Pareto Optimality Notion Research Articles

Multicriteria Evolutionary Weather Routing Algorithm in Practice

The Multicriteria Evolutionary Weather Routing Algorithm (MEWRA) has already been introduced by the author on earlier TransNav 2009 and 2011 conferences with a focus on theoretical application to a hybrid-propulsion or motor-driven ship. This paper addresses the topic of possible practical weather routing applications of MEWRA. In the paper some practical advantages of utilizing Pareto front as a result of multicriteria optimization in case of route finding are described. The paper describes the notion of Pareto-optimality of routes along with a simplified, easy to follow example. It also discusses a choice of the most suitable ranking method for MEWRA (a comparison between Fuzzy TOPSIS and Zero Unitarization Method is presented). In addition to that the paper briefly outlines a commercial application of MEWRA.

Optimization of Stability of Retained Austenite in TRIP-Aided Steel Using Data-Driven Models and Multi-Objective Genetic Algorithms

The important parameters that determine the properties of transformation-induced-plasticity (TRIP) -aided steel are the amount of retained austenite phase present in its initial microstructure and its stability. A large value of carbon equivalent leads to a high amount of retained austenite in the initial microstructure of these steels at room temperature. Looking at it from another angle, a high value of carbon equivalent is undesirable, as it adversely affects the weldability. In this study, we have attempted to resolve this conflict by bringing in the notion of Pareto optimality. Through an evolutionary neural network that evolved through multi-objective genetic algorithms, data-driven models were constructed for both carbon equivalent and fraction transformed. The effect of individual variables on the extent of austenite transformation as inferred by the model was found to be consistent with the principles of physical metallurgy of TRIP-aided steel. Next, using a predator–prey genetic algorithm, a bi-objective optimization task was conducted for simultaneous minimization of carbon equivalent and the extent of transformation. The resulting Pareto frontier was carefully analyzed, and the transformation behavior of different TRIP-assisted steels was also predicted for different straining conditions. Further need for optimizing the heat-treatment schedule is highlighted through selective experimentation.

An optimization modelling for string selection in molecular biology using Pareto optimality

A known class of computational problems in molecular biology is the consensus string problem, to which belongs the problem of string selection via comparison. This paper deals with one of these problems called Closest String Problem (CSP). A novel definition of CSP is provided, based upon the Pareto optimality notion, to obtain most useful sequences. Also, a zero-one optimization model to solve the new defined CSP is introduced. Finally, a comparison between the new definition (model) and a current one is given.

Relative importance of criteria in multiobjective programming: A cone-based approach

This article develops a convex polyhedral cone-based preference modeling framework for decision making with multiple criteria which extends the classical notion of Pareto optimality and accounts for relative importance of the criteria. The decision maker’s perception of the relative importance is quantified by an allowable tradeoffs between two objectives representing the maximum allowable amount of decay of a less important objective per one unit of improvement of a more important objective. Two cone-based models of relative importance are developed. In the first model, one criterion is designated as less important while all the others are more important. In the second model, more than one criterion may be classified as less important while all the others are considered more important. Complete algebraic characterization of the models is derived and the relationship between them and the classical Pareto preference is examined. Their relevance to decision making is discussed.

Robust design of a passive linear quarter car suspension system using a multi-objective evolutionary algorithm and analytical robustness indexes

This paper deals with the robust design of a passive vehicle suspension system. A robust design methodology based on a multi-objective evolutionary algorithm (MOEA) is used to handle the trade-off between the considered conflicting performance requirements under uncertainty and feasibility constraints. A constrained multi-objective optimisation problem is formulated and the notion of Pareto-optimality is used to increase the quality of the candidate design solutions obtained at each generation by the MOEA. To save computation time, a simplified physical model (quarter car) is considered and the optimisation is performed in the frequency domain, using relevant transmissibilities of the system. The robustness is directly investigated by means of analytical robustness indexes. Time-consuming a posteriori methods, like designs of experiments or Monte Carlo analysis, are therefore avoided. A set of non-dominated solutions is obtained. Thus the designer not only selects a special design, in accordance with the wanted vehicle configuration, but also includes the robustness of each performance requirement in his final decision.

Pareto Optimality and Equilibrium in an Insurance Market

The concept of economic equilibrium under uncertainty is applied to a model of insurance market where, in distinction to the classic Borch’s model of a reinsurance market, risk exchanges are allowed between the insurer and each insured only, not among insureds themselves. Conditions characterizing an equilibrium are found. A variant of the conditions, based on the Pareto optimality notion and involving risk aversion functions of the agents, is derived. An existence theorem is proved. Computation of the market premiums and optimal indemnities is illustrated by an example with exponential utility functions.

Pareto Optimality and Equilibrium in an Insurance Market

The concept of economic equilibrium under uncertainty is applied to a model of insurance market where, in distinction to the classic Borch’s model of a reinsurance market, risk exchanges are allowed between the insurer and each insured only, not among insureds themselves. Conditions characterizing an equilibrium are found. A variant of the conditions, based on the Pareto optimality notion and involving risk aversion functions of the agents, is derived. An existence theorem is proved. Computation of the market premiums and optimal indemnities is illustrated by an example with exponential utility functions.

Partial Similarity of Objects, or How to Compare a Centaur to a Horse

Similarity is one of the most important abstract concepts in human perception of the world. In computer vision, numerous applications deal with comparing objects observed in a scene with some a priori known patterns. Often, it happens that while two objects are not similar, they have large similar parts, that is, they are partially similar. Here, we present a novel approach to quantify partial similarity using the notion of Pareto optimality. We exemplify our approach on the problems of recognizing non-rigid geometric objects, images, and analyzing text sequences.

