Candidate Objective Functions Research Articles

Randomized Strategies for Robust Combinatorial Optimization with Approximate Separation

In this paper, we study the following robust optimization problem. Given a set family representing feasibility and candidate objective functions, we choose a feasible set, and then an adversary chooses one objective function, knowing our choice. The goal is to find a randomized strategy (i.e., a probability distribution over the feasible sets) that maximizes the expected objective value in the worst case. This problem is fundamental in wide areas such as artificial intelligence, machine learning, game theory, and optimization. To solve the problem, we provide a general framework based on the dual linear programming problem. In the framework, we utilize the ellipsoid algorithm with the approximate separation algorithm. We prove that there exists an α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}-approximation algorithm for our robust optimization problem if there exists an α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}-approximation algorithm for finding a (deterministic) feasible set that maximizes a nonnegative linear combination of the candidate objective functions. Using our result, we provide approximation algorithms for the max–min fair randomized allocation problem and the maximum cardinality robustness problem with a knapsack constraint.

A coupled multi-linear regression and genetic algorithm-based modelling and optimisation of surface roughness in machining of brass

In this paper, the authors present a multi-linear regression-based approach for the modelling of surface roughness during the turning of a commercial brass alloy. Three regression models are developed by utilising the experimental data gathered following a full-factorial-based design-of-experiments (DoEs) methodology. While the conventional practice has been to develop regression models using the entire experimental datasets, we deviate from the same and employ only a subset of the available data for the purpose, the remaining data being used for the model validation. The results obtained herein reveal that the second order regression model is statistically better than the other two in predicting the surface roughness for both the datasets. The global minimum surface roughness is determined by using the developed regression models in conjunction with the genetic algorithm-based single objective optimisation. The regression models serve as candidate objective functions for the genetic algorithm. The optimisation results reveal that the global minimum obtained using the second order regression model is in close agreement (accuracy - 94%) with the experimentally obtained minimum surface roughness and thus reaffirms the effectiveness of the second order regression model in predicting the surface roughness of brass during turning operation.

Randomized Strategies for Robust Combinatorial Optimization

In this paper, we study the following robust optimization problem. Given an independence system and candidate objective functions, we choose an independent set, and then an adversary chooses one objective function, knowing our choice. The goal is to find a randomized strategy (i.e., a probability distribution over the independent sets) that maximizes the expected objective value in the worst case. This problem is fundamental in wide areas such as artificial intelligence, machine learning, game theory and optimization. To solve the problem, we propose two types of schemes for designing approximation algorithms. One scheme is for the case when objective functions are linear. It first finds an approximately optimal aggregated strategy and then retrieves a desired solution with little loss of the objective value. The approximation ratio depends on a relaxation of an independence system polytope. As applications, we provide approximation algorithms for a knapsack constraint or a matroid intersection by developing appropriate relaxations and retrievals. The other scheme is based on the multiplicative weights update (MWU) method. The direct application of the MWU method does not yield a strict multiplicative approximation algorithm but yield one with an additional additive error term. A key technique to overcome the issue is to introduce a new concept called (η,γ)-reductions for objective functions with parameters η and γ. We show that our scheme outputs a nearly α-approximate solution if there exists an α-approximation algorithm for a subproblem defined by (η,γ)-reductions. This improves approximation ratios in previous results. Using our result, we provide approximation algorithms when the objective functions are submodular or correspond to the cardinality robustness for the knapsack problem.

Multi-purpose economic optimal experiment design applied to model based optimal control

Abstract In contrast to classical experiment design methods, often based on alphabetic criteria, economic optimal experiment design assumes that our ultimate goal is to solve an optimization or optimal control problem. As the system parameters of physical models are in practice always estimated from measurements, they cannot be assumed to be exact. Thus, if we solve the model based optimization problem using the estimated, non-exact parameters, an inevitable loss of optimality is faced. The aim of economic optimal experiment design is precisely to plan an experiment in such a way that the expected loss of optimality in the optimization is minimized. This paper analyzes the question how to design economic experiments under the assumption that we have more than one candidate objective function. Here, we want to take measurements and estimate the parameters before we actually decide which objective we want to minimize.

