Optimising a nonlinear utility function in multi-objective integer programming

In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the optimal utility value. This is done using already known solutions, linear programming relaxations, utility function inversion, and integer programming. We develop a general optimisation algorithm for use with k objectives, and we illustrate our approach using a tri-objective integer programming problem.Comment: 11 pages, 2 tables; v3: minor revisions, to appear in Journal of Global Optimizatio

Multi crteria decision making and its applications : a literature review

This paper presents current techniques used in Multi Criteria Decision Making (MCDM) and their applications. Two basic approaches for MCDM, namely Artificial Intelligence MCDM (AIMCDM) and Classical MCDM (CMCDM) are discussed and investigated. Recent articles from international journals related to MCDM are collected and analyzed to find which approach is more common than the other in MCDM. Also, which area these techniques are applied to. Those articles are appearing in journals for the year 2008 only. This paper provides evidence that currently, both AIMCDM and CMCDM are equally common in MCDM

XVI Congresso da Associação Portuguesa de Investigação Operacional: livro de resumos

Fundação para a Ciência e a Tecnologia - FC

Appropriate choice of aggregation operators in fuzzy decision support systems

Fuzzy logic provides a mathematical formalism for a unified treatment of vagueness and imprecision that are ever present in decision support and expert systems in many areas. The choice of aggregation operators is crucial to the behavior of the system that is intended to mimic human decision making. This paper discusses how aggregation operators can be selected and adjusted to fit empirical data&mdash;a series of test cases. Both parametric and nonparametric regression are considered and compared. A practical application of the proposed methods to electronic implementation of clinical guidelines is presented<br /

A Bayesian approach to find Pareto optima in multiobjective programming problems using Sequential Monte Carlo algorithms

In this paper we consider a new approach to multicriteria decision making problems. Such problems are, usually, cast into a Pareto framework where the objective functions are aggregated into a single one using certain weights. The problem is embedded into a statistical framework by adopting a posterior distribution for both the decision variables and the Pareto weights. This embedding dates back to [25] but in this work we operationalize the concept further. We propose a Metropolis-Hastings and a Sequential Monte Carlo (SMC) to trace out the entire Pareto frontier and / or find the global optimum of the problem. We apply the new techniques to a multicriteria portfolio decision making problem proposed in [37] and to a test problem proposed by [27]. The good performance of new techniques suggests that SMC and other algorithms, like the classical Metropolis-Hastings algorithm, can be used profitably in the context of multicriteria decision making problems to trace out the Pareto frontier and / or find a global optimum. Most importantly SMC can be considered as an off-the-shelf technique to solve arbitrary multicriteria decision making problems routinely and efficiently

A Bayesian approach to find Pareto optima in multiobjective programming problems using Sequential Monte Carlo algorithms

In this paper we consider a new approach to multicriteria decision making problems. Such problems are, usually, cast into a Pareto framework where the objective functions are aggregated into a single one using certain weights. The problem is embedded into a statistical framework by adopting a posterior distribution for both the decision variables and the Pareto weights. This embedding dates back to [25] but in this work we operationalize the concept further. We propose a Metropolis-Hastings and a Sequential Monte Carlo (SMC) to trace out the entire Pareto frontier and / or find the global optimum of the problem. We apply the new techniques to a multicriteria portfolio decision making problem proposed in [37] and to a test problem proposed by [27]. The good performance of new techniques suggests that SMC and other algorithms, like the classical Metropolis-Hastings algorithm, can be used profitably in the context of multicriteria decision making problems to trace out the Pareto frontier and / or find a global optimum. Most importantly SMC can be considered as an off-the-shelf technique to solve arbitrary multicriteria decision making problems routinely and efficiently

New Techniques and Algorithms for Multiobjective and Lexicographic Goal-Based Shortest Path Problems