Multi-objective Meta-heuristics for the Traveling Salesman Problem with Profits

We introduce and test a new approach for the bi-objective routing problem known as the traveling salesman problem with profits. This problem deals with the optimization of two conflicting objectives: the minimization of the tour length and the maximization of the collected profits. This problem has been studied in the form of a single objective problem, where either the two objectives have been combined or one of the objectives has been treated as a constraint. The purpose of our study is to find solutions to this problem using the notion of Pareto optimality, i.e. by searching for efficient solutions and constructing an efficient frontier. We have developed an ejection chain local search and combined it with a multi-objective evolutionary algorithm which is used to generate diversified starting solutions in the objective space. We apply our hybrid meta-heuristic to synthetic data sets and demonstrate its effectiveness by comparing our results with a procedure that employs one of the best single-objective approaches.

Analysis of Two-Dimensional Non-Rigid Shapes

Analysis of deformable two-dimensional shapes is an important problem, encountered in numerous pattern recognition, computer vision and computer graphics applications. In this paper, we address three major problems in the analysis of non-rigid shapes: similarity, partial similarity, and correspondence. We present an axiomatic construction of similarity criteria for deformation-invariant shape comparison, based on intrinsic geometric properties of the shapes, and show that such criteria are related to the Gromov-Hausdorff distance. Next, we extend the problem of similarity computation to shapes which have similar parts but are dissimilar when considered as a whole, and present a construction of set-valued distances, based on the notion of Pareto optimality. Finally, we show that the correspondence between non-rigid shapes can be obtained as a byproduct of the non-rigid similarity problem. As a numerical framework, we use the generalized multidimensional scaling (GMDS) method, which is the numerical core of the three problems addressed in this paper.

A constrained nonlinear energy minimization framework for the regularization of the stereo correspondence problem

In this paper, we propose a novel approach to stereo correspondence based on the optimization of a continuous disparity surface defined parametrically using radial basis functions. Principal advantages over other methods include the use of constrained nonlinear programming to perform regularization as a hierarchical multiobjective optimization which differs from the standard weighted sum approach, so that regularization becomes more consistent with the notion of Pareto optimality. Furthermore, the optimization algorithm is capable of handling arbitrary constraints on the sought parameters, so that a variety of types of a priori scene information can be incorporated explicitly to the problem definition. To exemplify this we derive a new continuous unary formulation of the disparity gradient limit constraint and propose other types of potential constraints for a priori knowledge. Furthermore, the optimization employs a smoothness oriented regularization operator to preserve surface discontinuities, a flexible block decomposition approach of the disparity surface to allow parallelization and a correlation-based fitting with heuristics to initialize the parameters and avoid local optima effectively. Experiments with standard stereo imagery show that the method handles adequately the imposed constraints and produces surfaces with accurate level of elevation detail.

Mathematical and Pragmatic Perspectives of Physical Programming

Physical programming (PP) is an emerging multiobjective and design optimization method that has been applied successfully in diverse areas of engineering and operations research. The application of PP calls for the designer to express preferences by defining ranges of differing degrees of desirability for each design metric. Although this approach works well in practice, it has never been shown that the resulting optimal solution is not unduly sensitive to these numerical range definitions. PP is shown to be numerically well conditioned, and its sensitivity to designer input (with respect to optimal solution) is compared with that of other popular methods. The important proof is provided that all solutions obtained through PP are Pareto optimal and the notion of Pareto optimality is extended to one of pragmatic implication. The important notion of P dominance that extends the concept of Pareto optimality beyond the cases minimize and maximize is introduced. P dominance is shown to lead to the important concept of generalized Pareto optimality. Numerical results are provided that illustrate the favorable numerical properties of physical programming.

Multiobjective programming using uniform design and genetic algorithm

The notion of Pareto-optimality is one of the major approaches to multiobjective programming. While it is desirable to find more Pareto-optimal solutions, it is also desirable to find the ones scattered uniformly over the Pareto frontier in order to provide a variety of compromise solutions to the decision maker. We design a genetic algorithm for this purpose. We compose multiple fitness functions to guide the search, where each fitness function is equal to a weighted sum of the normalized objective functions and we apply an experimental design method called uniform design to select the weights. As a result, the search directions guided by these fitness functions are scattered uniformly toward the Pareto frontier in the objective space. With multiple fitness functions, we design a selection scheme to maintain a good and diverse population. In addition, we apply the uniform design to generate a good initial population and design a new crossover operator for searching the Pareto-optimal solutions. The numerical results demonstrate that the proposed algorithm can find the Pareto-optimal solutions scattered uniformly over the Pareto frontier.

Evaluating the administrative efficiency of courts

In addition to being held accountable for judicial decision, courts, like other public agencies, can and should be evaluated in terms of their administrative efficiency. This paper illustrates how courts can be evaluated in terms of their relative administrative efficiency, using a new approach—data envelopment analysis (DEA)—first proposed by Charnes et al. [1]. The DEA is based upon the economic notion of Pareto optimality which states that a given decision making unit (DMU) is inefficient if some other DMU, or some combination of other DMUs, can produce at least the same amounts of all outputs with less of some resource input and not more of any other resource. Conversely a DMU is said to be efficient if the above is not possible. Charnes et al. [1] generalized the usual input/output ratio measure of efficiency for a given unit in terms of a fractional linear program with fractional constraints. In the case of courts, the efficiency of any particular court is calculated by forming the ratio of a weighted sum of outputs to a weighted sum of inputs, where the weights for both outputs and inputs are to be selected in a manner that calculates the Pareto-Koopmans efficiency of the court. This paper reviews the DEA method and illustrates its application to a data base for 100 criminal superior courts in North Carolina.