Classical Optimization Techniques Research Articles

Classic Optimization Techniques Applied to Stormwater and Nonpoint Source Pollution Management at the Watershed Scale

AbstractLinear and dynamic programming formulations are introduced for optimizing the placement of distributed best management practices (BMPs) at the watershed scale. The results of linear programming optimization of infiltration-based stormwater management BMPs are compared with the results of genetic algorithm (GA)optimization using a nonlinear distributed model. Additionally, linear and dynamic programming optimization of sediment-trapping BMPs are compared with GA optimization using a nonlinear distributed model. The results indicate that the solution to stormwater peak-flow reduction is influenced primarily by distributed-flow arrival time, and a linear programming analog to a nonlinear optimization model can efficiently reproduce much of the same solution structure. Linear and dynamic programming solutions to the storm sediment-management problem indicate natural sediment trapping is an important consideration, and a solution to the sediment-management-optimization problem can be efficiently found ...

A faster optimization method based on support vector regression for aerodynamic problems

In this paper, a new strategy for optimal design of complex aerodynamic configuration with a reasonable low computational effort is proposed. In order to solve the formulated aerodynamic optimization problem with heavy computation complexity, two steps are taken: (1) a sequential approximation method based on support vector regression (SVR) and hybrid cross validation strategy, is proposed to predict aerodynamic coefficients, and thus approximates the objective function and constraint conditions of the originally formulated optimization problem with given limited sample points; (2) a sequential optimization algorithm is proposed to ensure the obtained optimal solution by solving the approximation optimization problem in step (1) is very close to the optimal solution of the originally formulated optimization problem. In the end, we adopt a complex aerodynamic design problem, that is optimal aerodynamic design of a flight vehicle with grid fins, to demonstrate our proposed optimization methods, and numerical results show that better results can be obtained with a significantly lower computational effort than using classical optimization techniques.

Robust, fast and optimal solution of practical economic dispatch by a new enhanced gradient‐based simplified swarm optimisation algorithm

Nowadays, the rising concern about the costs of fuel and operation of generating units in the energy control centre deserve progress of solution methodologies for the practical economic dispatch (ED) problems. ED aims to schedule the committed units’ output power while satisfying practical constraints and load demand. The generator ramp rate limits, non-convex and discontinuous nature of prohibited operating zones, non-smooth characteristic of valve-point effects, multi-fuel type of generation units, transmission line losses and the large number of units in practical power plants make this problem very hard to solve. In this study, a new solution method of integrating the classical gradient-based optimisation technique and a new enhanced simplified swarm optimisation algorithm is comprehensively presented and successfully applied to determine the feasible, robust, fast and globally or near-globally optimal solution within a rapid timeframe for the ED problems. The simulations are carried out on four-test systems, including 10-, 15-, 40- and 80-units using the proposed optimisation technique in the Fortran Power Station 4.0 software. The current proposal outperforms other methods showcased in the recent state-of-the art literature in the area.

A mixed-integer LP model for the reconfiguration of radial electric distribution systems considering distributed generation

The problem of reconfiguration of distribution systems considering the presence of distributed generation is modeled as a mixed-integer linear programming (MILP) problem in this paper. The demands of the electric distribution system are modeled through linear approximations in terms of real and imaginary parts of the voltage, taking into account typical operating conditions of the electric distribution system. The use of an MILP formulation has the following benefits: (a) a robust mathematical model that is equivalent to the mixed-integer non-linear programming model; (b) an efficient computational behavior with exiting MILP solvers; and (c) guarantees convergence to optimality using classical optimization techniques. Results from one test system and two real systems show the excellent performance of the proposed methodology compared with conventional methods.

