Hierarchical optimization on an unbounded parallel-batching machine

2018 ◽  
Vol 52 (1) ◽  
pp. 55-60
Author(s):  
Cheng He ◽  
Li Li
Keyword(s):  
Optimization Problem ◽  
Time Algorithm ◽  
Decision Makers ◽  
Hierarchical Optimization ◽  
Scheduling Problem ◽  
Objective Functions ◽  
Hierarchical Scheduling ◽  
Parallel Batching ◽  
Batching Machine

This paper studies a hierarchical optimization problem on an unbounded parallel-batching machine, in which two objective functions are maximum costs, representing different purposes of two decision-makers. By a hierarchical optimization problem, we mean the problem of optimizing the secondary criterion under the constraint that the primary criterion is optimized. A parallel-batching machine is a machine that can handle several jobs in a batch in which all jobs start and complete respectively at the same time. We present an O(n4)-time algorithm for this hierarchical scheduling problem.

scholarly journals Hierarchical minimization of two maximum costs on a bounded serial-batching machine

2020 ◽  
Author(s):  
Cheng He ◽  
Hao Lin ◽  
Li Li
Keyword(s):  
Processing Time ◽  
Optimization Problem ◽  
Setup Time ◽  
Time Algorithm ◽  
Hierarchical Optimization ◽  
Objective Functions ◽  
Processing Times ◽  
Hierarchical Minimization ◽  
Batching Machine ◽  
Special Case

This paper studies a hierarchical optimization problem of scheduling $n$ jobs on a serial-batching machine, in which two objective functions are maximum costs. By a hierarchical optimization problem, we mean the problem of optimizing the secondary criterion under the constraint that the primary criterion is optimized. A serial-batching machine is a machine that can handle up to $b$ jobs in a batch and jobs in a batch start and complete respectively at the same time and the processing time of a batch is equal to the sum of the processing times of jobs in the batch. When a new batch starts, a constant setup time $s$ occurs. We confine ourselves to the bounded model, where $b<n$. We present an $O(n^4)$-time algorithm for this hierarchical optimization problem. For the special case where two objective functions are maximum lateness, we give an $O(n^3\log n)$-time algorithm.

BATCHING MACHINE SCHEDULING WITH BICRITERIA: MAXIMUM COST AND MAKESPAN

2014 ◽  
Vol 31 (04) ◽  
pp. 1450025 ◽  
Author(s):  
CHENG HE ◽  
HAO LIN ◽  
JINJIANG YUAN ◽  
YUNDONG MU
Keyword(s):  
Processing Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Maximum Cost ◽  
Parallel Batching ◽  
Multicriteria Problem ◽  
Batching Machine

In this paper, the problem of minimizing maximum cost and makespan simultaneously on an unbounded parallel-batching machine is considered. An unbounded parallel-batching machine is a machine that can handle any number of jobs in a batch and the processing time of a batch is the largest processing time of jobs in the batch. The main goal of a multicriteria problem is to find Pareto optimal solutions. We present a polynomial-time algorithm to produce all Pareto optimal solutions of this bicriteria scheduling problem.

A DUAL CRITERIA PREEMPTIVE SCHEDULING PROBLEM FOR MINIMAX ERROR OF IMPRECISE COMPUTATION TASKS

2004 ◽  
Vol 15 (05) ◽  
pp. 717-731 ◽  
Author(s):  
KEVIN I.-J. HO ◽  
JOSEPH Y.-T. LEUNG
Keyword(s):  
Time Complexity ◽  
Optimization Problem ◽  
Hierarchical Optimization ◽  
Preemptive Scheduling ◽  
Scheduling Problem ◽  
Imprecise Computation ◽  
Single Processor ◽  
Weighted Error

We consider a hierarchical optimization problem for imprecise computation tasks, where each task is weighted with two weights, w and w'. The primary criterion is to minimize the total w-weighted error of all optional parts of tasks and the secondary criterion is to minimize the maximum w'-weighted error. An algorithm is given with time complexity O(kn3 log 2 n) for parallel and identical processors and O(kn2) for a single processor, where k is the number of distinct w-weights.

scholarly journals Optimization Issues of a Hammer Mill Working Process Using Statistical Modelling

2021 ◽  
Vol 13 (2) ◽  
pp. 973
Author(s):  
Gigel Paraschiv ◽  
Georgiana Moiceanu ◽  
Gheorghe Voicu ◽  
Mihai Chitoiu ◽  
Petru Cardei ◽  
...  
Keyword(s):  
Energy Consumption ◽  
Optimization Problem ◽  
Specific Energy Consumption ◽  
Statistical Modelling ◽  
Hammer Mill ◽  
Objective Functions ◽  
Working Process ◽  
Rotor Spinning ◽  
Milled Material ◽  
Different Types

Our paper presents the hammer mill working process optimization problem destined for milling energetic biomass (MiscanthusGiganteus and Salix Viminalis). For the study, functional and constructive parameters of the hammer mill were taken into consideration in order to reduce the specific energy consumption. The energy consumption dependency on the mill rotor spinning frequency and on the sieve orifices in use, as well as on the material feeding flow, in correlation with the vegetal biomass milling degree was the focus of the analysis. For obtaining this the hammer mill was successively equipped with 4 different types of hammers that grind the energetic biomass, which had a certain humidity content and an initial degree of reduction ratio of the material. In order to start the optimization process of hammer mill working process, 12 parameters were defined. The objective functions which minimize hammer mill energy consumption and maximize the milled material percentage with a certain specific granulation were established. The results obtained can serve as the basis for choosing the optimal working, constructive, and functional parameters of hammer mills in this field, and for a better design of future hammer mills.

