scholarly journals Bang-bang control as a design principle for classical and quantum optimization algorithms

2019 ◽  
Vol 19 (5&6) ◽  
pp. 424-446
Author(s):  
Aniruddha Bapat ◽  
Stephen Jordan
Keyword(s):  
Simulated Annealing ◽  
Optimization Algorithm ◽  
Control Strategy ◽  
Design Principle ◽  
Quantum Algorithms ◽  
Optimization Algorithms ◽  
Successful Control ◽  
Problem Instances ◽  
Quantum Optimization ◽  
Bang Bang Control

Physically motivated classical heuristic optimization algorithms such as simulated annealing (SA) treat the objective function as an energy landscape, and allow walkers to escape local minima. It has been argued that quantum properties such as tunneling may give quantum algorithms advantage in finding ground states of vast, rugged cost landscapes. Indeed, the Quantum Adiabatic Algorithm (QAO) and the recent Quantum Approximate Optimization Algorithm (QAOA) have shown promising results on various problem instances that are considered classically hard. Here, building on previous observations from \cite{mcclean2016, Yang2017}, we argue that the type of control strategy used by the optimization algorithm may be crucial to its success. Along with SA, QAO, and QAOA, we define a new, bang-bang version of simulated annealing, BBSA, and study the performance of these algorithms on two well-studied problem instances from the literature. Both classically and quantumly, the successful control strategy is found to be bang-bang, exponentially outperforming the quasistatic analogues on the same instances. Lastly, we construct O(1)-depth QAOA protocols for a class of symmetric cost functions, and provide an accompanying physical picture.

scholarly journals Variational Quantum Optimization with Multi-Basis Encodings

2021 ◽  
Author(s):  
Taylor Patti ◽  
Jean Kossaifi ◽  
Anima Anandkumar ◽  
Susanne Yelin
Keyword(s):  
Nonconvex Optimization ◽  
Quantum Algorithms ◽  
Optimization Algorithms ◽  
Quantum Algorithm ◽  
Activation Functions ◽  
Quantum Formalism ◽  
Classical Simulation ◽  
Circuit Depth ◽  
Quantum Optimization ◽  
Classical Optimization

Abstract Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization landscapes. We tackle these challenges by introducing a new variational quantum algorithm that utilizes multi-basis graph encodings and nonlinear activation functions. Our technique results in increased optimization performance, a factor of two increase in effective quantum resources, and a quadratic reduction in measurement complexity. While the classical simulation of many qubits with traditional quantum formalism is impossible due to its exponential scaling, we mitigate this limitation with exact circuit representations using factorized tensor rings. In particular, the shallow circuits permitted by our technique, combined with efficient factorized tensor-based simulation, enable us to successfully optimize the MaxCut of the nonlocal 512-vertex DIMACS library graphs on a single GPU. By improving the performance of quantum optimization algorithms while requiring fewer quantum resources and utilizing shallower, more error-resistant circuits, we offer tangible progress for variational quantum optimization.

scholarly journals A New “Good and Bad Groups-Based Optimizer” for Solving Various Optimization Problems

2021 ◽  
Vol 11 (10) ◽  
pp. 4382
Author(s):  
Ali Sadeghi ◽  
Sajjad Amiri Doumari ◽  
Mohammad Dehghani ◽  
Zeinab Montazeri ◽  
Pavel Trojovský ◽  
...  
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Fitness Function ◽  
Optimization Algorithms ◽  
Gravitational Search Algorithm ◽  
Gray Wolf ◽  
Good Group ◽  
Good Ability ◽  
Whale Optimization

Optimization is the science that presents a solution among the available solutions considering an optimization problem’s limitations. Optimization algorithms have been introduced as efficient tools for solving optimization problems. These algorithms are designed based on various natural phenomena, behavior, the lifestyle of living beings, physical laws, rules of games, etc. In this paper, a new optimization algorithm called the good and bad groups-based optimizer (GBGBO) is introduced to solve various optimization problems. In GBGBO, population members update under the influence of two groups named the good group and the bad group. The good group consists of a certain number of the population members with better fitness function than other members and the bad group consists of a number of the population members with worse fitness function than other members of the population. GBGBO is mathematically modeled and its performance in solving optimization problems was tested on a set of twenty-three different objective functions. In addition, for further analysis, the results obtained from the proposed algorithm were compared with eight optimization algorithms: genetic algorithm (GA), particle swarm optimization (PSO), gravitational search algorithm (GSA), teaching–learning-based optimization (TLBO), gray wolf optimizer (GWO), and the whale optimization algorithm (WOA), tunicate swarm algorithm (TSA), and marine predators algorithm (MPA). The results show that the proposed GBGBO algorithm has a good ability to solve various optimization problems and is more competitive than other similar algorithms.

