scholarly journals Black-box combinatorial optimization using models with integer-valued minima

2020 ◽  
Author(s):  
Laurens Bliek ◽  
Sicco Verwer ◽  
Mathijs de Weerdt
Keyword(s):  
Optimization Algorithm ◽  
Surrogate Model ◽  
Optimization Problems ◽  
Random Search ◽  
Continuous Optimization ◽  
Optimal Solution ◽  
Black Box ◽  
Combinatorial Problems ◽  
Bayesian Optimization ◽  
Bayesian Optimization Algorithm

Abstract When a black-box optimization objective can only be evaluated with costly or noisy measurements, most standard optimization algorithms are unsuited to find the optimal solution. Specialized algorithms that deal with exactly this situation make use of surrogate models. These models are usually continuous and smooth, which is beneficial for continuous optimization problems, but not necessarily for combinatorial problems. However, by choosing the basis functions of the surrogate model in a certain way, we show that it can be guaranteed that the optimal solution of the surrogate model is integer. This approach outperforms random search, simulated annealing and a Bayesian optimization algorithm on the problem of finding robust routes for a noise-perturbed traveling salesman benchmark problem, with similar performance as another Bayesian optimization algorithm, and outperforms all compared algorithms on a convex binary optimization problem with a large number of variables.

Decomposition of Black-Box Optimization Problems by Community Detection in Bayesian Networks

2012 ◽  
Vol 3 (4) ◽  
pp. 1-19 ◽  
Author(s):  
Marcio K. Crocomo ◽  
Jean P. Martins ◽  
Alexandre C. B. Delbem
Keyword(s):  
Probabilistic Models ◽  
Optimization Problems ◽  
Black Box ◽  
Point Of View ◽  
Bayesian Optimization ◽  
Genetic Operators ◽  
Step Method ◽  
Bayesian Optimization Algorithm ◽  
Probabilistic Sampling ◽  
Estimation Of Distribution

Estimation of Distribution Algorithms (EDAs) have proved themselves as an efficient alternative to Genetic Algorithms when solving nearly decomposable optimization problems. In general, EDAs substitute genetic operators by probabilistic sampling, enabling a better use of the information provided by the population and, consequently, a more efficient search. In this paper the authors exploit EDAs' probabilistic models from a different point-of-view, the authors argue that by looking for substructures in the probabilistic models it is possible to decompose a black-box optimization problem and solve it in a more straightforward way. Relying on the Building-Block hypothesis and the nearly-decomposability concept, their decompositional approach is implemented by a two-step method: 1) the current population is modeled by a Bayesian network, which is further decomposed into substructures (communities) using a version of the Fast Newman Algorithm. 2) Since the identified communities can be seen as sub-problems, they are solved separately and used to compose a solution for the original problem. The experiments showed strengths and limitations for the proposed method, but for some of the tested scenarios the authors’ method outperformed the Bayesian Optimization Algorithm by requiring up to 78% fewer fitness evaluations and being 30 times faster.

Cooperative Target Allocation for UCAV Team Air-to-Ground Attack Based on Decision Graph Bayesian Optimization Algorithm

2012 ◽  
Vol 457-458 ◽  
pp. 655-662
Author(s):  
Lu Cao ◽  
An Zhang ◽  
Feng Juan Guo
Keyword(s):  
Mathematical Model ◽  
Decision Making ◽  
Optimization Algorithm ◽  
Optimal Solution ◽  
Bayesian Optimization ◽  
Bayesian Optimization Algorithm ◽  
Decision Graph ◽  
Target Allocation ◽  
Cooperative Decision Making ◽  
The Mathematical Model

In order to control and optimize cooperative air-to-ground attack decision-making of the unmanned combat aerial vehicle (UCAV) team, the principle of income maximum and loss minimum of UCAV team is built firstly. Accordingly, the mathematical model of cooperative target allocation is built based on the decision variables and constraints. Then Bayesian optimization algorithm (BOA) is introduced which is one kind of the evolution algorithm. For improving the ability of the BOA, decision graph is introduced to enhance the represent and learn of Bayesian network and compress the parameter saving. Finally decision graph Bayesian optimization algorithm (DBOA) is utilized to optimize and analyze the model. The simulation results verify that the mathematical model of cooperative target allocation can reflect the importance of cooperative decision-making, the DBOA can converge quickly to the global optimal solution and can effectively solve the cooperative target allocation problem of UCAV team air-to-ground attack.

scholarly journals A Quantum Approximate Optimization Algorithm with Metalearning for MaxCut Problem and Its Simulation via TensorFlow Quantum