scholarly journals Braille Block Detection via Multi-Objective Optimization from an Egocentric Viewpoint

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2775
Author(s):  
Tsubasa Takano ◽  
Takumi Nakane ◽  
Takuya Akashi ◽  
Chao Zhang
Keyword(s):  
Optimization Problem ◽  
Line Pair ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Optimization Framework ◽  
Visually Impaired People ◽  
Comprehensive Comparison ◽  
Basic Characteristics ◽  
Support Devices

In this paper, we propose a method to detect Braille blocks from an egocentric viewpoint, which is a key part of many walking support devices for visually impaired people. Our main contribution is to cast this task as a multi-objective optimization problem and exploits both the geometric and the appearance features for detection. Specifically, two objective functions were designed under an evolutionary optimization framework with a line pair modeled as an individual (i.e., solution). Both of the objectives follow the basic characteristics of the Braille blocks, which aim to clarify the boundaries and estimate the likelihood of the Braille block surface. Our proposed method was assessed by an originally collected and annotated dataset under real scenarios. Both quantitative and qualitative experimental results show that the proposed method can detect Braille blocks under various environments. We also provide a comprehensive comparison of the detection performance with respect to different multi-objective optimization algorithms.

scholarly journals A Method for Integration of Preferences to a Multi-Objective Evolutionary Algorithm Using Ordinal Multi-Criteria Classification

2021 ◽  
Vol 26 (2) ◽  
pp. 27
Author(s):  
Alejandro Castellanos-Alvarez ◽  
Laura Cruz-Reyes ◽  
Eduardo Fernandez ◽  
Nelson Rangel-Valdez ◽  
Claudia Gómez-Santillán ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Selective Pressure ◽  
Optimization Problems ◽  
Region Of Interest ◽  
Decision Makers ◽  
Multiple Objective ◽  
Objective Functions ◽  
Multi Objective ◽  
Imperfect Knowledge ◽  
Real World Problems

Most real-world problems require the optimization of multiple objective functions simultaneously, which can conflict with each other. The environment of these problems usually involves imprecise information derived from inaccurate measurements or the variability in decision-makers’ (DMs’) judgments and beliefs, which can lead to unsatisfactory solutions. The imperfect knowledge can be present either in objective functions, restrictions, or decision-maker’s preferences. These optimization problems have been solved using various techniques such as multi-objective evolutionary algorithms (MOEAs). This paper proposes a new MOEA called NSGA-III-P (non-nominated sorting genetic algorithm III with preferences). The main characteristic of NSGA-III-P is an ordinal multi-criteria classification method for preference integration to guide the algorithm to the region of interest given by the decision-maker’s preferences. Besides, the use of interval analysis allows the expression of preferences with imprecision. The experiments contrasted several versions of the proposed method with the original NSGA-III to analyze different selective pressure induced by the DM’s preferences. In these experiments, the algorithms solved three-objectives instances of the DTLZ problem. The obtained results showed a better approximation to the region of interest for a DM when its preferences are considered.

scholarly journals An Analytical Study in Multi-physics and Multi-criteria Shape Optimization

2021 ◽  
Author(s):  
Hanno Gottschalk ◽  
Marco Reese
Keyword(s):  
Shape Optimization ◽  
Physical System ◽  
Pareto Front ◽  
Optimization Problem ◽  
Analytical Study ◽  
Static Pressure ◽  
Hausdorff Metric ◽  
Objective Functions ◽  
Hölder Continuous ◽  
Turbine Vane

AbstractA simple multi-physical system for the potential flow of a fluid through a shroud, in which a mechanical component, like a turbine vane, is placed, is modeled mathematically. We then consider a multi-criteria shape optimization problem, where the shape of the component is allowed to vary under a certain set of second-order Hölder continuous differentiable transformations of a baseline shape with boundary of the same continuity class. As objective functions, we consider a simple loss model for the fluid dynamical efficiency and the probability of failure of the component due to repeated application of loads that stem from the fluid’s static pressure. For this multi-physical system, it is shown that, under certain conditions, the Pareto front is maximal in the sense that the Pareto front of the feasible set coincides with the Pareto front of its closure. We also show that the set of all optimal forms with respect to scalarization techniques deforms continuously (in the Hausdorff metric) with respect to preference parameters.

scholarly journals A Fast and Exact Greedy Algorithm for the Core–Periphery Problem

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 94 ◽  
Author(s):  
Dario Fasino ◽  
Franca Rinaldi
Keyword(s):  
Structural Analysis ◽  
Optimization Problem ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Combinatorial Optimization Problem ◽  
Connected Subgraph ◽  
Optimal Solutions ◽  
The Core ◽  
Core Set ◽  
Key Concepts

The core–periphery structure is one of the key concepts in the structural analysis of complex networks. It consists of a partitioning of the node set of a given graph or network into two groups, called core and periphery, where the core nodes induce a well-connected subgraph and share connections with peripheral nodes, while the peripheral nodes are loosely connected to the core nodes and other peripheral nodes. We propose a polynomial-time algorithm to detect core–periphery structures in networks having a symmetric adjacency matrix. The core set is defined as the solution of a combinatorial optimization problem, which has a pleasant symmetry with respect to graph complementation. We provide a complete description of the optimal solutions to that problem and an exact and efficient algorithm to compute them. The proposed approach is extended to networks with loops and oriented edges. Numerical simulations are carried out on both synthetic and real-world networks to demonstrate the effectiveness and practicability of the proposed algorithm.

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