introductory, this tutorial is intended for both novices and regular users of EMO. Those without any knowledge will learn about the foundations of multiobjective optimization and the basic working principles of state-of-the-art EMO algorithms. Open questions, presented throughout the tutorial, can serve for all participants as a starting point for future research and/or discussions during the conference.

Many optimization problems are multiobjective in nature in the sense that multiple, conflicting criteria need to be optimized simultaneously. Due to the conflict between objectives, usually, no single optimal solution exists. Instead, the optimum corresponds to a set of so-called Pareto-optimal solutions for which no other solution has better function values in all objectives. Evolutionary Multiobjective Optimization (EMO) algorithms are widely used in practice for solving multiobjective optimization problems due to several reasons. As randomized blackbox algorithms, EMO approaches allow to tackle problems with nonlinear, nondifferentiable, or noisy objective functions. As set-based algorithms, they allow to compute or approximate the full set of Pareto-optimal solutions in one algorithm runeopposed to classical solution-based techniques from the multicriteria decision making (MCDM) field. Using EMO approaches in practice has two other advantages: they allow to learn about a problem formulation, for example, by automatically revealing common design principles among (Pareto-optimal) solutions (innovization) and it has been shown that certain single-objective problems become easier to solve with randomized search heuristics if the problem is reformulated as a multiobjective one (multiobjectivization). This tutorial aims at giving a broad introduction to the EMO field and at presenting some of its recent research results in more detail. More specifically, we are going to (i) introduce the basic principles of EMO algorithms in comparison to classical solution-based approaches, (ii) show a few practical examples which motivate the use of EMO in terms of the mentioned innovization and multiobjectivization principles, and (iii) present a general overview of state-of-the-art algorithms and techniques. Moreover, we will present some of the most important research results in areas such as indicator-based EMO, preference articulation, surrogate-assisted EMO, and performance assessment. Though classified as introductory, this tutorial is intended for both novices and regular users of EMO. Those without any knowledge will learn about the foundations of multiobjective optimization and the basic working principles of state-of-the-art EMO algorithms. Open questions, presented throughout the tutorial, can serve for all participants as a starting point for future research and/or discussions during the conference.

During the implementations of enterprise resource planning (ERP) systems, most companies have experienced some problems, one of which is how to determine the best ERP software satisfying their needs and expectations. Because improperly selected ERP software may have an impact on the time required, and the costs and market share of a company, selecting the best desirable ERP software has been the most critical problem for a long time. On the other hand, selecting ERP software is a multiple-criteria decision-making (MCDM) problem, and in the literature, many methods have been introduced to evaluate this kind of problem, one of which is the analytic hierarchy process (AHP), which has been widely used in MCDM selection problems. However, in this paper, we use a fuzzy extension of an analytic network process (ANP), a more general form of AHP, which uses uncertain human preferences as input information in the decision-making process, because the AHP cannot accommodate the variety of interactions, dependencies, and feedback between higher- and lower-level elements. Instead of using the classical eigenvector prioritization method in the AHP, only employed in the prioritization stage of ANP, a fuzzy-logic method providing more accuracy on judgements is applied. The resulting fuzzy ANP enhances the potential of the conventional ANP for dealing with imprecise and uncertain human comparison judgements. In short, in this paper, an intelligent approach to ERP software selection through a fuzzy ANP is proposed by taking into consideration quantitative and qualitative elements to evaluate ERP software alternatives.

Many optimization problems are multiobjective in nature in the sense that multiple, conflicting criteria need to be optimized simultaneously. Due to the conflict between objectives, usually, no single optimal solution exists. Instead, the optimum corresponds to a set of so-called Pareto-optimal solutions for which no other solution has better function values in all objectives. Evolutionary Multiobjective Optimization (EMO) algorithms are widely used in practice for solving multiobjective optimization problems due to several reasons. As randomized blackbox algorithms, EMO approaches allow to tackle problems with nonlinear, nondifferentiable, or noisy objective functions. As set-based algorithms, they allow to compute or approximate the full set of Pareto-optimal solutions in one algorithm run---opposed to classical solution-based techniques from the multicriteria decision making (MCDM) field. Using EMO approaches in practice has two other advantages: they allow to learn about a problem formulation, for example, by automatically revealing common design principles among (Pareto-optimal) solutions (innovization) and it has been shown that certain single-objective problems become easier to solve with randomized search heuristics if the problem is reformulated as a multiobjective one (multiobjectivization).This tutorial aims at giving a broad introduction to the EMO field and at presenting some of its recent research results in more detail. More specifically, we are going to (i) introduce the basic principles of EMO algorithms in comparison to classical solution-based approaches, (ii) show a few practical examples which motivate the use of EMO in terms of the mentioned innovization and multiobjectivization principles, and (iii) present a general overview of state-of-the-art algorithms and techniques. Moreover, we will present some of the most important research results in areas such as indicator-based EMO, preference articulation, and performance assessment.Though classified as introductory, this tutorial is intended for both novices and regular users of EMO. Those without any knowledge will learn about the foundations of multiobjective optimization and the basic working principles of state-of-the-art EMO algorithms. Open questions, presented throughout the tutorial, can serve for all participants as a starting point for future research and/or discussions during the conference.