Shortest Path Problems (SPP) are one of the most extensively studied problems in the fields of Artificial Intelligence (AI) and Operations Research (OR). It consists in finding the shortest path between two given nodes in a graph such that the sum of the weights of its constituent arcs is minimized. However, real life problems frequently involve the consideration of multiple, and often conflicting, criteria. When multiple objectives must be simultaneously optimized, the concept of a single optimal solution is no longer valid. Instead, a set of efficient or Pareto-optimal solutions define the optimal trade-off between the objectives under consideration. The Multicriteria Search Problem (MSP), or Multiobjective Shortest Path Problem, is the natural extension to the SPP when more than one criterion are considered. The MSP is computationally harder than the single objective one. The number of label expansions can grow exponentially with solution depth, even for the two objective case. However, with the assumption of bounded integer costs and a fixed number of objectives the problem becomes tractable for polynomially sized graphs. A wide variety of practical application in different fields can be identified for the MSP, like robot path planning, hazardous material transportation, route planning, optimization of public transportation, QoS in networks, or routing in multimedia networks. Goal programming is one of the most successful Multicriteria Decision Making (MCDM) techniques used in Multicriteria Optimization. In this thesis we explore one of its variants in the MSP. Thus, we aim to solve the Multicriteria Search Problem with lexicographic goal-based preferences. To do so, we build on previous work on algorithm NAMOA*, a successful extension of the A* algorithm to the multiobjective case. More precisely, we provide a new algorithm called LEXGO*, an exact label-setting algorithm that returns the subset of Pareto-optimal paths that satisfy a set of lexicographic goals, or the subset that minimizes deviation from goals if these cannot be fully satisfied. Moreover, LEXGO* is proved to be admissible and expands only a subset of the labels expanded by an optimal algorithm like NAMOA*, which performs a full Multiobjective Search. Since time rather than memory is the limiting factor in the performance of multicriteria search algorithms, we also propose a new technique called t-discarding to speed up dominance checks in the process of discarding new alternatives during the search. The application of t-discarding to the algorithms studied previously, NAMOA* and LEXGO*, leads to the introduction of two new time-efficient algorithms named NAMOA*dr and LEXGO*dr , respectively. All the algorithmic alternatives are tested in two scenarios, random grids and realistic road maps problems. The experimental evaluation shows the effectiveness of LEXGO* in both benchmarks, as well as the dramatic reductions of time requirements experienced by the t-discarding versions of the algorithms, with respect to the ones with traditional pruning

Enterprise resource planning selection using fuzzy entropy-based fuzzy MOORA method: case study in a bearing company

Seçim problemleri işletmeler açısından sıklıkla karşılaşılan ve karar vermesi zor olan problem tiplerindendir. Zor problem olmasının sebebi birçok kriter ve alternatifin aynı anda dikkate alınması gerektiği içindir. Bu problemlerin çözümü için genellikle çok kriterli karar verme yaklaşımları kullanılmaktadır. Seçim problemleri hayatın her aşamasında karşılaştığı için çok fazla çeşitlilik gösterebilmektedir. Bu çal ışmada bir işletmenin kurumsal kaynak planlaması (KKP) seçim süreci ele al ınmıştır. Yeni bir yazılım satın almak isteyen i şletmenin satın alma departmanı birçok kriter ve alternatif yazılım belirlemiştir. Bu kriterlerin en uygun düzeyde karşılandığı alternatif yazılımın seçilmesi planlanmıştır. Bu problemin çözümü için kriter ağırlıkların belirlenmesi aşamasında bulanık Entropi yöntemi kullanılmıştır. Yazılım alternatiflerinin değerlendirilmesi sürecinde bulanık Oran Analiziyle Çok Amaçlı Optimizasyon (MOORA) yöntemi kullanılmış ve yazılımlardan en uygun olanına karar verilmiştir. Çalışma sonucunda belirlenen üç yazılım sisteminden en uygun olanın üçüncü yazılım sistemi olduğu görülmüştür