An Exact Algorithm for Large-Scale Continuous Nonlinear Resource Allocation Problems with Minimax Regret Objectives

2021 ◽  
Author(s):  
Jungho Park ◽  
Hadi El-Amine ◽  
Nevin Mutlu
Keyword(s):  
Resource Allocation ◽  
Objective Function ◽  
Large Scale ◽  
Computational Study ◽  
Optimal Solution ◽  
Exact Algorithm ◽  
Minimax Regret ◽  
Optimal Solutions ◽  
Heuristic Approaches ◽  
Exact Approach

We study a large-scale resource allocation problem with a convex, separable, not necessarily differentiable objective function that includes uncertain parameters falling under an interval uncertainty set, considering a set of deterministic constraints. We devise an exact algorithm to solve the minimax regret formulation of this problem, which is NP-hard, and we show that the proposed Benders-type decomposition algorithm converges to an [Formula: see text]-optimal solution in finite time. We evaluate the performance of the proposed algorithm via an extensive computational study, and our results show that the proposed algorithm provides efficient solutions to large-scale problems, especially when the objective function is differentiable. Although the computation time takes longer for problems with nondifferentiable objective functions as expected, we show that good quality, near-optimal solutions can be achieved in shorter runtimes by using our exact approach. We also develop two heuristic approaches, which are partially based on our exact algorithm, and show that the merit of the proposed exact approach lies in both providing an [Formula: see text]-optimal solution and providing good quality near-optimal solutions by laying the foundation for efficient heuristic approaches.

scholarly journals Temporal concatenation for Markov decision processes

2021 ◽  
pp. 1-28
Author(s):  
Ruiyang Song ◽  
Kuang Xu
Keyword(s):  
Markov Decision Processes ◽  
Large Scale ◽  
Optimal Solution ◽  
Upper Bounds ◽  
Black Box ◽  
Decision Processes ◽  
Optimal Solutions ◽  
Wide Range ◽  
Markov Decision ◽  
Speed Up

We propose and analyze a temporal concatenation heuristic for solving large-scale finite-horizon Markov decision processes (MDP), which divides the MDP into smaller sub-problems along the time horizon and generates an overall solution by simply concatenating the optimal solutions from these sub-problems. As a “black box” architecture, temporal concatenation works with a wide range of existing MDP algorithms. Our main results characterize the regret of temporal concatenation compared to the optimal solution. We provide upper bounds for general MDP instances, as well as a family of MDP instances in which the upper bounds are shown to be tight. Together, our results demonstrate temporal concatenation's potential of substantial speed-up at the expense of some performance degradation.

Towards Intelligent Road Traffic Management over Weighted Large Graphs Hybrid Meta-heuristic-Based Approach

2022 ◽  
Vol 24 (3) ◽  
pp. 0-0
Keyword(s):  
Traffic Management ◽  
Large Scale ◽  
Road Traffic ◽  
Optimization Technique ◽  
Shortest Paths ◽  
Hybrid Genetic Algorithm ◽  
Optimal Solution ◽  
Computation Time ◽  
Exact Algorithm ◽  
On The Road

This paper introduces a new approach of hybrid meta-heuristics based optimization technique for decreasing the computation time of the shortest paths algorithm. The problem of finding the shortest paths is a combinatorial optimization problem which has been well studied from various fields. The number of vehicles on the road has increased incredibly. Therefore, traffic management has become a major problem. We study the traffic network in large scale routing problems as a field of application. The meta-heuristic we propose introduces new hybrid genetic algorithm named IOGA. The problem consists of finding the k optimal paths that minimizes a metric such as distance, time, etc. Testing was performed using an exact algorithm and meta-heuristic algorithm on random generated network instances. Experimental analyses demonstrate the efficiency of our proposed approach in terms of runtime and quality of the result. Empirical results obtained show that the proposed algorithm outperforms some of the existing technique in term of the optimal solution in every generation.

