Continuous Optimization Tasks Research Articles

Toward Large-Scale Evolutionary Multitasking: A GPU-Based Paradigm

Evolutionary multitasking (EMT), which shares knowledge across multiple tasks while the optimization progresses online, has demonstrated superior performance in terms of both optimization quality and convergence speed over its single-task counterpart in solving complex optimization problems. However, most of the existing EMT algorithms only consider handling two tasks simultaneously. As the computational cost incurred in the evolutionary search and knowledge transfer increased rapidly with the number of optimization tasks, these EMT algorithms cannot meet today’s requirements of optimization service on the cloud for many real-world applications, where hundreds or thousands of optimization requests (labeled as large-scale EMT) are often received simultaneously and require to be optimized in a short time. Recently, graphics processing unit (GPU) computing has attracted extensive attention to accelerate the applications possessing large-scale data volume that are traditionally handled by the central processing unit (CPU). Taking this cue, toward large-scale EMT, in this article, we propose a new EMT paradigm based on the island model with the compute unified device architecture (CUDA), which is able to handle a large number of continuous optimization tasks efficiently and effectively. Moreover, under the proposed paradigm, we develop the GPU-based <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">implicit</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">explicit</i> knowledge transfer mechanisms for EMT. To evaluate the performance of the proposed paradigm, comprehensive empirical studies have been conducted against its CPU-based counterpart in large-scale EMT.

Fuzzy Adaptive Teaching Learning-Based Optimization for Solving Unconstrained Numerical Optimization Problems

Teaching learning-based optimization is one of the widely accepted metaheuristic algorithms inspired by teaching and learning within classrooms. It has successfully addressed several real-world optimization problems, but it may still be trapped in local optima and may suffer from the problem of premature convergence in the case of solving some challenging optimization problems. To overcome these drawbacks and to achieve an appropriate percentage of exploitation and exploration, this study presents a new modified teaching learning-based optimization algorithm called the fuzzy adaptive teaching learning-based optimization algorithm. The proposed fuzzy adaptive teaching learning-based optimization algorithm uses three measures from the search space, namely, quality measure, diversification measure, and intensification measure. As the 50-50 probabilities for exploitation and exploration in the basic teaching learning-based optimization algorithm may be counterproductive, the Mamdani-type fuzzy inference system of the new algorithm takes these measures as a crisp inputs and generates selection as crisp output to choose either exploitation or exploration based on the current search requirement. This fuzzy-based adaptive selection helps to adequately balance global search or exploration and local search or exploitation operations during the search process as these operations are intrinsically dynamic. The performance of the fuzzy adaptive teaching learning-based optimization is evaluated against other metaheuristic algorithms including basic teaching learning-based optimization on 23 unconstrained global test functions. Moreover, adaptive teaching learning-based optimization is used to search for near-optimal values for the four parameters of the COCOMO II model, which are then tested for validity on a software project of NASA. Analysis and comparison of the obtained results indicate the efficiency and competitiveness of the proposed algorithm in addressing unconstrained continuous optimization tasks.

Method for splitting the feasible region to increase the variability of continuous optimization test problems

The solution of optimization problems is essential for the design and control of technical systems. The optimization problem arising in practice has a high dimension, nonlinear criteria, and constraints. There are a lot of continuous optimization tasks for testing and research of optimization algorithms performance. These tasks have a convex range of acceptable values limited to a specified range for each parameter. The problem of generating test multidimensional continuous optimization tasks with nonlinear constraints and splitting the feasible region is considered. A method was proposed for splitting the feasible region by separate domains using the multidimensional grid of forbidden solutions. As a result, the problem acquires properties closer to optimizing technical systems with complex constraints. The method allows creating an unlimited number of test optimization problems, which can be used to research and develop optimization algorithms. The method is simple to implement, and the impact on the computational complexity of tasks is insignificant. Research has been carried out on four widely used continuous single-objective optimization test functions, with the Genetic algorithm and the Particle Swarm Optimization algorithm. It is shown that the proposed method has an influence on the process of solving multidimensional continuous optimization problems by population algorithms and on the dependence of the accuracy of the algorithm on its heuristic coefficients.

METHOD FOR SPLITTING THE FEASIBLE REGION TO INCREASE THE VARIABILITY OF CONTINUOUS OPTIMIZATION TEST PROBLEMS

The solution of optimization problems is essential for the design and control of technical systems. The optimization problem arising in practice has a high dimension, nonlinear criteria, and constraints. There are a lot of continuous optimization tasks for testing and research of optimization algorithms performance. These tasks have a convex range of acceptable values limited to a specified range for each parameter. The problem of generating test multidimensional continuous optimization tasks with nonlinear constraints and splitting the feasible region is considered. A method was proposed for splitting the feasible region by separate domains using the multidimensional grid of forbidden solutions. As a result, the problem acquires properties closer to optimizing technical systems with complex constraints. The method allows creating an unlimited number of test optimization problems, which can be used to research and develop optimization algorithms. The method is simple to implement, and the impact on the computational complexity of tasks is insignificant. Research has been carried out on four widely used continuous single-objective optimization test functions, with the Genetic algorithm and the Particle Swarm Optimization algorithm. It is shown that the proposed method has an influence on the process of solving multidimensional continuous optimization problems by population algorithms and on the dependence of the accuracy of the algorithm on its heuristic coefficients.

