Optimal Solution Subject Research Articles

Optimizing resource allocation in service systems via simulation: A Bayesian formulation

The service sector has become increasingly important in today's economy. To meet the rising expectation of high‐quality services, efficiently allocating resources is vital for service systems to balance service qualities with costs. In particular, this paper focuses on a class of resource allocation problems where the service‐level objective and constraints are in the form of probabilistic measures. Further, process complexity and system dynamics in service systems often render their performance evaluation and optimization challenging and relying on simulation models. To this end, we propose a generalized resource allocation model with probabilistic measures, and subsequently, develop an optimal computing budget allocation (OCBA) formulation to select the optimal solution subject to random noises in simulation. The OCBA formulation minimizes the expected opportunity cost that penalizes based on the quality of the selected solution. Further, the formulation takes a Bayesian approach to consider the prior knowledge and potential performance correlations on candidate solutions. Then, the asymptotic optimality conditions of the formulation are derived, and an iterative algorithm is developed accordingly. Numerical experiments and a case study inspired by a real‐world problem in a hospital emergency department demonstrate the effectiveness of the proposed algorithm for solving the resource allocation problem via simulation.

Learning-Based 6-DOF Control for Autonomous Proximity Operations Under Motion Constraints

This article proposes areinforcement learning (RL)-based six-degree-of-freedom (6-DOF) control scheme for the final-phase proximity operations of spacecraft. The main novelty of the proposed method are from two aspects: 1) The closed-loop performance can be improved in real-time through the RL technique, achieving an online approximate optimal control subject to the full 6-DOF nonlinear dynamics of spacecraft; 2) nontrivial motion constraints of proximity operations are considered and strictly obeyed during the whole control process. As a stepping stone, the dual-quaternion formalism is employed to characterize the 6-DOF dynamics model and motion constraints. Then, an RL-based control scheme is developed under the dual-quaternion algebraic framework to approximate the optimal control solution subject to a cost function and a Hamilton–Jacobi–Bellman equation. In addition, a specially designed barrier function is embedded in the reward function to avoid motion constraint violations. The Lyapunov-based stability analysis guarantees the ultimate boundedness of state errors and the weight of NN estimation errors. Besides, we also show that a PD-like controller under dual-quaternion formulation can be employed as the initial control policy to trigger the online learning process. The boundedness of it is proved by a special Lyapunov strictification method. Simulation results of prototypical spacecraft missions with proximity operations are provided to illustrate the effectiveness of the proposed method.

Role of Magnetic field on the Dynamical Analysis of Second Grade Fluid: An Optimal Solution subject to Non-integer Differentiable Operators

The dynamical analysis of MHD second grade fluid based on their physical properties has stronger resistance capabilities, low-frequency responses, lower energy consumption, and higher sensitivities; due to these facts externally applied magnetic field always takes the forms of diamagnetic, ferromagnetic and paramagnetic. The mathematical modeling based on the fractional treatment of governing equation subject to the temperature distribution, concentration, and velocity field is developed within a porous surfaced plate. Fractional differential operators with and without non-locality have been employed on the developed governing partial differential equations. The mathematical analysis of developed fractionalized governing partial differential equations has been established by means of systematic and powerful techniques of Laplace transform with its inversion. The fractionalized analytical solutions have been traced out separately through Atangana-Baleanu and Caputo-Fabrizio fractional differential operators. Our results suggest that the velocity profile decrease by increasing the value of the Prandtl number. The existence of a Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity.

Sampling with removal in LP-type problems

Random sampling is an important tool in optimization subject to finitely or infinitely many constraints. Here we are interested in obtaining solutions of low cost that violate only few constraints. Under convexity or similar favorable conditions, and assuming fixed dimension, one can indeed derive combinatorial bounds on the expected number (or probability mass) of constraints violated by the optimal solution subject to a (small) random sample of constraints. The cost of the sample solution, however, cannot be bounded combinatorially. Suppose that after picking the sample, we remove $k$ constraints from it in such a way that the best improvement of objective function is achieved. Can we still guarantee (good) bounds on the number or mass of violated constraints? This question was asked and partially answered in the framework of chance-constrained optimization . Here we study the question in the completely combinatorial setting LP-type problems , which allows a unified treatment of many different optimization problems. Given a nondegenerate LP-type problem of combinatorial dimension $\delta$, we consider sampling with subsequent removal of the $k$ constraints that lead to the best improvement of objective function. We show that this induces an LP-type problem of combinatorial dimension $O(\delta^{k+1})$, and that this bound is tight in the worst case. It follows that through this kind of removal, the expected number of violated constraints blows up by a factor of at most $O(\delta^{k})$; for relevant sample sizes, however, a matching lower bound for the blowup factor is not implied. At the same time, our results show that further improvements require new tools that go beyond combinatorial dimension.

