Multi-criteria Setting Research Articles

Classes of multiojectives games possessing Pareto equilibria

In this paper we study non cooperative games with potential as introduced by Monderer and Shapley in 1996. We extend the notions of weighted and ordinal potential games to a multicriteria setting and study their Pareto equilibria. The importance of these games is the existence of Pareto equilibria in pure strategies and in the finite case and the approximate equilibria for some classes of infinite potential games. Some applications are studied via potential games: a water resource problem, a voluntary contribution model, peering games for telecommunication models.

A SURVEY ON MULTIOBJECTIVE DESCENT METHODS

We present a rigorous and comprehensive survey on extensions to the multicriteria setting of three well-known scalar optimization algorithms. Multiobjective versions of the steepest descent, the projected gradient and the Newton methods are analyzed in detail. At each iteration, the search directions of these methods are computed by solving real-valued optimization problems and, in order to guarantee an adequate objective value decrease, Armijo-like rules are implemented by means of a backtracking procedure. Under standard assumptions, convergence to Pareto (weak Pareto) optima is established. For the Newton method, superlinear convergence is proved and, assuming Lipschitz continuity of the objectives second derivatives, it is shown that the rate is quadratic

A Bayesian Design Space for Analytical Methods Based on Multivariate Models and Predictions

The International Conference for Harmonization (ICH) has released regulatory guidelines for pharmaceutical development. In the document ICH Q8, the design space of a process is presented as the set of factor settings providing satisfactory results. However, ICH Q8 does not propose any practical methodology to define, derive, and compute design space. In parallel, in the last decades, it has been observed that the diversity and the quality of analytical methods have evolved exponentially, allowing substantial gains in selectivity and sensitivity. However, there is still a lack of a rationale toward the development of robust separation methods in a systematic way. Applying ICH Q8 to analytical methods provides a methodology for predicting a region of the space of factors in which results will be reliable. Combining design of experiments and Bayesian standard multivariate regression, an identified form of the predictive distribution of a new response vector has been identified and used, under noninformative as well as informative prior distributions of the parameters. From the responses and their predictive distribution, various critical quality attributes can be easily derived. This Bayesian framework was then extended to the multicriteria setting to estimate the predictive probability that several critical quality attributes will be jointly achieved in the future use of an analytical method. An example based on a high-performance liquid chromatography (HPLC) method is given. For this example, a constrained sampling scheme was applied to ensure the modeled responses have desirable properties.

An integrated case-based reasoning approach for personalized itinerary search in multimodal transportation systems

Suggesting personalized itinerary search for travelers in a multimodal transportation system is a challenging problem. This is due to the increased complexity and diversity of transportation means, the intricacy and multitude of destinations along with the amount of rapidly changing information available to the traveler. Providing the transportation user with the relevant information that only meets his needs, preferences and personal profile is of foremost importance in efficiently supporting passenger mobility requirements in a large urban agglomeration.In this paper, we propose a multi-criteria approach for suggesting personalized itinerary to transportation users based on their preferences and needs. The proposed approach integrates case-based reasoning with Choquet integral to suggest the itinerary that best matches the user’s preferences. Further, the proposed method predicts the user’s behavior by comparing his preferences to those of other users with the same preferences for a given context. This will help the user to adopt the best action when facing a new situation in his itinerary search.This will help the user adopt the best action facing a new situation. Personalized information retrieval is processed based on criteria which weights are determined using the two-additive Choquet integral. The performance of the proposed algorithm was assessed by solving a real-life itinerary planning problem defined in the Tunisian urban public transit network. A comparison study involving both qualitative and quantitative assessment of the proposed approach as compared to two other methods was also carried out. Based on the performance analysis, as well as the comparison study, our new approach provides the best solutions for applications requiring personalization based user’s preferences in a multi-criteria setting.