Preface. Acknowledgements. 1. Introduction. 1.1 Planning and decision support. 1.2 Forest management planning. 1.3 History of forest planning.- Discrete problems. 2. Unidimensional problems. 2.1 Decisions under risk and uncertainty. 2.2 Measuring utility and value. 2.2.1 Estimating a utility function. 2.2.2 Estimating a value function.- 3. Multi-criteria decision problems. 3.1 Theoretical aspects. 3.2 Multi-attribute utility functions. 3.2.1 Function forms. 3.2.2 Basis for estimating the weights. 3.2.3 SMART. 3.3 Even Swaps. 3.4 Analytic hierarchy process. 3.4.1 Decision problem. 3.4.2 Phases of AHP. 3.4.3 Uncertainty in AHP. 3.4.4 ANP. 3.5 A'WOT.- 4. Uncertainty in multi-criteria decision making. 4.1 Nature of uncertainty. 4.2 Fuzzy set theory. 4.2.1 Membership functions and fuzzy numbers. 4.2.2 Fuzzy goals in decision making. 4.2.3 Fuzzy additive weighting. 4.3 Possibility theory in decision making. 4.4 Evidence theory. 4.5 Outranking methods. 4.5.1 Outline. 4.5.2 PROMETHEE method. 4.5.3 ELECTRE method. 4.5.4 Other outranking methods. 4.6 Probabilistic uncertainty in decision analysis. 4.6.1 Stochastic multicriteria acceptability analysis (SMAA). 4.6.2 SMAA-O. 4.6.3 Pairwise probabilities.- Continuous problems. 5. Optimization. 5.1 Linear programming. 5.1.1 Primal problem. 5.1.2 Dual problem. 5.1.3 Forest planning problem with several stands. 5.1.4 JLP software. 5.2 Goal programming. 5.3 Integer programming. 5.4 Uncertainty in optimization. 5.5 Robust portfolio modelling. 5.5.1 Principles of the method. 5.5.2 Use of RPM in forest planning.- 6. Heuristic optimization. 6.1 Principles. 6.2 Objective function forms. 6.3 HERO. 6.4 Simulated annealing and threshold accepting. 6.5 Tabu search. 6.6 Genetic algorithms. 6.7 Improving the heuristic search. 6.7.1 Parameters of heuristic optimisation techniques. 6.7.2 Expanding the neighbourhood. 6.7.3 Combining optimisation techniques.- Cases with several decision makers. 7. Group decision making and participatory planning. 7.1 Decision makers and stakeholders. 7.2 Public participation process. 7.2.1 Types of participation process. 7.2.2 Success of the participation process. 7.2.3 Defining the appropriate process. 7.3 Tools for eliciting the public preferences. 7.3.1 Surveys. 7.3.2 Public hearings. 7.4 Problem structuring methods. 7.4.1 Background. 7.4.2 Strategic options development and analysis (SODA). 7.4.3 Soft systems methodology (SSM). 7.5 Decision support for group decision making.- 8. Voting methods. 8.1 Social choice theory. 8.1.1 Outline. 8.1.2 Evaluation criteria for voting systems. 8.2 Positional voting schemes. 8.2.1 Plurality voting. 8.2.2 Approval voting. 8.2.3 Borda count. 8.3 Pairwise voting. 8.4 Fuzzy voting. 8.5 Probability voting. 8.6 Multicriteria approval. 8.6.1 Original method. 8.6.2 Fuzzy MA. 8.6.3 Multicriteria approval voting.- Application viewpoints. 9. Behavioural aspects. 9.1 Criticism towards decision theory. 9.1.1 Outline. 9.1.2 Satisficing or maximizing?. 9.1.3 Rules or rational behaviour?. 9.2 Image theory. 9.3 Prospect theory.- 10. Practical examples of using MCDS methods. 10.1 Landscape ecological planning. 10.2 Participatory planning. 10.3 Spatial objectives and heuristic optimisation in practical forest planning.- 11. Final remarks.-

Selection of suitable sites for wind power plants is one of the most important decision on wind resources development. Site selection for the establishment of large wind power plants requires spatial evaluation taking technical, economic, and environmental considerations into account. This study has applied a combination of PROMETHEE and Fuzzy AHP methods in a geographical information system environment to carry out spatial site selection for wind power plants in Lorestan Province of Iran. The fuzzy analytic hierarchy process method is used to determine the weights of the criteria whereas the PROMETHEE method is used to prioritise the alternatives based on the weights obtained from the fuzzy AHP. The integration of GIS and MCDM makes a powerful tool for the selection of the best suitable sites because GIS provides efficient manipulation, analysis and presentation of spatial data while MCDM supplies consistent weight of alternatives and criteria.The results showed that about 7.38 % of the area of Lorestan province is most suitable for wind power plants development. Sensitivity analysis shows that suitable zones coincide with suitable divisions of the input layers. The sensitivity analysis showed satisfactory results for the combination of PROMETHEE and Fuzzy AHP methods in wind power plant site selection.

