Search results for "Mathematical optimization"
showing 10 items of 1300 documents
Connections Between Single-Level and Bilevel Multiobjective Optimization
2011
The relationship between bilevel optimization and multiobjective optimization has been studied by several authors and there have been repeated attempts to establish a link between the two. We unify the results from the literature and generalize them for bilevel multiobjective optimization. We formulate sufficient conditions for an arbitrary binary relation to guarantee equality between the efficient set produced by the relation and the set of optimal solutions to a bilevel problem. In addition, we present specially structured bilevel multiobjective optimization problems motivated by real-life applications and an accompanying binary relation permitting their reduction to single-level multiob…
A branch-and-cut algorithm for the Team Orienteering Problem
2017
The Team Orienteering Problem aims at maximizing the total amount of profit collected by a fleet of vehicles while not exceeding a predefined travel time limit on each vehicle. In the last years, several exact methods based on different mathematical formulations were proposed. In this paper, we present a new two-index formulation with a polynomial number of variables and constraints. This compact formulation, reinforced by connectivity constraints, was solved by means of a branch-and-cut algorithm. The total number of instances solved to optimality is 327 of 387 benchmark instances, 26 more than any previous method. Moreover, 24 not previously solved instances were closed to optimality.
A Multi-Objective Design Approach for the c Chart Considering Taguchi Loss Function
2013
The present paper proposes a multi-objective design approach for the c chart, considering in the optimization process of the chart parameters both the statistical and the economic objectives. In particular, the minimization of the hourly total quality related costs is the considered objective to carry out the economic goal, whereas the statistical objective is reached by the minimization the out-of-control average run length of the chart. A mixed integer non-linear constrained mathematical model is formulated to solve the treated multi-objective optimization problem, whereas the Pareto optimal frontier is described by the e-constraint method. In order to show the employment of the proposed …
Comparing the Economic Effectiveness of Various Adaptive Schemes for the c Chart
2013
In an attempt to improve the effectiveness of statistical process control (SPC) procedures, a variety of adaptive schemes has been developed in the last decades. However, considering control charts for attributes, relatively few works about adaptive schemes have been proposed, and most of them were proposed only recently. The common characteristic of those schemes is that one or more chart parameters are allowed to adaptively vary during the SPC operations according to the sampling information history, typically the current point plotted on the chart. In this way, the adaptive schemes are smarter than the related static ones, but they are also more complicated in terms of implementation. Th…
An Effective Double Sampling Scheme for thecControl Chart
2013
In the present paper is developed a statistical process control inspection procedure based on a new simple-to-implement and effective double sampling scheme for the c control chart, aimed at the minimization of the number of inspected observation units and warranting fixed levels for the type I and II error risks. In particular, the formulations of the false alarm risk α, the power P of the chart, and the expected number of inspected observation units for the developed inspection procedure are given, whereas a macro of Microsoft Excel is adopted to solve the tackled problem. In order to illustrate the application of the developed approach and to investigate on the influence of several opera…
Economic Design Approach for an SPC Inspection Procedure Implementing The Adaptive C Chart
2013
The present paper proposes a design approach for a statistical process control (SPC) procedure implementing a c control chart for non-conformities, with the aim to minimize the hourly total quality-related costs. The latter take into account the costs arising from the non-conforming products while the process is in-control and out-of-control, for false alarms, for assignable cause locations and system repairs, for sampling and inspection activities and for the system downtime. The proposed economic optimization approach is constrained by the expected hourly false alarms frequency, as well as the available labor resource level. A mixed integer non-linear constrained mathematical model is dev…
A fast Monte Carlo algorithm for studying bottle-brush polymers
2011
Obtaining reliable estimates of the statistical properties of complex macromolecules by computer simulation is a task that requires high computational effort as well as the development of highly efficient simulation algorithms. We present here an algorithm combining local moves, the pivot algorithm, and an adjustable simulation lattice box for simulating dilute systems of bottle-brush polymers with a flexible backbone and flexible side chains under good solvent conditions. Applying this algorithm to the bond fluctuation model, very precise estimates of the mean square end-to-end distances and gyration radii of the backbone and side chains are obtained, and the conformational properties of s…
Computable majorants of the limit load in Hencky’s plasticity problems
2018
Abstract We propose a new method for analyzing the limit (safe) load of elastoplastic media governed by the Hencky plasticity law and deduce fully computable bounds of this load. The main idea of the method is based on a combination of kinematic approach and new estimates of the distance to the set of divergence free fields. We show that two sided bounds of the limit load are sharp and the computational efficiency of the method is confirmed by numerical experiments.
Modeling long-range memory with stationary Markovian processes
2009
In this paper we give explicit examples of power-law correlated stationary Markovian processes y(t) where the stationary pdf shows tails which are gaussian or exponential. These processes are obtained by simply performing a coordinate transformation of a specific power-law correlated additive process x(t), already known in the literature, whose pdf shows power-law tails 1/x^a. We give analytical and numerical evidence that although the new processes (i) are Markovian and (ii) have gaussian or exponential tails their autocorrelation function still shows a power-law decay =1/T^b where b grows with a with a law which is compatible with b=a/2-c, where c is a numerical constant. When a<2(1+c) th…
Data-Driven Interactive Multiobjective Optimization Using a Cluster-Based Surrogate in a Discrete Decision Space
2019
In this paper, a clustering based surrogate is proposed to be used in offline data-driven multiobjective optimization to reduce the size of the optimization problem in the decision space. The surrogate is combined with an interactive multiobjective optimization approach and it is applied to forest management planning with promising results. peerReviewed