A column-generation-based method for multi-criteria direct aperture optimization

Navigation-based multi-criteria optimization has been introduced to radiotherapy planning in order to allow the interactive exploration of trade-offs between conflicting clinical goals. However, this has been mainly applied to fluence map optimization. The subsequent leaf sequencing step may cause dose discrepancy, leading to human iteration loops in the treatment planning process that multi-criteria methods were meant to avoid. To circumvent this issue, this paper investigates the application of direct aperture optimization methods in the context of multi-criteria optimization. We develop a solution method to directly obtain a collection of apertures that can adequately span the entire Pareto surface. To that end, we extend the column generation method for direct aperture optimization to a multi-criteria setting in which apertures that can improve the entire Pareto surface are sequentially identified and added to the treatment plan. Our proposed solution method can be embedded in a navigation-based multi-criteria optimization framework, in which the treatment planner explores the trade-off between treatment objectives directly in the space of deliverable apertures. Our solution method is demonstrated for a paraspinal case where the trade-off between target coverage and spinal-cord sparing is studied. The computational results validate that our proposed method obtains a balanced approximation of the Pareto surface over a wide range of clinically relevant plans.

SU‐E‐T‐853: Robust Multicriteria Optimization for IMPT

Purpose: A time and memory efficient projection algorithm for solving large scale IMPT treatment plans in a multicriteria setting has been published. However, the more conformal dose distribution of IMPT compared with that of IMRT comes with its sensitivity to uncertainties such as proton range uncertainty and set‐up error. To design a practically efficacious IMPT treatment system, robustness has to be accounted for to reduce the uncertainties. Methods: A nominal scenario and eight worst‐case scenarios (six extreme patient positions,proton beam undershoot and overshoot) are used to sample the uncertainty space. A solution can be constrained using a subset or all of the nine scenarios to be robust given any realization of the random errors. Moreover, the best quality plan can be pursued by navigating the Pareto space constituted by a number of optimal plans according to their own criteria of optimality. The method deals with very fine dose grid and tens of thousands modulated proton beamlets, therefore fully utilizes the potential of IMPT. Results: A base of skull case with 1mm dose‐grid resolution is applied to demonstrate the robustness of the solution. Compared to the plan obtained by the same problem formulation but considering only the nominal scenario, the DVH band of the robust plan is more stable, meaning the dose distribution varies little under even the worst scenario. The optimization for each task takes only seconds on a standard computer, making a computationally friendly interface possible to the planner. Conclusions: The uncertainty pertinent to the IMPT procedure can be reduced during treatment planning by optimizing some best plans that emphasize different treatment objectives and then interactively seeking for a compromised one from the Pareto solution space. The method works very fast for rather fine dose grid and sufficiently large beamlet numbers, thus streamlines the IMPT treatment process.

Pricing decisions in a multi-criteria setting for product recovery facilities

Unpredictability in the arrival time and quantity of discarded products at product recovery facilities (PRFs) and varying demand for recovered components contribute to the volatility in their inventory levels. Achieving profit under such capricious inventory levels and stringent environmental legislations remains a challenge to many PRFs. This paper presents a multi-criteria decision model to determine a pricing policy that can simultaneously address two issues: stabilize inventory fluctuations and boost profits. The model considers that PRFs passively accepts discarded products as well as acquires them proactively if necessary. Under a multi-criteria setting, the current work determines prices of reusable and recyclable components to maximize revenue and minimize product recovery costs. A genetic algorithm is employed to solve the multi-criteria decision making problem. Sensitivity analysis is performed to investigate the effect of sorting yield, disassembly yield, and reusable component yield on the profits, prices, inventory levels, and disposal quantities.

Supporting Collaborative Multi-Criteria Evaluation

This article presents the VIP Analysis plug-in of Decision Deck 1.1, a platform that hosts different evaluation methods to support decision makers in the collaborative evaluation of alternatives in a multi-criteria and multi-experts setting. VIP Analysis is a tool for aggregation of multicriteria performances by means of an additive value function under imprecise information. It allows conducting a multicriteria analysis for selecting an alternative when the decision makers are not able to (or do not wish to) fix precise values for the importance parameters. These parameters are seen as variables that may take several values subject to constraints. VIP Analysis incorporates different methods to support the progressive reduction of the number of alternatives, introducing a concept of tolerance that lets decision makers use some of the methods in a more flexible manner. When compared with the original standalone VIP Analysis (programmed in the late 1990s) the main innovation of the VIP Analysis plug-in is to allow several users working on the same problem under different roles: coordinator, evaluator, and decision-maker, thus defining a workflow process and enabling concurrent and remote access to the data over a network. By being included in the Decision Deck platform, VIP Analysis is now integrated with other decision aiding methods within a coherent interface. A final advantage is that the platform is open-source, which facilitates customization and collaborative improvement of the software.