The integration of Multi-Objective Optimization (MOO) and Multi-Criteria Decision-Making (MCDM) has gathered significant attention across various scientific research domains to facilitate integrated sustainability assessment. Recently, there has been a growing interest in hybrid approaches that combine MCDM with MOO, aiming to enhance the efficacy of the final decisions. However, a critical gap exists in terms of providing clear methodological guidance, particularly when dealing with data uncertainties. To address this gap, this systematic review is designed to develop a generic decision tree that serves as a practical roadmap for practitioners seeking to perform MOO and MCDM in an integrated fashion, with a specific focus on accounting for uncertainties. The systematic review identified the recent studies that conducted both MOO and MCDM in an integrated way. It is important to note that this review does not aim to identify the superior MOO or MCDM methods, but rather it delves into the strategies for integrating these two common methodologies. The prevalent MOO methods used in the reviewed articles were evolution-based metaheuristic methods. TOPSIS and PROMETHEE II are the prevalent MCDM ranking methods. The integration of MOO and MCDM methods can occur either a priori, a posteriori, or through a combination of both, each offering distinct advantages and drawbacks. The developed decision tree illustrated all three paths and integrated uncertainty considerations in each path. Finally, a real-world case study for the pulse fractionation process in Canada is used as a basis for demonstrating the various pathways presented in the decision tree and their application in identifying the optimized processing pathways for sustainably obtaining pulse protein. This study will help practitioners in different research domains use MOO and MCDM methods in an integrated way to identify the most sustainable and optimized system.

Started during 1993-95 with three different algorithms, evolutionary multi-objective optimization (EMO) has come a long way in a quick time to establish itself as a useful field of research and application. Till to date, there exist numerous textbooks and edited books, commercial softwares dedicated to EMO algorithms, freely downloadable codes in most-used computer languages, a biannual conference series (called EMO conference series) running successfully since 2001, and special sessions and workshops held in almost all major evolutionary computing conferences. In this paper, we discuss briefly the principles of EMO through an illustration of one specific algorithm.Thereafter, we focus on mentioning a few recent research and application developments of EMO. Specifically, we discuss EMO's use with multiple criterion decision making (MCDM) procedures and EMO's applicability in handling of a large number of objectives. Besides, the concept of multi-objectivization and innovization --- which are practically motivated, is discussed next. A few other key advancements are also highlighted. The development and application of EMO to multi-objective optimization problems and their continued extensions to solve other related problems have elevated the EMO research to a level which may now undoubtedly be termed as an active field of research with a wide range of theoretical and practical research and application opportunities. EMO concepts are ready to be applied to search based software engineering (SBSE) problems.

This report documents the program and outcomes of the Dagstuhl Seminar 15031 Understanding Complexity in Multiobjective Optimization. This seminar carried on the series of four previous Dagstuhl Seminars (04461, 06501, 09041 and 12041) that were focused on Multiobjective Optimization, and strengthening the links between the Evolutionary Multiobjective Optimization (EMO) and Multiple Criteria Decision Making (MCDM) communities. The purpose of the seminar was to bring together researchers from the two communities to take part in a wide-ranging discussion about the different sources and impacts of complexity in multiobjective optimization. The outcome was a clarified viewpoint of complexity in the various facets of multiobjective optimization, leading to several research initiatives with innovative approaches for coping with complexity. Seminar January 11–16, 2015 – http://www.dagstuhl.de/15031 1998 ACM Subject Classification G.1.6 Optimization, H.4.2 Types of Systems, I.2.6 Learning, I.2.8 Problem Solving, Control Methods, and Search, I.5.1 Models

This report documents the program and outcomes of the Dagstuhl Seminar 15031 Understanding Complexity in Multiobjective Optimization. This seminar carried on the series of four previous Dagstuhl Seminars (04461, 06501, 09041 and 12041) that were focused on Multiobjective Optimization, and strengthening the links between the Evolutionary Multiobjective Optimization (EMO) and Multiple Criteria Decision Making (MCDM) communities. The purpose of the seminar was to bring together researchers from the two communities to take part in a wide-ranging discussion about the different sources and impacts of complexity in multiobjective optimization. The outcome was a clarified viewpoint of complexity in the various facets of multiobjective optimization, leading to several research initiatives with innovative approaches for coping with complexity.