Optimization of the Annealing Parameters for Improved Tensile Properties in Cold Drawn 0.12 wt% C Steel

Drawn low carbon steel is characterized by brittle fracture. These defects are associated with the poor ductility and high strain hardening due to the cold work. There is a need therefore to determine optimum heat treatment parameters that could ensure improved toughness and ductility. Determining the optimum annealing parameters ensures valued recrystallization and also minimizes grain growth that could be detrimental to the resulting product. 40% and 55% cold drawn steels were annealed at temperatures 500℃ to 650℃ at intervals of 50℃ and soaked for 10 to 60 minutes at interval of 10 minutes to identify the temperature range and soaking time where optimum combination of properties could be obtained. Tensile test and impact toughness experiments were done to determine the required properties of the steel. Polynomial regression analysis was used to fit the properties relationship with soaking time and temperatures and the classical optimization technique was used to determine the minimum soaking time and temperature required for improved properties of the steel. Annealing treatment at 588℃ for 11 minutes at grain size of 44.7 mm can be considered to be the optimum annealing treatment for the 40% cold drawn 0.12 wt% C steel and 539℃ for 17 minutes at grain size of 19.5 mm for the 55% cold drawn 0.12 wt% C steel.

Estimation of Open Boundary Conditions for an Internal Tidal Model with Adjoint Method: A Comparative Study on Optimization Methods

Based on an internal tidal model, the practical performances of the limited-memory BFGS (L-BFGS) method and two gradient descent (GD) methods (the normal one with Wolfe’s line search and the simplified one) are investigated computationally through a series of ideal experiments in which the open boundary conditions (OBCs) are inverted by assimilating the interior observations with the adjoint method. In the case that the observations closer to the unknown boundary are included for assimilation, the L-BFGS method performs the best. As compared with the simplified GD method, the normal one really uses less iteration to reach a satisfactory solution, but its advantage over the simplified one is much smaller than expected. In the case that only the observations that are further from the unknown boundary are assimilated, the simplified GD method performs the best instead, whereas the performances of the other two methods are not satisfactory. The advanced L-BFGS algorithm and Wolfe’s line search still need to be improved when applied to the practical cases. The simplified GD method, which is controllable and easy to implement, should be regarded seriously as a choice, especially when the classical advanced optimization techniques fail or perform poorly.

Multimodal optimization by artificial weed colonies enhanced with localized group search optimizers

Multimodal optimization aims at finding multiple global and local optima (as opposed to a single solution) of a function, so that the user can have a better knowledge about different optimal solutions in the search space and as and when needed, the current solution may be switched to another suitable one while still maintaining the optimal system performance. Evolutionary Algorithms (EAs) due to their population-based approach are able to detect multiple solutions within a population in a single simulation run and have a clear advantage over the classical optimization techniques, which need multiple restarts and multiple runs in the hope that a different solution may be discovered every run, with no guarantee however. This article proposes a hybrid two-stage optimization technique that firstly employs Invasive Weed Optimization (IWO), an ecologically inspired algorithm to find the promising Euclidean sub-regions surrounding multiple global and local optima. IWO is run for 80% of the total budget of function evaluations (FEs), and consecutively the search is intensified by using a modified Group Search Optimizer (GSO), in each detected sub-region. GSO, invoked in each sub-region discovered with IWO, is continued for 20% of the total budget of FEs. Both IWO and GSO have been modified from their original forms to meet the demands of the multimodal problems used in this work. Performance of the proposed algorithm is compared with a number of state-of-the-art multimodal optimization algorithms over a benchmark-suite comprising of 21 basic multimodal problems and 7 composite multimodal problems. A practical multimodal optimization problem concerning the design of dielectric composites has also been used to test the performance of the algorithm. Experimental results suggest that the proposed technique is able to provide better and more consistent performance over the existing well-known multimodal algorithms for majority of the test problems without incurring any serious computational burden.

Constrained Nonlinear Optimal Control via a Hybrid BA-SD

The non-convex behavior presented by nonlinear systems limits the application of classical optimization techniques to solve optimal control problems for these kinds of systems. This paper proposes a hybrid algorithm, namely BA-SD, by combining Bee algorithm (BA) with steepest descent (SD) method for numerically solving nonlinear optimal control (NOC) problems. The proposed algorithm includes the merits of BA and SD simultaneousl y. The motivation of presenting the proposed algorithm includes that BA is showed to converge to the region that global optimum is settled, rapidly during the initial stages of its search. However, around global optimum, the search process will become slowly. In contrast, SD method has low ability to convergence to local optimum, but it can achieve faster convergent speed around global optimum and the convergent accuracy can be higher. In the proposed algorithm, at the beginning step of search procedure, BA is utilized to find a near optimum solution. In this case, the hybrid algorithm is used to enhance global search ability. When the change in fitness value is smaller than a predefined value, the searching procedure is switched to SD to accelerate the search procedure and find an accurate solution. In this way, the algorithm finds an optimum solution more accurately. Simulations demonstrate the feasibility of the proposed algorithm.