Genetic Algorithm and Other Meta-Heuristics

2005 ◽  
pp. 144-173 ◽  
Author(s):  
Bernard K.S. Cheung
Keyword(s):  
Genetic Algorithm ◽  
Large Scale ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Schema Theory ◽  
Heuristic Methods ◽  
Optimal Solutions ◽  
Corporate Globalization ◽  
Global Optimal ◽  
Mutation And Selection

Genetic algorithms have been applied in solving various types of large-scale, NP-hard optimization problems. Many researchers have been investigating its global convergence properties using Schema Theory, Markov Chain, etc. A more realistic approach, however, is to estimate the probability of success in finding the global optimal solution within a prescribed number of generations under some function landscapes. Further investigation reveals that its inherent weaknesses that affect its performance can be remedied, while its efficiency can be significantly enhanced through the design of an adaptive scheme that integrates the crossover, mutation and selection operations. The advance of Information Technology and the extensive corporate globalization create great challenges for the solution of modern supply chain models that become more and more complex and size formidable. Meta-heuristic methods have to be employed to obtain near optimal solutions. Recently, a genetic algorithm has been reported to solve these problems satisfactorily and there are reasons for this.

scholarly journals Security-Aware Data Offloading and Resource Allocation For MEC Systems: A Deep Reinforcement Learning

2021 ◽  
Author(s):  
Ibrahim Elgendy ◽  
Ammar Muthanna ◽  
Mohammad Hammoudeh ◽  
Hadil Ahmed Shaiba ◽  
Devrim Unal ◽  
...  
Keyword(s):  
Resource Allocation ◽  
Large Scale ◽  
Optimal Solution ◽  
Security Requirements ◽  
Optimization Approach ◽  
Shared Resources ◽  
Data Offloading ◽  
Daily Lives ◽  
Industrial Iot ◽  
Iot Devices

The Internet of Things (IoT) is permeating our daily lives where it can provide data collection tools and important measurement to inform our decisions. In addition, they are continually generating massive amounts of data and exchanging essential messages over networks for further analysis. The promise of low communication latency, security enhancement and the efficient utilization of bandwidth leads to the new shift change from Mobile Cloud Computing (MCC) towards Mobile Edge Computing (MEC). In this study, we propose an advanced deep reinforcement resource allocation and securityaware data offloading model that considers the computation and radio resources of industrial IoT devices to guarantee that shared resources between multiple users are utilized in an efficient way. This model is formulated as an optimization problem with the goal of decreasing the consumption of energy and computation delay. This type of problem is NP-hard, due to the curseof-dimensionality challenge, thus, a deep learning optimization approach is presented to find an optimal solution. Additionally, an AES-based cryptographic approach is implemented as a security layer to satisfy data security requirements. Experimental evaluation results show that the proposed model can reduce offloading overhead by up to 13.2% and 64.7% in comparison with full offloading and local execution while scaling well for large-scale devices.

A Continuous Model for Designing Corridor Systems with Modular Autonomous Vehicles Enabling Station-wise Docking

2021 ◽  
Author(s):  
Zhiwei Chen ◽  
Xiaopeng Li ◽  
Xiaobo Qu
Keyword(s):  
Large Scale ◽  
Original Problem ◽  
Optimal Solution ◽  
Continuum Approximation ◽  
Optimal Solutions ◽  
Property A ◽  
Passenger Demand ◽  
Operational Design ◽  
Wide Range ◽  
Ca Model