Combustion engine optimization: a multiobjective approach

To simulate the physical and chemical processes inside combustion engines is possible by appropriate software and high performance computers. For combustion engines a good design is such that it combines a low fuel consumption with low emissions of soot and nitrogen oxides. These are however partly conflicting requirements. In this paper we approach this problem in a multi-criteria setting which has the advantage that it is possible to estimate the trade off between the different objectives and the decision of the optimal solution is postponed until all possibilities and limitations are known. The optimization algorithm is based on surrogate models and is here applied to optimize the design of a diesel combustion engine.

Multicriteria–multistage planning for the optimal path selection using hybrid genetic algorithms

The problem of the competence set expansion involves determining the optimal expansion path under the minimum cost and time. As we know, the conventional competence set model only considers the problems of the static situation and the single objective. However, the dynamic situation and the multicriteria should also be simultaneously considered in practice. In this paper, a multicriteria and multistage competence set model is proposed. In order to efficiently obtain an optimal expansion path, hybrid genetic algorithms (HGA) are employed. In addition, a numerical example is used to demonstrate the proposed method. On the basis of the numerical results, we can conclude that the proposed method can provide a sound competence set model by simultaneously considering the multicriteria and multistage situations.

Decisionarium - aiding decisions, negotiating and collecting opinions on the web

Decisionarium (www.decisionarium.hut.fi) is the first public site for interactive multicriteria decision support with tools for individual decision-making as well as for group collaboration and negotiation. Web-HIPRE (www.hipre.hut.fi) supports value tree and AHP analysis including group models. The RICH methodology (www.rich.hut.fi) allows the decision maker to provide incomplete ordinal preference statements when considering the relative importance of attributes in a value tree. Opinions-Online (www.opinion.huf.fi) is a platform for surveys voting and group collaboration. There are different ways for voting, multiattribute scoring, surveys as well as interactive viewing of the results. Joint Gains (www.jointgains.hut.fi) applies the method of improving directions to support multiparty negotiations in a multicriteria setting. Smart Swaps offers an implementation of the even swaps procedure (www.smart-swaps.hut.fi). All of the tools above are web-based, so global interaction is natural and links can be utilized for multimedia information support. Decisionarium also offers access to complete e-learning modules (www.dm.hut.fi) based on the use of the software. There are also illustrative powerpoint presentations and additional Windows software WINPRE and PRIME-Decisions for value tree analysis under incomplete information. Copyright © 2004 John Wiley & Sons, Ltd.

Decisionarium—aiding decisions, negotiating and collecting opinions on the web

AbstractDecisionarium (www.decisionarium.hut.fi) is the first public site for interactive multicriteria decision support with tools for individual decision‐making as well as for group collaboration and negotiation. Web‐HIPRE (www.hipre.hut.fi) supports value tree and AHP analysis including group models. The RICH methodology (www.rich.hut.fi) allows the decision maker to provide incomplete ordinal preference statements when considering the relative importance of attributes in a value tree. Opinions‐Online (www.opinion.hut.fi) is a platform for surveys voting and group collaboration. There are different ways for voting, multiattribute scoring, surveys as well as interactive viewing of the results. Joint Gains (www.jointgains.hut.fi) applies the method of improving directions to support multiparty negotiations in a multicriteria setting. Smart Swaps offers an implementation of the even swaps procedure (www.smart‐swaps.hut.fi). All of the tools above are web‐based, so global interaction is natural and links can be utilized for multimedia information support. Decisionarium also offers access to complete e‐learning modules (www.dm.hut.fi) based on the use of the software. There are also illustrative powerpoint presentations and additional Windows software WINPRE and PRIME‐Decisions for value tree analysis under incomplete information. Copyright © 2004 John Wiley & Sons, Ltd.