A novel multi-objective directed bee colony optimization algorithm for multi-objective emission constrained economic power dispatch

In this paper, a multi-objective directed bee colony optimization algorithm (MODBC) is comprehensively developed and successfully applied for solving a multi-objective problem of optimizing the conflicting economic dispatch and emission cost with both equality and inequality constraints is showcased. Classical optimization techniques like direct search and gradient methods fail to give the global optimum solution. The proposed algorithm is an integration of the deterministic search, the multi-agent system (MAS) environment and the bee decision-making process. Thus making use of deterministic search, multi-agent environment and bee swarms, the MODBC realizes the purpose of optimization. The hybridization makes MODBC to obtain a unique and fast solution and hence generate a better pareto front for multi-objective problems. The above mentioned multi-objective evolutionary algorithms have been applied to the standard IEEE 30 bus six generator test system. Results of the proposed algorithm have been compared with traditional methods like linear programming (LP) and multi-objective stochastic search technique (MOSST). The performance of the introduced algorithm is also compared with other evolutionary algorithms like Non-dominated Sorting Genetic Algorithm (NSGA), Niched Pareto Genetic Algorithm (NPGA) and Strength Pareto Evolutionary Algorithm (SPEA) and Particle Swarm Optimization (PSO). The results show the robustness and accuracy of the proposed algorithm over the traditional methods and its other multi-objective evolutionary algorithm (MOEA) counterparts.

Coordinated tuning of power system stabilizers based on Fourier Transform and neural networks

This paper analyzes optimal tuning of power system stabilizers (PSSs) as the main resource for small-signal stability enhancement in power systems. The procedure is based on dynamic power system response and its frequency amplitude spectrum. Since the optimization model is very complex, there are difficulties in defining the algebraic relation between optimization criteria and PSS parameters and the authors concluded that classical optimization techniques are inappropriate for application in practice. To avoid these problems, application of artificial neural networks (ANNs) as efficient functional approximators is proposed. Optimal PSS parameters are determined by trust region based optimization, where the ANN represents an input function. Robustness of the optimization is ensured with the proposed ANN structure which considers an arbitrary number of different power system operating conditions (including single contingencies). For verification of the proposed methodology, two test systems are used: the New England-New York 68-node, 16-machine test system and the 75-machine dynamic model of the Serbian power system. Poorly damped modes of oscillation are identified and damped by installation of PSSs at appropriate locations with ANN-based optimally tuned parameters.

Application of an anisotropic growth and remodelling formulation to computational structural design

A classical structural optimisation problem consists of a problem-specific objective function which has to be minimised in consideration of particular constraints with respect to design and state variables. In this contribution we adopt a conceptually different approach for the design of a structure which is not based on a classical optimisation technique. Instead, we establish a constitutive micro-sphere-framework in combination with an energy-driven anisotropic microstructural growth formulation, which was originally proposed for the simulation of adaptation and remodelling phenomena in hard biological tissues such as bones.The goal of this contribution is to investigate this anisotropic growth formulation with a special emphasis on its application to structural design problems. To this end, four illustrative three-dimensional benchmark-type boundary value problems are discussed and compared qualitatively with the results obtained by classical structural optimisation strategies. The simulation results capture the densification effects and clearly identify the main load bearing regions. It turns out, that even though making use of this conceptually different growth formulation as compared to the procedures used in a classical structural optimisation context, we identify qualitatively very similar structures or rather regions of densification. Moreover, in contrast to common structural optimisation strategies, which mostly aim to optimise merely the size, shape or topology, our formulation also contains the improvement of the material itself, which—apart from the structural improvement—results in the generation of problem-specific local material anisotropy and textured evolution.