An efficient hybrid genetic algorithm to solve assembly line balancing problem with sequence-dependent setup times

In this paper the setup assembly line balancing and scheduling problem (SUALBSP) is considered. Since this problem is NP-hard, a hybrid genetic algorithm (GA) is proposed to solve the problem. This problem involves assigning the tasks to the stations and scheduling them inside each station. A simple permutation is used to determine the sequence of tasks. To determine the assignment of tasks to stations, the algorithm is hybridized using a dynamic programming procedure. Using dynamic programming, at any time a chromosome can be converted to an optimal solution (subject to the chromosome sequence).Since population diversity is very important to prevent from being trapped in local optimum solutions some diversity maintaining schemes are used to overcome this issue. Operators and parameters of the algorithm is calibrated using design of experiments (DOEs) method. The computational results show that the proposed GA outperforms all of the algorithms presented to solve SUALBSP so far.

Generalized Random Walks for Fusion of Multi-Exposure Images

A single captured image of a real-world scene is usually insufficient to reveal all the details due to under- or over-exposed regions. To solve this problem, images of the same scene can be first captured under different exposure settings and then combined into a single image using image fusion techniques. In this paper, we propose a novel probabilistic model-based fusion technique for multi-exposure images. Unlike previous multi-exposure fusion methods, our method aims to achieve an optimal balance between two quality measures, i.e., local contrast and color consistency, while combining the scene details revealed under different exposures. A generalized random walks framework is proposed to calculate a globally optimal solution subject to the two quality measures by formulating the fusion problem as probability estimation. Experiments demonstrate that our algorithm generates high-quality images at low computational cost. Comparisons with a number of other techniques show that our method generates better results in most cases.

Feature selection based on linear discriminant analysis

The paper proposed a new approach of feature selection based on Constrained Linear Discriminant Analysis(CLDA),which modeled feature selection as a search problem in subspace and made optimal solution subject to some restrictions.Furthermore,CLDA optimization problem was transformed into a process of scoring and sorting features.Experiments on UCI machine learning repository and Reuters-21578 dataset show that the proposed approach can consistently obtain better results with fewer features than that with all features.

A simple and effective evolutionary algorithm for the vehicle routing problem

The vehicle routing problem (VRP) plays a central role in the optimization of distribution networks. Since some classical instances with 75 nodes resist the best exact solution methods, most researchers concentrate on metaheuristics for solving real-life problems. Contrary to the VRP with time windows, no genetic algorithm (GA) can compete with the powerful tabu search (TS) methods designed for the VRP. This paper bridges the gap by presenting a relatively simple but effective hybrid GA. In terms of average solution cost, this algorithm outperforms most published TS heuristics on the 14 classical Christofides instances and becomes the best solution method for the 20 large-scale instances generated by Golden et al. Scope and purpose The framework of this research is the development of effective metaheuristics for hard combinatorial optimization problems met in vehicle routing. It is surprising to notice in the literature the absence of effective genetic algorithms (GA) for the vehicle routing problem (VRP, the main capacitated node routing problem), contrary to node routing problems with time windows or arc routing problems. Earlier attempts were based on chromosomes with trip delimiters and needed a repair procedure to get feasible children after each crossover. Such procedures are known to weaken the genetic transmission of information from parents to children. This paper proposes a GA without trip delimiters, hybridized with a local search procedure. At any time, a chromosome can be converted into an optimal VRP solution (subject to chromosome sequence), thanks to a special splitting procedure. This design choice avoids repair procedures and enables the use of classical crossovers like OX. The resulting algorithm is flexible, relatively simple, and very effective when applied to two sets of standard benchmark instances ranging from 50 to 483 customers.

A Simple Sampling Lemma: Analysis and Applications in Geometric Optimization

Random sampling is an efficient method to deal with constrained optimization problems in computational geometry. In a first step, one finds the optimal solution subject to a random subset of the constraints; in many cases, the expected number of constraints still violated by that solution is then significantly smaller than the overall number of constraints that remain. This phenomenon can be exploited in several ways, and typically results in simple and asymptotically fast algorithms.Very often the analysis of random sampling in this context boils down to a simple identity (the sampling lemma ) which holds in a general framework, yet has not been stated explicitly in the literature.In the more restricted but still general setting of LP-type problems , we prove tail estimates for the sampling lemma, giving Chernoff-type bounds for the number of constraints violated by the solution of a random subset. As an application, we provide the first theoretical analysis of multiple pricing , a heuristic used in the simplex method for linear programming in order to reduce a large problem to few small ones. This follows from our analysis of a reduction scheme for general LP-type problems, which can be considered as a simplification of an algorithm due to Clarkson. The simplified version needs less random resources and allows a Chernoff-type tail estimate.

On a Simple Sampling Lemma

Random sampling is an efficient method to deal with constrained optimization problems in computational geometry. In a first step, one finds the optimal solution subject to a random subset of the constraints; in many cases, the expected number of constraints still violated by that solution is then significantly smaller than the overall number of constraints that remain. This phenomenon can be exploited in several ways, and typically results in simple and asymptotically fast algorithms.Virtually every analysis of random sampling in this context boils down to a simple identity (the sampling lemma) which holds in an amazingly general framework, yet has not explicitly been stated in the literature.We present the sampling lemma, along with some of its applications, and we outline further results in the specific scenario of LP-type problems.