Multi-fidelity Optimization Approach Under Prior and Posterior Constraints and Its Application to Compliance Minimization

Covariance matrix adaptation evolution strategy based on ensemble of mutations for parking navigation and maneuver of autonomous vehicles

The relationship between Constraint Handling Techniques (CHTs) and Constrained Optimization Problems (COPs) is an important issue as it gives some direction on deciding when and how to use these CHTs effectively. In the previous studies, the relationship between problems and algorithms as well as the CHTs are studied from the qualitative and quantitative aspects. This paper tries to study the relationship between COPs and two simple CHTs, i.e., Deb’s feasibility-based rule and multiobjective optimization technique, with a new set of benchmark functions adopted. The experimental results show the importance of the classification of problems, which is a basis for related research.

Modern power systems which integrate renewable energy sources (RESs), such as wind or solar energy sources and plug-in electric vehicles (PEVs), need to carry out the uncertainty due to the access of demanded or injected power. Therefore, it is necessary to consider uncertainty costs in optimal power flow problems. To develop the uncertainty cost functions, log-normal probability distribution function (PDF) for solar irradiance, normal PDF for unloading and loading behavior of PEVs, and Rayleigh PDF for wind speed are considered. In this work, a dynamic optimal power flow (DOPF) model is formulated by considering the uncertainties of RESs and PEVs. A newly hybrid metaheuristic algorithm named cross entropy (CE) covariance matrix adaption evolutionary strategy (CMAES) is proposed to evaluate the DOPF problem in a modified IEEE 118-bus system. The application of adaptive step length in the CMAES method improves the local exploitation capability, while the CE method is used in the initial stage for global exploration due to its fast convergence. Simulation results indicate that the proposed technique can solve the DOPF problems with RESs and PEVs effectively and can provide high-quality solutions compared to different techniques. The conventional statistical method called ANOVA test is performed for comparative analysis of different techniques. The results of this test show the validation of CE-CMAES compared to different optimization techniques. Therefore, the proposed method could be easily and efficiently applied by power system operators in real-time optimal power flow operations.

Optimization of fed-batch fermentation processes using the Backtracking Search Algorithm

This paper presents an extended variant of the distance-weighted exponential natural evolution strategy (DXNES) that works well in uncertain environments. Since we often face objective functions with uncertain parameters in real-world problems, function optimization in uncertain environments is an important problem. The covariance matrix adaptation evolution strategy (CMA-ES) and DX-NES have been proposed as promising methods for function optimization in deterministic environments. The performance of these methods, however, deteriorates in uncertain environments. The uncertain handling CMA-ES (TIH-CMA-ES) has been proposed as an extended variant of CMA-ES for uncertain environments and has shown relatively good performance on problems with uncertain parameters. In this paper, we propose an extended variant of DX-NES named DX-NES for uncertain environments (DX-NES-TIE). DX-NES-TIE approximates the objective function by a quadratic function. DXNES-TIE uses approximation function values for updating the mutation distribution if the noise is strong; otherwise it uses observed objective function values. The strength of the noise is quantified by using the approximation function and the evolution path. Through numerical experiments on 20-dimensional uncertain benchmark problems, we demonstrate that DX-NES-TIE can find ten to 2,000 times as accurate solutions as TIH-CMA-ES can. We also apply DX-NES-TIE to 80-dimensional problems and confirm that DX-NES-TIE is scalable with respect to problem dimensionality.

A fast constrained state transition algorithm

This paper presents a novel boundary approach which is included as a constraint-handling technique in an ant colony algorithm. The necessity of approaching the boundary between the feasible and infeasible search space for many constrained optimization problems is a paramount challenge for every constraint-handling technique. Our proposed technique precisely focuses the search on the boundary region and can be either used alone or in combination with other constraint-handling techniques depending on the type and number of problem constraints. For validation purposes, an ant algorithm is adopted as our search engine. We compare our proposed approach with respect to constraint-handling techniques that are representative of the state-of-the-art in constrained evolutionary optimization using a set of standard test functions.

The big bang--big crunch (BB--BC) algorithm has been proposed as a novel optimization method that relies on one of the theories of the evolution of the universe, namely the big bang and big crunch theory. It has been shown that this algorithm is capable of quick convergence, even in long, narrow parabolic-shaped flat valleys or in the existence of several local extremes. In this work, the BB--BC optimization algorithm is hybridized with local search moves in between the ``banging'' and ``crunching'' phases of the algorithm. These 2 original phases of the BB--BC algorithm are preserved, but the representative point (``best'' or ``fittest'' point) attained after the crunching phase of the iteration is modified with some local directional moves, using the previous representative points so far attained, with the hope that a better representative point would be obtained. The effect of imposing local directional moves is inspected by comparing the results of the original and enhanced BB--BC algorithm on various benchmark test functions. Moreover, the crunching phase of the algorithm is improved with the addition of a simplex-based local search routine. The results of the new hybridized algorithm are compared with the state-of-the-art variants of widely used evolutionary computation methods, namely genetic algorithms, covariance matrix adaptation evolutionary strategies, and particle swarm optimization. The results over the benchmark test functions have proven that the BB--BC algorithm, enhanced with local directional moves, has provided more accuracy with the same computation time or for the same number of function evaluations.