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Haibin Wang ◽  
Jiaojiao Zhao ◽  
Bosi Wang ◽  
Lian Tong
Keyword(s):  
Neural Network ◽  
Optimization Algorithm ◽  
Short Term Memory ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Combinatorial Problems ◽  
Quantum Neural Network ◽  
Approximate Optimization ◽  
Combinatorial Optimization Problems ◽  
Maxcut Problem

A quantum approximate optimization algorithm (QAOA) is a polynomial-time approximate optimization algorithm used to solve combinatorial optimization problems. However, the existing QAOA algorithms have poor generalization performance in finding an optimal solution from a feasible solution set of combinatorial problems. In order to solve this problem, a quantum approximate optimization algorithm with metalearning for the MaxCut problem (MetaQAOA) is proposed. Specifically, a quantum neural network (QNN) is constructed in the form of the parameterized quantum circuit to detect different topological phases of matter, and a classical long short-term memory (LSTM) neural network is used as a black-box optimizer, which can quickly assist QNN to find the approximate optimal QAOA parameters. The experiment simulation via TensorFlow Quantum (TFQ) shows that MetaQAOA requires fewer iterations to reach the threshold of the loss function, and the threshold of the loss value after training is smaller than comparison methods. In addition, our algorithm can learn parameter update heuristics which can generalize to larger system sizes and still outperform other initialization strategies of this scale.

An improved 2-pentanone low to high-temperature kinetic model using Bayesian Optimization algorithm

2021 ◽  
Vol 231 ◽  
pp. 111453
Author(s):  
Qianjin Lin ◽  
Chun Zou ◽  
Shibo Liu ◽  
Yunpeng Wang ◽  
Lixin Lu ◽  
...  
Keyword(s):  
High Temperature ◽  
Kinetic Model ◽  
Optimization Algorithm ◽  
Bayesian Optimization ◽  
Bayesian Optimization Algorithm

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.

Study on Mix-Variable Collaborative Design Optimization

2012 ◽  
Vol 215-216 ◽  
pp. 592-596
Author(s):  
Li Gao ◽  
Rong Rong Wang
Keyword(s):  
Design Optimization ◽  
Product Design ◽  
Optimization Algorithm ◽  
Collaborative Design ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Collaborative Optimization ◽  
Continuous Variables ◽  
Complex Product ◽  
Divide And Rule

In order to deal with complex product design optimization problems with both discrete and continuous variables, mix-variable collaborative design optimization algorithm is put forward based on collaborative optimization, which is an efficient way to solve mix-variable design optimization problems. On the rule of “divide and rule”, the algorithm decouples the problem into some relatively simple subsystems. Then by using collaborative mechanism, the optimal solution is obtained. Finally, the result of a case shows the feasibility and effectiveness of the new algorithm.

A Novel Approach to Designing Surrogate-assisted Genetic Algorithms by Combining Efficient Learning of Walsh Coefficients and Dependencies

2021 ◽  
Vol 1 (2) ◽  
pp. 1-23
Author(s):  
Arkadiy Dushatskiy ◽  
Tanja Alderliesten ◽  
Peter A. N. Bosman
Keyword(s):  
Boolean Functions ◽  
Surrogate Model ◽  
Optimization Problems ◽  
State Of The Art ◽  
Fitness Function ◽  
Optimal Solution ◽  
Problem Structure ◽  
Novel Approach ◽  
Efficient Learning ◽  
Nk Landscapes

Surrogate-assisted evolutionary algorithms have the potential to be of high value for real-world optimization problems when fitness evaluations are expensive, limiting the number of evaluations that can be performed. In this article, we consider the domain of pseudo-Boolean functions in a black-box setting. Moreover, instead of using a surrogate model as an approximation of a fitness function, we propose to precisely learn the coefficients of the Walsh decomposition of a fitness function and use the Walsh decomposition as a surrogate. If the coefficients are learned correctly, then the Walsh decomposition values perfectly match with the fitness function, and, thus, the optimal solution to the problem can be found by optimizing the surrogate without any additional evaluations of the original fitness function. It is known that the Walsh coefficients can be efficiently learned for pseudo-Boolean functions with k -bounded epistasis and known problem structure. We propose to learn dependencies between variables first and, therefore, substantially reduce the number of Walsh coefficients to be calculated. After the accurate Walsh decomposition is obtained, the surrogate model is optimized using GOMEA, which is considered to be a state-of-the-art binary optimization algorithm. We compare the proposed approach with standard GOMEA and two other Walsh decomposition-based algorithms. The benchmark functions in the experiments are well-known trap functions, NK-landscapes, MaxCut, and MAX3SAT problems. The experimental results demonstrate that the proposed approach is scalable at the supposed complexity of O (ℓ log ℓ) function evaluations when the number of subfunctions is O (ℓ) and all subfunctions are k -bounded, outperforming all considered algorithms.

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