Optimization of Solar Tower Hybrid Pressurized Air Receiver Using CFD and Mathematical Optimization

Solar receivers used for central tower Concentrated Solar Plants (CSPs) use either a surface-based or volumetric heat transfer region. Volumetric receivers are more efficient but require more sophisticated and expensive materials that can withstand the elevated temperatures (in excess of 1000°C). If pressurized air is used as heat transfer fluid (HTF) in order to increase both the density and heat capacity of the HTF, the volumetric receiver needs to be located in a pressure vessel with a pressurized quartz window located at the aperture of the concentrator. An alternative approach to utilize pressurized air in a pseudo-volumetric fashion is to populate a volumetric region with piped pressurized air (Kretzschmar & Gauché, 2012). This tubular-type volumetric receiver provides the challenge of enabling maximum heat transfer without causing hot spots on the side of the solar irradiation source. Heat transfer would not be as effective as for a true volumetric receiver because the heat transfer area is limited by the tube wall. A Computational Fluid Dynamics (CFD) model is generated of the solar receiver cavity. The commercial CFD code ANSYS Fluent v14.5 is used to evaluate the heat transfer between the incoming solar flux and the HTF. The incoming solar irradiation is modeled using the Discrete Ordinates (DO) radiation model ANSYS Fluent. The DO model also predicts the resulting thermal radiation in the conjugate heat transfer problem. The geometry is parameterized in order to allow for the selection of design variables in a formal design optimization formulation. Results include typical CFD results of a candidate geometry to illustrate the solar irradiation input, the effect of tubular layout as well as temperature and heat flux distributions that provide candidate objective functions for optimization. Recommendations are made for the implementation of the optimization process.

Control of natural ventilation for aerodynamic high-rise buildings

The aim of the paper is to present a framework for the optimal control of natural ventilation. To account for the significant crossflow between zones, the notion of ASHRAE-equivalent airflow is proposed which is used to evaluate the quality of ventilation provided to different zones within a building. A model-based predictive control approach is developed which is used to simulate different ventilation strategies and select the most appropriate strategy. To this end, the rationale behind choosing an objective function that captures the goals of a ventilation system is described, and candidate objective functions are discussed. Finally, an illustrative example with an elliptical cross-section building is discussed in detail. The framework for model-predictive control developed in this paper is applicable beyond natural ventilation and high-rise buildings.

Alienation, indifference and the choice of ideological position

In this paper we describe a simple model of individual voting behavior and present its implications for the candidate positioning problem under both vote and plurality maximization. Under our assumptions, some voters at the extremes of the ideological spectrum typically will not vote because they are alienated by the equilibrium location of candidates. There will also be some voters in the middle of the ideological spectrum who will not vote because they are indifferent between the equilibrium locations of the candidates. Both the abstention from alienation and from indifference arise explicitly from utility maximization. Once we allow for alienation and indifference, the two alternative candidate objective functions (vote maximization and plurality maximization) yield different outcomes. In particular, we show that under vote maximization the Median Voter (or Minimum Differentiation) outcome will not arise. On the other hand, under plurality maximization, the Median Voter outcome may or may not hold, depending on the distribution of voter preferences.

A general probabilistic spatial theory of elections

In this paper, we construct a general probabilistic spatial theory of elections and examine sufficient conditions for equilibrium in two-candidate contests with expected vote-maximizing candidates. Given strict concavity of the candidate objective function, a unique equilibrium exists and the candidates adopt the same set of policy positions. Prospective uncertainty, reduced policy salience, degree of concavity of voter utility functions, some degree of centrality in the feasible set of policy locations, and restrictions on the dimensionality of the policy space are all stabilizing factors in two-candidate elections.