The “asymmetry” between spatiotemporally varying passenger demand and fixed-capacity transportation supply has been a long-standing problem in urban mass transportation (UMT) systems around the world. The emerging modular autonomous vehicle (MAV) technology offers us an opportunity to close the substantial gap between passenger demand and vehicle capacity through station-wise docking and undocking operations. However, there still lacks an appropriate approach that can solve the operational design problem for UMT corridor systems with MAVs efficiently. To bridge this methodological gap, this paper proposes a continuum approximation (CA) model that can offer near-optimal solutions to the operational design for MAV-based transit corridors very efficiently. We investigate the theoretical properties of the optimal solutions to the investigated problem in a certain (yet not uncommon) case. These theoretical properties allow us to estimate the seat demand of each time neighborhood with the arrival demand curves, which recover the “local impact” property of the investigated problem. With the property, a CA model is properly formulated to decompose the original problem into a finite number of subproblems that can be analytically solved. A discretization heuristic is then proposed to convert the analytical solution from the CA model to feasible solutions to the original problem. With two sets of numerical experiments, we show that the proposed CA model can achieve near-optimal solutions (with gaps less than 4% for most cases) to the investigated problem in almost no time (less than 10 ms) for large-scale instances with a wide range of parameter settings (a commercial solver may even not obtain a feasible solution in several hours). The theoretical properties are verified, and managerial insights regarding how input parameters affect system performance are provided through these numerical results. Additionally, results also reveal that, although the CA model does not incorporate vehicle repositioning decisions, the timetabling decisions obtained by solving the CA model can be easily applied to obtain near-optimal repositioning decisions (with gaps less than 5% in most instances) very efficiently (within 10 ms). Thus, the proposed CA model provides a foundation for developing solution approaches for other problems (e.g., MAV repositioning) with more complex system operation constraints whose exact optimal solution can hardly be found with discrete modeling methods.

scholarly journals Security-Aware Data Offloading and Resource Allocation For MEC Systems: A Deep Reinforcement Learning

2021 ◽  
Author(s):  
Ibrahim Elgendy ◽  
Ammar Muthanna ◽  
Mohammad Hammoudeh ◽  
Hadil Ahmed Shaiba ◽  
Devrim Unal ◽  
...  
Keyword(s):  
Resource Allocation ◽  
Large Scale ◽  
Optimal Solution ◽  
Security Requirements ◽  
Optimization Approach ◽  
Shared Resources ◽  
Data Offloading ◽  
Daily Lives ◽  
Industrial Iot ◽  
Iot Devices

The Internet of Things (IoT) is permeating our daily lives where it can provide data collection tools and important measurement to inform our decisions. In addition, they are continually generating massive amounts of data and exchanging essential messages over networks for further analysis. The promise of low communication latency, security enhancement and the efficient utilization of bandwidth leads to the new shift change from Mobile Cloud Computing (MCC) towards Mobile Edge Computing (MEC). In this study, we propose an advanced deep reinforcement resource allocation and securityaware data offloading model that considers the computation and radio resources of industrial IoT devices to guarantee that shared resources between multiple users are utilized in an efficient way. This model is formulated as an optimization problem with the goal of decreasing the consumption of energy and computation delay. This type of problem is NP-hard, due to the curseof-dimensionality challenge, thus, a deep learning optimization approach is presented to find an optimal solution. Additionally, an AES-based cryptographic approach is implemented as a security layer to satisfy data security requirements. Experimental evaluation results show that the proposed model can reduce offloading overhead by up to 13.2% and 64.7% in comparison with full offloading and local execution while scaling well for large-scale devices.

scholarly journals APLIKASI FUZZY PADA PERMASALAHAN PROGRAM TAK-LINIER

2011 ◽  
Vol 5 (2) ◽  
pp. 35-38
Author(s):  
Abraham Z. Wattimena
Keyword(s):  
Objective Function ◽  
Value Function ◽  
Optimal Solution ◽  
Optimal Solutions ◽  
Non Linear ◽  
Fuzzy Parameter

One of the most purpose of non linear programing is to determine the optimal solution of its objective function. If the objective function of a certain non linear programing only possess a uniqe value function, it is easy to calculate its optimal solution. However, if the objective function of non linier programing possess multi functions, so there are two possibilities to determine their optimal solutions. Theses depend on whether there are conflic among them or not. In order to make them more easier, the fuzzy parameter could be applied to calculate the optimal solution.

scholarly journals Towards Intelligent Road Traffic Management Over a Weighted Large Graphs Hybrid Meta-Heuristic-Based Approach

2022 ◽  
Vol 24 (3) ◽  
pp. 1-18
Author(s):  
Mohamed Yassine Hayi ◽  
Zahira Chouiref ◽  
Hamouma Moumen
Keyword(s):  
Traffic Management ◽  
Large Scale ◽  
Road Traffic ◽  
Optimization Technique ◽  
Shortest Paths ◽  
Hybrid Genetic Algorithm ◽  
Optimal Solution ◽  
Computation Time ◽  
Exact Algorithm ◽  
On The Road

