João Clímaco

Relating reference points and weights in MOLP

A frequent problem for decision makers (DMs) analysing decisions involving multiple objectives is the identification and selection of the most preferred option from the set of non-dominated solutions. Two techniques, weighted sum optimization and reference point optimization, have been developed to address this problem for multiobjective linear programming problems (MOLP). In this paper, we examine the relationship between these two techniques. We demonstrate that the values of the dual variables associate with auxiliary constraints of the reference point technique are equal to the weight values used to compute the same non-dominated solution via the weighted sum technique. This insight will enable the development of new interactive solution procedures for MOLPs which allow the DM to readily switch from one method to the other during the search for the most preferred non-dominated solution. The advantages of the approach are discussed in the paper. Copyright

Multicriteria Analysis in Telecommunication Network Planning and Design: A Survey

The interaction between a complex socio-economic environment and the extremely fast pace of development of new telecommunication technologies and services justifies the interest of multicriteria evaluation in decision making processes associated with several phases of network planning and design. Based on an overview of current and foreseen evolutions in telecommunication network technologies and services we begin by identifying and discussing challenges and issues concerning the use of multicriteria analysis in telecommunication network planning and design problems. Next we present a review of contributions on these areas, with particular emphasis on routing and network design models. We will also outline an agenda of current and future research trends and issues in this application area of multicriteria modelling.

DECISION SUPPORT IN RURAL TELECOMMUNICATION NETWORK PLANNING

In this work we present the relevant features and methodological approaches of a DSS (Decision Support System) for dynamic planning of rural telecommunication networks. We outline the complexities and difficulties of the formulation and of the planning process. A relevant feature of the model is the attempt to integrate AI techniques and specialized heuristics (using mathematical programming algorithms for particular sub-problems), aiming at obtaining solutions of better quality. The structure of the DSS is presented and justified as well as the main procedures of the model, regarded from the point of view of the decision environment.

Surrogate Scalar Functions and Scalarizing Techniques

The most common procedure to compute efficient/nondominated solutions in MOP is using a scalarizing technique, which consists in transforming the original multiobjective problem into a single objective problem that may be solved repeatedly with different parameters. The functions employed in scalarizing techniques are called surrogate scalar functions or scalarizing functions. The optimal solution to these functions should be anon dominated solution to the multiobjective problem. These functions temporarily aggregate in a single dimension the p objective functions of the original model and include parameters derived from the elicitation of the DM’s preference information. Surrogate scalar functions should be able to generate nondominated solutions only, obtain any nondominated solution and be independent of dominated solutions. In addition, the computational effort involved in the optimization of surrogate scalar functions should not be too demanding (e.g., increasing too much the dimension of the surrogate problem or resorting to nonlinear scalarizing functions when all original objective functions are linear) and the preference information parameters should have a simple interpretation (i.e., not imposing an excessive cognitive burden on the DM). Surrogate scalar functions should not be understood as “true” analytical representations of the DM’s preferences but rather as an operational means to transitorily aggregate the multiple objective functions and generate nondominated solutions to be proposed to the DM, which expectedly are in accordance with his/her (evolving) preferences.

A Guided Tour of iMOLPe

The interactive MOLP explorer (iMOLPe) software is a computational package to deal with MOLP problems, which has been developed by the authors and accompanies this book. This computational package is mainly designed for teaching and decision support purposes in MOLP problems. The aim is to offer students in engineering, management, economics and applied mathematics an intuitive environment as the entrance door to multiobjective optimization in which the main theoretical and methodological concepts can be apprehended through experimentation, thus enabling them to learn at their own pace (Alves et al. 2015).

Formulations and Definitions

Multiobjective Programming (MOP) may be faced as the extension of classical single objective programming to the cases in which more than one objective function is explicitly considered in mathematical optimization models. However, if these functions are conflicting, a paradigm change is at stake. The concept of optimal solution no longer makes sense since, in general, there is no feasible solution that simultaneously optimizes all objective functions. Single objective programming follows the optimality paradigm, that is, there is a complete comparability between pairs of feasible alternatives and transitivity applies. This is a mathematically well-formulated problem, since we possess enough mathematical tools to solve the three fundamental questions of analysis: existence, unicity and construction of the solution. When more than one objective function is considered these properties are no longer valid.

Interactive Methods in Multiobjective Linear Programming

In multiobjective programming problems, the methods dedicated to the generation of the whole set of nondominated solutions are in most cases inadequate from a practical point of view. In general, in real world models, the computational burden required for computing the entire set of nondominated solutions is too high. Moreover, proposing hundreds or thousands of solutions to a decision maker (DM) is not useful for the exploitation of results in practice, even limiting the computation to a subset of the nondominated solutions, for instance vertices of the feasible region in MOLP problems.

Stochastic hierarchical multiobjective routing model in MPLS networks with two service classes: an experimental study on imprecision and uncertainty issues

The paper begins by reviewing a two-level hierarchical multicriteria routing model for Multiprotocol Label Switching networks with two service classes (Quality of Service and Best Effort services) and alternative routing, previously proposed by the authors. The features of the considered resolution heuristic are described. Some key issues raised by its complexity are discussed, as well as the major factors that constitute the sources of imprecision, inaccuracy, and uncertainty of the model and the way in which they are dealt with in the adopted resolution approach. Analytic and stochastic discrete-event simulation experiments are performed for different test networks, including experiments with a dynamic version of the routing method. This case study allows for the evaluation of the inaccuracies intrinsic to the analytic/numerical resolution procedures and of the uncertainty associated with the estimates of the mean of the stochastic traffic flows. An analysis focused on key robustness aspects of the model is also carried out.AMS Subject ClassificationPrimary 90B50; secondary 90B18; 90B15

On the potentialities of AI to deal with the combinatorial complexity of a telecommunication network planning problem

Abstract The mathematical modeling of many real world problems is a complex and eventually an impracticable task when it leads to a combinatorial explosion. Previous papers have described the structure of a decision support system (DSS) for rural telephone network planning 1 and the structure of a knowledge based system, integrated in the DSS, to support a post-optimal analysis of the results obtained using heuristic techniques. 2 This paper attempts to show the potentialities of AI knowledge-representation techniques for improving heuristic approaches to combinatorially complex problems arising in a rural telephone network planning model.