Almost all real-world and engineering problems involve multi-objective optimization of some sort that is often constrained. To solve these constrained multi-objective optimization problems, constrained multi-objective optimization evolutionary algorithms (CMOEAs) are enlisted. These CMOEAs require specific constraint handling techniques. This study aims to address and test the most successful constraint handling techniques, seven different penalty constraint techniques, as applied to the Non-dominated Sorting Genetic Algorithm II (NSGA-II). In this paper, NSGA-II is chosen because of its high popularity amongst evolutionary algorithms. Inverted Generational Distance and Hypervolume are the main metrics that are discussed to compare the constraint handling techniques. NSGA-II is applied on 13 constrained multi-objective problems known as CF1-CF10, C1-DTLZ1, C2-DTLZ2, and C3-DTLZ4. The result of IGD and HV values are compared and the feasibility proportions of each combination on each problem are shown. The results of simulation present interesting findings that have been presented at the end of paper as discussion and conclusion.

This chapter considers a class of optimization techniques that were developed to imitate processes found in nature. Nature is a wonderful source of inspiration for global optimization because so many aspects of natural phenomenon can be mimicked and employed for solving challenging design problems, from the very process of evolution to the coordinated search behavior of various swarming organisms. Nature inspired search algorithms have played an important role in electromagnetic design, as they have proven to be very robust at solving complex problems with many design parameters. Also, as the field of metamaterials has developed, optimization has become an important tool in the quest to overcome performance limitations such as high loss and narrow bandwidth, which have limited the widespread use of metamaterials in practical device applications. In the first part of this chapter, three prominent nature inspired optimization algorithms are described in detail, including the genetic algorithm (GA), particle swarm optimization (PSO), and the covariance matrix adaptation evolutionary strategy (CMA-ES). Following this, several examples of metamaterial surfaces are presented that have each been optimized by one of the three nature inspired techniques. Finally, two homogenization techniques that can be employed to invert scattering parameters for a slab of metamaterial to obtain isotropic or anisotropic effective medium parameters are examined and used in conjunction with a GA to overcome previous limitations in terms of loss and angular stability in metamaterials.

Two approaches for solving numerical continuous domain constrained optimization problems are proposed and experimented with. The first approach is based on particle swarm optimization algorithm with a new mutation operator in its velocity updating rule. Also, a gradient mutation is proposed and incorporated into the algorithm. This algorithm uses e-level constraint handling method. The second approach is based on covariance matrix adaptation evolutionary strategy with the same method for handling constraints. It is experimentally shown that the first approach needs less number of function evaluations than the second one to find a feasible solution while the second approach is more effective in optimizing the objective value. Thus, a hybrid approach is proposed (third approach) which uses the first approach for locating potentially different feasible solutions and the second approach for further improving the solutions found so far. Also, a multi-swarm mechanism is used in which several instances of the first approach are run to locate potentially different feasible solutions. The proposed hybrid approach is applied to 18 standard constrained optimization benchmarks with up to 30 dimensions. Comparisons with two other state-of-the-art approaches show that the hybrid approach performs better in terms of finding feasible solutions and minimizing the objective function.

A hybrid particle swarm with a time-adaptive topology for constrained optimization

Real world problems are often formularised as constrained optimisation problems (COPs). Constraint handling techniques are important for efficient search, and various approaches such as penalty methods or feasibility rule have been studied. The penalty methods deal with a single fitness function by combining an objective function value and a constraint violation with a penalty factor. Moreover, the penalty factor can be flexibly adapted by feeding back information on search process in adaptive penalty methods. However, setting parameters properly and keeping the good balance between the objective function value and the constraint violation are difficult. In this paper, we propose a new parameter-free adaptive penalty method with balancing the objective function value and the constraint violation. L-SHADE is adopted as a base search algorithm, and the optimisation results of 28 benchmark functions provided by the CEC2017 and CEC2018 competitions on constrained single-objective numerical optimisations are compared with other methods.

How to balance diversity and convergence as well as constraint violation and objective function in Constrained Optimization Problems (COPs) is an important and key issue when designing a new Constrained Optimization Evolutionary Algorithms (COEAs). C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> oDE set a good example on this point, and obtains promising results. In C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> oDE, the two Constraint Handling Techniques (CHTs) are adopted fixed in two phases. To verify whether there are some other more efficient combinations, Stochastic Ranking (SR) is adopted to balance the combination. Experimental results show a good performance, which also give some inspiration for other research.

Currently, rehabilitation systems with closed kinematic chain mechanisms are low-cost alternatives for treatment and health care. In designing these systems, the dimensional synthesis is commonly stated as a constrained optimization problem to achieve repetitive rehabilitation movements, and metaheuristic algorithms for constrained problems are promising methods for searching solutions in the complex search space. The Constraint Handling Techniques (CHTs) in metaheuristic algorithms have different capacities to explore and exploit the search space. However, the study of the relationship in the CHT performance of the mechanism dimensional synthesis for rehabilitation systems has not been addressed, resulting in an important gap in the literature of such problems. In this paper, we present a comparative empirical study to investigate the influence of four CHTs (penalty function, feasibility rules, stochastic-ranking, and ϵ-constraint) on the performance of ten representative algorithms that have been reported in the literature for solving mechanism synthesis for rehabilitation (four-bar linkage, eight-bar linkage, and cam-linkage mechanisms). The study involves analysis of the overall performance, six performance metrics, and evaluation of the obtained mechanism. This identified that feasibility rules usually led to efficient optimization for most analyzed algorithms and presented more consistency of the obtained results in these kinds of problems.