Multiple Objective Optimization Theory Research Articles

Approach to optimization of part machining service combination

To find out the best part machining service provider combination, the theory of multiple objective optimization is discussed in detail via mathematic formulation. Relationships among service provider candidates, service types and parameters are analyzed and uncovered by matrix accumulation. The evaluation index and the practical strength are defined as parameters’ functions. Typical evaluation indexes, such as assembly quality and cost, are chosen to be analyzed in detail, and dimensionless method is put forward to combine them together. A problem-solving algorithm is designed on the basis of the particle swarm optimization. An example is presented to validate that the proposed methods is efficient in solving the multiple objective optimization of the part machining service provider combination problem.

Gene discovery using Pareto depth sampling distributions

Most methods for finding interesting gene expression profiles from gene microarray data are based on a single discriminant, e.g. the classical paired t-test. Here a different approach is introduced based on gene ranking according to Pareto depth in multiple discriminants. The novelty of our approach, which is an extension of our previous work on Pareto front analysis (PFA), is that a gene's relative rank is determined according to the ordinal theory of multiple objective optimization. Furthermore, the distribution of each gene's rank, called Pareto depth, is determined by resampling over the microarray replicates. This distribution is called the Pareto depth sampling distribution (PDSD) and it is used to assess the stability of each ranking. We illustrate and compare the PDSD approach with both simulated and real gene microarray experiments.

Time-optimal motion of a cooperating multiple robot system along a prescribed path

This paper deals with a systematic analysis of the time-optimal motion of a multiple robot system carrying an object along a prescribed path. In our approach, the time-optimal motion planning problem is formulated in a concise form by employing a parameter describing the movement along the path and a vector representing the internal force. Various constraints governing the motion yield the so-called admissible region in the phase plane of the parameter. The orthogonal projection technique and the theory of multiple objective optimization make it possible to construct the admissible region, while taking into account the load distribution problem that is coupled with the motion. Furthermore, our approach provides a way of detailed investigation for the admissible region that is not simply connected. The resulting velocity profile of the path parameter and the internal force at every instant determine the optimal actuator torques for each robot. Computer simulation results reinforce the physical interpretation on the characteristics of the optimal actuator torques.

Path constrained time-optimal motion of a cooperative two robot system

SummaryThis paper presents a systematic approach to the time-optimal motion planning of a cooperative two robot system along a prescribed path. First, the minimum-time motion planning problem is formulated in a concise form by parameterizing the dynamics of the robot system through a single variable describing the path. The constraints imposed on the input actuator torques and the exerted forces on the object are then converted into those on that variable, which result in the so-called admissible region in the phase plane of the variable. Considering the load distribution problem that is also involved in the motion, we present a systematic method to construct the admissible region by employing the orthogonal projection technique and the theory of multiple objective optimization. Especially, the effects of viscous damping and state-dependent actuator bounds are incorporated into the problem formulation so that the case where the admissible region is not simply connected can be investigated in detail. The resultant time-optimal solution specifies not only the velocity profile, but also the force assigned to each robot at each instant. Physical interpretation on the characteristics of the optimal actuator torques is also included with computer simulation results.

Multiple objective optimization approach to adaptive and learning control

This paper formulates a new approach to the classical learning/adaptive control. problem. Our approach is based on two key observations: (1( the inherent conflict between control and identification as they compete for the only available resource, namely the input to the plant; (2) when designing and optimizing the performance of a control system the current task, as well as the repertoire of other typical future tasks which the system may encounter during its life time, should be considered. Our approach is formulated for a general nonlinear time-varying plant; thus, unlike existing adaptive control theory, the theory for a linear time-invariant system evolves as a special case of the general case. The design for the full lifetime of the system creates a methodology that specifies what current actions should be taken in addition to the tracking of the current reference trajectory, at the expense of some performance degradation in the current task, so as to improve the performance of future tasks: this is the learning trade off. The conflicting objectives, namely, tracking versus learning and current task versus future tasks, are most naturally posed and partially solved in the domain of ‘multiple objective optimization theory’. We demonstrate for linear time-invariant plants with quadratic cost, that Pareto optimal learning adaptive controllers may be obtained by simple ‘out of loop’ mixing, where a scalar controls the tracking versus learning trade off in a reliable way.

Application of multiple objective optimization techniques to finite element model tuning

This report examines tuning a finite element model using vector optimization techniques. Structural models using finite element theory often need to be adjusted so they can accurately simulate the real structure. The goal is to tune the model such that it will reproduce data derived from structural tests. First, the performance indices are extremized using multiple objective optimization theory, producing a set of possible solutions. Next, the solutions are rank ordered according to a decision maker's preferences to select the best answer. The tuning process was applied to a T-38 horizontal stabilizer. Numerous weighted solutions contained a best static deformation model, a best frequency model and three intermediate combinations of these two models. This automated procedure proved to be a versatile method capable of producing solutions for many types of tuning problems.

Application of multiple objective optimization theory to a preliminary missile design study

In this large-scale project, the design tasks were divided into two parts which allowed for increased efficiency. The modelling and generation of optimal candiatte missile designs were separated from the preference-laden design selection process. A set of performance indices including range, cost, trajectory error, system susceptibility, and reliability were established as the system measures with which all the subsystems were subsequently optimized. A team of technical designers used computer-based submodels in the areas of propulsion, lifecycle cost, and system susceptibility along with analytical models in the areas of trajectory analysis and system reliability to construct a statespace model. The system statespace included a set of established constants, and it mathematically linked the various subsystems to the performance measures. This model was then nested inside a vector optimization algorithm on a digital computer. The output of this interactive computer program is a set of efficient or nondominated missile designs. Each design is defined by its set of state variables, and accompanied by a set of performance index scores and control variables which define its particular trajectory. These nondominated designs show explicitly the tradeoffs among the performance indices for the missile systems as one moves along the efficient frontier of designs. Additional sensitivity analysis is provided by the optimization software for each efficient design. The second phase of the design process consisted of identifying one missile design from the efficient set for further development. This identification process results from ranking of the efficient designs according to a scalar scoring function which relies on the decision maker's preferences.

A computer based application of non-linear multiple objective optimization

Multiple Objective Optimization Theory (MOOT) techniques are receiving increasing attention due to their ability to incorporate salient non-commensurate and conflicting objectives of a situation into the choice making process. This effort describes the modeling and optimization of an application which utilizes computer aided MOOT for candidate policy evaluation prior to a production process. The specific application discussed is an airborne tactical missile where the pre-production decision depends on such attributes as reliability, cost, technical performance, and survivability. A modeling and analysis effort produced non-linear performance indicers of the aforementioned attributes, and a set of constraints. This vector optimization problem is solved by implementing a constraint optimization technique on a digital computer. The resulting non-dominated solution set provides the information needed to proceed to a production stage.

On the application of multiple criteria decision making to a problem in defence systems acquisition

Multiple criteria decision theory (MCDT) approaches to choice making are receiving increased attention due to the increasing importance society places on incorporating the non-commensurate and conflicting objectives of a situation into the choice making process. Process algorithms for multiple objective optimization theory (MOOT) and multiple attribute utility, theory (MAI5T) motivated a combined approach which utilizes, in an efficient manner, the complementary aspects of both processes. An appropriate application for the multiple criteria approach is a specific military equipment acquisition involving aircraft retrofit. The retrofit of a particular aircraft with equipment designed for a mission which the aircraft was not originally designed to fly typically requires a large systems effort. Specifically, the retrofit of an aircraft with sophisticated electronic warfare (EW) equipment has historically involved inefficiencies and inadequacies including schedule and budgetary overruns and a lack of initiall...