This paper introduces a new approach of hybrid meta-heuristics based optimization technique for decreasing the computation time of the shortest paths algorithm. The problem of finding the shortest paths is a combinatorial optimization problem which has been well studied from various fields. The number of vehicles on the road has increased incredibly. Therefore, traffic management has become a major problem. We study the traffic network in large scale routing problems as a field of application. The meta-heuristic we propose introduces new hybrid genetic algorithm named IOGA. The problem consists of finding the k optimal paths that minimizes a metric such as distance, time, etc. Testing was performed using an exact algorithm and meta-heuristic algorithm on random generated network instances. Experimental analyses demonstrate the efficiency of our proposed approach in terms of runtime and quality of the result. Empirical results obtained show that the proposed algorithm outperforms some of the existing technique in term of the optimal solution in every generation.

scholarly journals Fighting Wildfires under Uncertainty - A Sequential Resource Allocation Approach

2020 ◽  
Author(s):  
Hau Chan ◽  
Long Tran-Thanh ◽  
Vignesh Viswanathan
Keyword(s):  
Resource Allocation ◽  
Disaster Response ◽  
Optimal Solution ◽  
Optimal Solutions ◽  
Resource Allocation Algorithm ◽  
Efficient Resource ◽  
Resource Allocation Strategy ◽  
Sequential Resource Allocation ◽  
Utility Estimation ◽  
Allocation Approach

Standard disaster response involves using drones (or helicopters) for reconnaissance and using people on the ground to mitigate the damage. In this paper, we look at the problem of wildfires and propose an efficient resource allocation strategy to cope with both dynamically changing environment and uncertainty. In particular, we propose Firefly, a new resource allocation algorithm, that can provably achieve optimal or near optimal solutions with high probability by first efficiently allocating observation drones to collect information to reduce uncertainty, and then allocate the firefighting units to extinguish fire. For the former, Firefly uses a combination of maximum set coverage formulation and a novel utility estimation technique, and it uses a knapsack formulation to calculate the allocation for the latter. We also demonstrate empirically by using a real-world dataset that Firefly achieves up to 80-90% performance of the offline optimal solution, even with a small amount of drones, in most of the cases.

scholarly journals Improving ADMMs for solving doubly nonnegative programs through dual factorization

4OR ◽  
2020 ◽  
Author(s):  
Martina Cerulli ◽  
Marianna De Santis ◽  
Elisabeth Gaar ◽  
Angelika Wiegele
Keyword(s):  
Objective Function ◽  
Large Scale ◽  
Objective Function Value ◽  
Optimal Solution ◽  
Stable Set ◽  
Dual Variable ◽  
Post Processing ◽  
Semidefinite Programs ◽  
The Matrix ◽  
The Impact

Abstract Alternating direction methods of multipliers (ADMMs) are popular approaches to handle large scale semidefinite programs that gained attention during the past decade. In this paper, we focus on solving doubly nonnegative programs (DNN), which are semidefinite programs where the elements of the matrix variable are constrained to be nonnegative. Starting from two algorithms already proposed in the literature on conic programming, we introduce two new ADMMs by employing a factorization of the dual variable. It is well known that first order methods are not suitable to compute high precision optimal solutions, however an optimal solution of moderate precision often suffices to get high quality lower bounds on the primal optimal objective function value. We present methods to obtain such bounds by either perturbing the dual objective function value or by constructing a dual feasible solution from a dual approximate optimal solution. Both procedures can be used as a post-processing phase in our ADMMs. Numerical results for DNNs that are relaxations of the stable set problem are presented. They show the impact of using the factorization of the dual variable in order to improve the progress towards the optimal solution within an iteration of the ADMM. This decreases the number of iterations as well as the CPU time to solve the DNN to a given precision. The experiments also demonstrate that within a computationally cheap post-processing, we can compute bounds that are close to the optimal value even if the DNN was solved to moderate precision only. This makes ADMMs applicable also within a branch-and-bound algorithm.

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