When causal inference meets deep learning

Bayesian networks can capture causal relations, but learning such a network from data is NP-hard. Recent work has made it possible to approximate this problem as a continuous optimization task that can be solved efficiently with well-established numerical techniques.

Nonlinear Optimization Strategies for Process Separations and Process Intensification

AbstractAdvanced nonlinear programming (NLP) strategies based on equation‐oriented (EO) process models are leading to significant improvements in computer‐aided process engineering. The EO paradigm allows the development of large, integrated optimization platforms that expand the scope of continuous optimization tasks in process engineering. In particular, these platforms deploy significantly faster NLP strategies than in commercial simulation tools. Moreover, they exploit exact derivatives and system structure in order to consider much larger and more challenging systems. Finally, they allow the incorporation of much more general models, such as multi‐level optimization and complementarity constraints. For process optimization this allows the treatment of extended models for complex phase equilibrium and process separations. These advances facilitate the optimization of novel integrated systems that arise in process intensification. Several separation case studies are presented that illustrate these optimization concepts and demonstrate their effectiveness for hybrid membrane/distillation separations and reactive distillation systems that typify novel systems in process intensification.

A binary social spider algorithm for continuous optimization task

The social spider algorithm (SSA) is a new heuristic algorithm created on spider behaviors. The original study of this algorithm was proposed to solve continuous problems. In this paper, the binary version of SSA (binary SSA) is introduced to solve binary problems. Currently, there is insufficient focus on the binary version of SSA in the literature. The main part of the binary version is at the transfer function. The transfer function is responsible for mapping continuous search space to discrete search space. In this study, four of the transfer functions divided into two families, S-shaped and V-shaped, are evaluated. Thus, four different variations of binary SSA are formed as binary SSA-Tanh, binary SSA-Sigm, binary SSA-MSigm and binary SSA-Arctan. Two different techniques (SimSSA and LogicSSA) are developed at the candidate solution production schema in binary SSA. SimSSA is used to measure similarities between two binary solutions. With SimSSA, binary SSA’s ability to discover new points in search space has been increased. Thus, binary SSA is able to find global optimum instead of local optimums. LogicSSA which is inspired by the logic gates and a popular method in recent years has been used to avoid local minima traps. By these two techniques, the exploration and exploitation capabilities of binary SSA in the binary search space are improved. Eighteen unimodal and multimodal standard benchmark optimization functions are employed to evaluate variations of binary SSA. To select the best variations of binary SSA, a comparative study is presented. The Wilcoxon signed-rank test has applied to the experimental results of variations of binary SSA. Compared to well-known evolutionary and recently developed methods in the literature, the variations of binary SSA performance is quite good. In particular, binary SSA-Tanh and binary SSA-Arctan variations of binary SSA showed superior performance.

A novel algorithm for integrated control model using swarm robots for intruder detection and rescue schedules

Due to the development of computer controlled tools and expansion of integrated computing applications, more and more controller functions are turning to software implementations. A novel controlling algorithm is designed for continuous optimization tasks. However, they are used to thoroughly optimize and apply different areas. The most intelligent swarm algorithms have been designed for continuous optimization problems. However, they have been applied to discreet optimization and applications in different areas. This article gives experimental results on the control of swarm robots with the help of integrated control model (ICM), around its own axis. Such methodology is quite impressive in development of applications for surveillance, path planning, intruder and obstacle detection, model errors in communication to remove uncertainty. The ICM control design performance is based on comprehensive swarm robot model for the identification of actuators from testing data. The same ICM controllers are designed to be compared with the PID controllers in a variety of tests and collected feedback found 12.37%, 8.69% and 12.09% improved on the basis of thrust produced in the propellers for surveillance.

A Comparative Study on Prominent Swarm Intelligence Methods for Function Optimization

Optimization includes finding best available values of some objective function given a defined domain. Function optimization (FO) is the well-studied continuous optimization task which aim is to find best suited parameter values to get optimal value of a function. A number of techniques have been investigated in last few decades to solve FO and recently Swarm Intelligence (SI) methods, imitating power of the collective behavior of insects or animals, become popular to solve it. A number of SI methods have been developed on different time and tested on different test functions; therefore, it is important to compare the algorithms on a common test bench to identify their capability as well as best suited method for FO. The objective of this study is to draw a fair comparison among prominent SI methods in solving benchmark test functions. The SI methods considered in this study are Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC) optimization, Firefly Algorithm (FFA), Cuckoo Search Optimization (CSO), Group Search Optimization (GSO) and Grey Wolf Optimizer (GWO). Among the methods PSO is the pioneer and most popular in recent time; and GWO is the most recently developed method. The performance of the methods is compared in solving a suite of 22 well known benchmark test functions having different ranges, dimensions and types. Experimental results as well as analysis revealed that GWO is the overall best method among the SI methods and PSO is still promising to solve bench mark functions.

