Solving large scale assignment problem using the successive complementary slackness conditions

2016 ◽  
Author(s):  
Warut Boonphakdee ◽  
Peerayuth Charnsethikul
Keyword(s):  
Assignment Problem ◽  
Large Scale ◽  
Complementary Slackness ◽  
Complementary Slackness Conditions

Optimal control of higher order differential inclusions with functional constraints

2020 ◽  
Vol 26 ◽  
pp. 37 ◽  
Author(s):  
Elimhan N. Mahmudov
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Higher Order ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Functional Constraints ◽  
Complementary Slackness ◽  
Complementary Slackness Conditions

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler–Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

scholarly journals Taxonomic assignment for large-scale metagenomic data on high-perfomance systems

2017 ◽  
Vol 33 (2) ◽  
pp. 119-130
Author(s):  
Vinh Van Le ◽  
Hoai Van Tran ◽  
Hieu Ngoc Duong ◽  
Giang Xuan Bui ◽  
Lang Van Tran
Keyword(s):  
High Performance Computing ◽  
Assignment Problem ◽  
High Performance ◽  
Large Scale ◽  
Computing System ◽  
Metagenomic Data ◽  
Taxonomic Assignment ◽  
High Performance Computing System ◽  
Powerful Approach ◽  
Performance Computing

Metagenomics is a powerful approach to study environment samples which do not require the isolation and cultivation of individual organisms. One of the essential tasks in a metagenomic project is to identify the origin of reads, referred to as taxonomic assignment. Due to the fact that each metagenomic project has to analyze large-scale datasets, the metatenomic assignment is very much computation intensive. This study proposes a parallel algorithm for the taxonomic assignment problem, called SeMetaPL, which aims to deal with the computational challenge. The proposed algorithm is evaluated with both simulated and real datasets on a high performance computing system. Experimental results demonstrate that the algorithm is able to achieve good performance and utilize resources of the system efficiently. The software implementing the algorithm and all test datasets can be downloaded at http://it.hcmute.edu.vn/bioinfo/metapro/SeMetaPL.html.

The Discrete Optimal Assignment Problem

2016 ◽  
Author(s):  
Alfred Galichon
Keyword(s):  
Linear Programming ◽  
Assignment Problem ◽  
Linear Programming Problem ◽  
Matrix Algebra ◽  
Probability Distributions ◽  
Marginal Probability ◽  
Finite Support ◽  
Complementary Slackness ◽  
Finite Dimensional ◽  
Finite Dimensional Case

This chapter considers the finite-dimensional case, which is the case when the marginal probability distributions are discrete with finite support. In this case, the Monge–Kantorovich problem becomes a finite-dimensional linear programming problem; the primal and the dual solutions are related by complementary slackness, which is interpreted in terms of stability. The solutions can be conveniently computed by linear programming solvers, and the chapter shows how this is done using some matrix algebra and Gurobi.

scholarly journals Stochastic Bilevel Program for Optimal Coordinated Energy Trading of an EV Aggregator

Energies ◽  
2019 ◽  
Vol 12 (20) ◽  
pp. 3813 ◽  
Author(s):  
Yelena Vardanyan ◽  
Henrik Madsen
Keyword(s):  
Large Scale ◽  
Stackelberg Game ◽  
Strong Duality ◽  
Bilevel Optimization ◽  
Transport Sector ◽  
Global Optimality ◽  
Complementary Slackness ◽  
Bilevel Program ◽  
Ev Charging ◽  
Stochastic Bilevel Program