A multi-objective operation strategy optimization for ice storage systems based on decentralized control structure

2020 ◽  
Vol 42 (1) ◽  
pp. 62-81
Author(s):  
Yanhuan Ren ◽  
Junqi Yu ◽  
Anjun Zhao ◽  
Wenqiang Jing ◽  
Tong Ran ◽  
...  
Keyword(s):  
Energy Saving ◽  
Decentralized Control ◽  
Optimization Algorithm ◽  
Control Strategy ◽  
Load Distribution ◽  
Air Conditioning ◽  
Control Structure ◽  
Ice Storage ◽  
Swarm Optimization ◽  
Multi Objective

Improving the operational efficiency of chillers and science-based planning the cooling load distribution between the chillers and ice tank are core issues to achieve low-cost and energy-saving operations of ice storage air-conditioning systems. In view of the problems existing in centralized control architecture applied in heating, ventilation, and air conditioning, a distributed multi-objective particle swarm optimization improved by differential evolution algorithm based on a decentralized control structure was proposed. The energy consumption, operating cost, and energy loss were taken as the objectives to solve the chiller’s hourly partial load ratio and the cooling ratio of ice tank. A large-scale shopping mall in Xi’an was used as a case study. The results show that the proposed algorithm was efficient and provided significantly higher energy-savings than the traditional control strategy and particle swarm optimization algorithm, which has the advantages of good convergence, high stability, strong robustness, and high accuracy. Practical application: The end equipment of the electromechanical system is the basic component through the building operation. Based on this characteristic, taken electromechanical equipment as the computing unit, this paper proposes a distributed multi-objective optimization control strategy. In order to fully explore the economic and energy-saving effect of ice storage system, the optimization algorithm solves the chillers operation status and the load distribution. The improved optimization algorithm ensures the diversity of particles, gains fast optimization speed and higher accuracy, and also provides a better economic and energy-saving operation strategy for ice storage air-conditioning projects.

scholarly journals GMBO: Group Mean-Based Optimizer for Solving Various Optimization Problems

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1190
Author(s):  
Mohammad Dehghani ◽  
Zeinab Montazeri ◽  
Štěpán Hubálovský
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Random Search ◽  
Optimization Algorithms ◽  
Gravitational Search Algorithm ◽  
Main Idea ◽  
Population Based ◽  
Grey Wolf Optimizer ◽  
Whale Optimization

There are many optimization problems in the different disciplines of science that must be solved using the appropriate method. Population-based optimization algorithms are one of the most efficient ways to solve various optimization problems. Population-based optimization algorithms are able to provide appropriate solutions to optimization problems based on a random search of the problem-solving space without the need for gradient and derivative information. In this paper, a new optimization algorithm called the Group Mean-Based Optimizer (GMBO) is presented; it can be applied to solve optimization problems in various fields of science. The main idea in designing the GMBO is to use more effectively the information of different members of the algorithm population based on two selected groups, with the titles of the good group and the bad group. Two new composite members are obtained by averaging each of these groups, which are used to update the population members. The various stages of the GMBO are described and mathematically modeled with the aim of being used to solve optimization problems. The performance of the GMBO in providing a suitable quasi-optimal solution on a set of 23 standard objective functions of different types of unimodal, high-dimensional multimodal, and fixed-dimensional multimodal is evaluated. In addition, the optimization results obtained from the proposed GMBO were compared with eight other widely used optimization algorithms, including the Marine Predators Algorithm (MPA), the Tunicate Swarm Algorithm (TSA), the Whale Optimization Algorithm (WOA), the Grey Wolf Optimizer (GWO), Teaching–Learning-Based Optimization (TLBO), the Gravitational Search Algorithm (GSA), Particle Swarm Optimization (PSO), and the Genetic Algorithm (GA). The optimization results indicated the acceptable performance of the proposed GMBO, and, based on the analysis and comparison of the results, it was determined that the GMBO is superior and much more competitive than the other eight algorithms.

scholarly journals A New Approach for Real Time Train Energy Efficiency Optimization

Energies ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 2660 ◽  
Author(s):  
Agostinho Rocha ◽  
Armando Araújo ◽  
Adriano Carvalho ◽  
João Sepulveda
Keyword(s):  
Energy Efficiency ◽  
Simulated Annealing ◽  
Energy Consumption ◽  
Real Time ◽  
Optimization Algorithm ◽  
Normal Operation ◽  
Speed Profile ◽  
Railway Systems ◽  
Optimal Speed ◽  
Advisory System

Efficient use of energy is currently a very important issue. As conventional energy resources are limited, improving energy efficiency is, nowadays, present in any government policy. Railway systems consume a huge amount of energy, during normal operation, some routes working near maximum energy capacity. Therefore, maximizing energy efficiency in railway systems has, recently, received attention from railway operators, leading to research for new solutions that are able to reduce energy consumption without timetable constraints. In line with these goals, this paper proposes a Simulated Annealing optimization algorithm that minimizes train traction energy, constrained to existing timetable. For computational effort minimization, re-annealing is not used, the maximum number of iterations is one hundred, and generation of cruising and braking velocities is carefully made. A Matlab implementation of the Simulated Annealing optimization algorithm determines the best solution for the optimal speed profile between stations. It uses a dynamic model of the train for energy consumption calculations. Searching for optimal speed profile, as well as scheduling constraints, also uses line shape and velocity limits. As results are obtained in seconds, this new algorithm can be used as a real-time driver advisory system for energy saving and railway capacity increase. For now, a standalone version, with line data previously loaded, was developed. Comparison between algorithm results and real data, acquired in a railway line, proves its success. An implementation of the developed work as a connected driver advisory system, enabling scheduling and speed constraint updates in real time, is currently under development.

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