Intensity-based image registration using scatter search

We present a novel intensity-based algorithm for medical image registration (IR). The IR problem is formulated as a continuous optimization task, and our work focuses on the development of the optimization component. Our method is designed over an advanced scatter search template, and it uses a combination of restart and dynamic boundary mechanisms integrated within a multi-resolution strategy. The experimental validation is performed over two datasets of human brain magnetic resonance imaging. The algorithm is evaluated in both a stand-alone registration application and an atlas-based segmentation process targeted to the deep brain structures, considering a total of 16 and 18 scenarios, respectively. Five established IR techniques, both feature- and intensity-based, are considered for comparison purposes, and ground-truth data is used to quantitatively assess the quality of the results. Our approach ranked first in both studies and it is able to outperform all competitors in 12 of 16 registration scenarios and in 14 of 18 registration-based segmentation tasks. A statistical analysis confirms with high confidence (p<0.014) the accuracy and applicability of our method. With a proper, problem-specific design, scatter search is able to provide a robust, global optimization. The accuracy and reliability of the registration process are superior to those of classic gradient-based techniques.

New MINLP Model and Modified Outer Approximation Algorithm for Distillation Column Synthesis

A new, R-graph based, superstructure and corresponding MINLP model for designing conventional distillation columns are presented. A GDP representation (GR) of the superstructure is first constructed, then it is transformed to MINLP representation to which, in turn, additional trivial improvements are added. The new model has been tested on binary mixture examples, and the obtained results are compared to the results of an MINLP model which developed according to the GDP model of Yeomans and Grossmann. 9 The new model yields shorter computation time and provides better local optima. Additionally, the new model has been used for optimizing a complex multicomponent separation system consisting of several distillation columns. In order to handle such a complex system with a huge number of nonlinear equations, the outer approximation algorithm is modified to provide good initial values for the NLP subproblems. Distillation is one of the most widespread processes applied for separating multicomponent liquid mixtures. It is used for working up large volume or stream, and it requires high investment and operation outlays. The significance of the design of economically optimal distillation processes is of no question. Enormous interest has also been addressed to the area of designing optimal heat integrated distillation columns and distillation sequences. Minimizing the cost of a distillation process implies finding the optimal configuration of each individual column, as well. In the present article we consider staged column models only. The number of stages, and the stage numbers of the feed and side-stream points, are discrete decision variables. The total cost of a column may be modeled as the sum of the fix (capital) cost, depending on the number of stages and on the column diameter, and the variable (operation) cost related to the utility consumption. The objective of the design procedure is to find the optimal configuration of the column, which has the minimum total (annualized) cost. In order to model these processes, discrete decisions are required for calculating the number of stages. Optimizing single columns is a well-known procedure; all the basic textbooks outline how to do it in an easy manner. 1 After approximately determining the minimum and the estimated optimal number of theoretical stages, optimizing over the continuous variables is performed at varied values of the discrete variables. This is a 2-dimension discrete array of continuous optimization tasks in the case of a single-feed, two-product column, because there are merely two column sections in this case. This task becomes much more difficult if several feeds and side-products are to be taken into account. The real problem, however, is synthesizing a distillation sequence, or a system of advanced distillation columns, or a complex flowsheet containing distillation units when the number of distillation columns and their connections are not known in advance. In order to solve the complex synthesis problem outlined above, a proper superstructure for a single column, together with a proper generalized disjunctive programming (GDP) model or a proper mixed-integer nonlinear programming (MINLP) model, is a minimum requirement. Once such a model works well for a single column, the problem of more complex flowsheets may also be addressed. Mixed-integer nonlinear programming (MINLP) and generalized disjunctive programming (GDP) are the two exact methodologies commonly applied for solving process engineering problems with discrete decisions. The former includes algebraic equations describing the process, and binary variables related to discrete decisions. The latter method uses logic variables and expressions to represent the problem. 2 Both formulations have been successfully applied to rigorous models of distillation columns. Both methods apply a fixed maximum number of stages, and the actually used stages are selected from this set. Mathematical formulations that represent rigorous models of distillation column configurations fall into two categories: (i) one task-one equipment (OTOE) representations and (ii) variable task-equipment (VTE) representations. 3

Convergence of taboo search in continuous global optimization

While taboo search (TS), a method of global optimization, has successfully solved many optimization problems, little is known about its convergence properties, especially for continuous optimization tasks. We consider the global convergence of the original TS for solving continuous optimization problems, and give a condition which guarantees the convergence of the objective value sequence of the method. We also prove that the minimum objective value sequence converges to the vicinity of the global optimal value with probability 1.