Gradually replacing fossil-fueled vehicles in the transport sector with Electric Vehicles (EVs) may help ensure a sustainable future. With regard to the charging electric load of EVs, optimal scheduling of EV batteries, controlled by an aggregating agent, may provide flexibility and increase system efficiency. This work proposes a stochastic bilevel optimization problem based on the Stackelberg game to create price incentives that generate optimal trading plans for an EV aggregator in day-ahead, intra-day and real-time markets. The upper level represents the profit maximizer EV aggregator who participates in three sequential markets and is called a Stackelberg leader, while the second level represents the EV owner who aims at minimizing the EV charging cost, and who is called a Stackelberg follower. This formulation determines endogenously the profit-maximizing price levels constraint by cost-minimizing EV charging plans. To solve the proposed stochastic bilevel program, the second level is replaced by its optimality conditions. The strong duality theorem is deployed to substitute the complementary slackness condition. The final model is a stochastic convex problem which can be solved efficiently to determine the global optimality. Illustrative results are reported based on a small case with two vehicles. The numerical results rely on applying the proposed methodology to a large scale fleet of 100, 500, 1000 vehicles, which provides insights into the computational tractability of the current formulation.

A Hybrid Swarm Optimization Algorithm for Complex Assignment Problem

2010 ◽  
Vol 26-28 ◽  
pp. 1151-1154
Author(s):  
Zong Li Liu ◽  
Jie Cao ◽  
Zhan Ting Yuan
Keyword(s):  
Assignment Problem ◽  
Production Scheduling ◽  
Large Scale ◽  
Optimization Problems ◽  
Graph Model ◽  
Task Assignment ◽  
Hybrid Swarm ◽  
Swarm Optimization ◽  
Computing Technique ◽  
Task Assignment Problem

The optimization of complex systems, such as production scheduling systems and control systems, often encounters some difficulties, such as large-scale, hard to model, time consuming to evaluate, NP-hard, multi-modal, uncertain and multi-objective, etc. It is always a hot research topic in academic and engineering fields to propose advanced theory and effective algorithms. As a novel evolutionary computing technique, particle swarm optimization (PSO) is characterized by not being limited by the representation of the optimization problems, and by global optimization ability, which has gained wide attentation and research from both academic and industry fields. The task assignment problem in the enterprise with directed graph model is presented. Task assignment problem with buffer zone is solved via a hybrid PSO algorithm. Simulation result shows that the model and the algorithm are effective to the problem.

scholarly journals Optimization algorithms for large-scale real-world instances of the frequency assignment problem

2010 ◽  
Vol 15 (5) ◽  
pp. 975-990 ◽  
Author(s):  
Francisco Luna ◽  
César Estébanez ◽  
Coromoto León ◽  
José M. Chaves-González ◽  
Antonio J. Nebro ◽  
...  
Keyword(s):  
Real World ◽  
Assignment Problem ◽  
Large Scale ◽  
Optimization Algorithms ◽  
Frequency Assignment ◽  
Frequency Assignment Problem

scholarly journals A multi-start iterated tabu search algorithm for the multi-resource agent bottleneck generalized assignment problem

2019 ◽  
Vol 10 (1) ◽  
pp. 37-46
Author(s):  
Gülçin Bektur
Keyword(s):  
Tabu Search ◽  
Assignment Problem ◽  
Large Scale ◽  
Search Algorithm ◽  
Maximum Load ◽  
Mixed Integer ◽  
Generalized Assignment Problem ◽  
Generalized Assignment ◽  
Iterated Tabu Search ◽  
Resource Agent

In this study, a multi-resource agent bottleneck generalized assignment problem (MRBGAP) is addressed. In the bottleneck generalized assignment problem (BGAP), more than one job can be assigned to an agent, and the objective function is to minimize the maximum load over all agents. In this problem, multiple resources are considered and the capacity of the agents is dependent on these resources and it has minimum two indices. In addition, agent qualifications are taken into account. In other words, not every job can be assignable to every agent. The problem is defined by considering the problem of assigning jobs to employees in a firm. BGAP has been shown to be NP- hard. Consequently, a multi-start iterated tabu search (MITS) algorithm has been proposed for the solution of large-scale problems. The results of the proposed algorithm are compared by the results of the tabu search (TS) algorithm and mixed integer linear programming (MILP) model.

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