Particle Swarm Optimization Technique for Solving Economic Emission Dispatch Problems

This paper presents a new approach to Economic Emission Dispatch (EED) with the consideration of five thermal generating units using Particle Swarm Particle Swarm Optimization Technique (PSO). To reduce SO2 and NOX emission, there are various methods, such as installing post-combustion cleaning system, switching to fuels with low emission potential and dispatching load with consideration of an environmental issue. Among them, formulation of environmental economic dispatch is preferred in operation of the existing systems because it is easy to implement and requires minimal additional costs. Economic emission dispatch is subject to a number of inequality and equality constraints. Many of these techniques suffer from natural complexity and converge slowly. The PSO method has been applied successfully meeting all the constraints and compared with the classical optimization technique. In this project the results of PSO are compared with the results of conventional method and proved to be better

Design Optimization of Micro-channel Heat Exchanger embedded in LTCC

Increase in the density of electronic packaging leads to the investigation of highly efficient thermal management systems. The challenge in these micro-systems is to maximize heat transfer per unit volume. In the author's previous work, experimental and computational analysis has been performed on LTCC substrates using embedded silver vias. This novel technique of embedding silver vias along with forced convection resulted in higher heat transfer rates. The present work further investigates into the optimization of this model. A Multi-objective optimization problem has been formulated for the heat transfer in the LTCC model. The Log Mean Temperature Difference (LMTD) method of heat exchangers has been used in the formulation. Optimization is done based on maximization of the total heat transferred and minimization of the coolant pumping power. Structural and thermal design variables are considered to meet the manufacturability and energy requirements. Demanded pressure loss and volume of the silver metal are used as constraints. The classical optimization technique Sequential Quadratic Programming (SQP) is used to solve the micro-heat exchanger problem. The optimal design is presented and sensitivity analysis results are discussed.

Shape optimization of the hydrogen fuel cell cathode air channels

In this paper we deal with the shape optimization of the hydrogen fuel cell cathode air channel. We consider a 2d isothermal model given by a nonlinear PDEs system, involving the oxygen and vapor concentrations, 2 the velocity of the gas mixture and the pressure. The shape energy associated to this system “measures” the concentration of the oxygen on the catalyst layer, the concentration of the vapor on the outlet and the pressure drop. By using a fixed point approach we prove the existence of solution to the PDE system without restriction on data, and the uniqueness of the solution if the inlet oxygen concentration is small. Using classical shape optimization techniques we prove the shape differentiability of the state variables and of the shape energy. By using an appropriate adjoint problem we transform the shape energy derivative to a form appropriate for numerical computations. Finally, we present several numerical solutions of optimal cathode air channel shape. 2 Here concentration means mass fraction.

Single-vendor single-buyer inventory model with discrete delivery order, random machine unavailability time and lost sales

Integrated single-vendor single-buyer inventory model with multiple deliveries has proved to result in less inventory cost. However, many researchers assumed that the production run is perfect and there is no production delay. In reality, production delay is prevalent due to random machine unavailability and shortages. This study considers lost sales, and two kinds of machine unavailability distributions—uniformly and exponentially distributed. A classical optimization technique is used to derive an optimal solution and a numerical example is provided to illustrate the theory. The results show that delivery frequency has significant effect on the optimal total cost, and a higher lost sales cost will result in a higher delivery frequency.

Portfolio Selection in Asset Liability Management Using Probabilistic Utility Functions

This paper develops a new portfolio selection method within an asset liability framework (ALM) using Bayesian theory. We propose the portfolio selection approach of Marschinski, Rossi, Tavoni and Cocco (2007) to overcome the drawbacks of classical optimization techniques based on maximization of expected utility (MEU). While there is no objective rule about how to scale the risk-aversion parameter, which stands in contrast to the strong effect this parameter causes on portfolio weights, we reinterpret the optimal portfolio as the logarithm of a probability distribution for optimal portfolios and no longer as the (single) extremum of a suitably chosen utility function. Numerical results illustrate that we are able to overcome the extreme sensitivity to external parameters and consider the uncertainty obtained from finite historical time series.

Guest editorial: model selection and optimization in machine learning

Machine learning methods largely benefit from optimization techniques in order to find an optimal model for future predictions and decisions. The interplay of machine learning and optimization methods is much like operations research (OR). Optimization, also called mathematical programming, is a subfield of OR. Both machine learning and OR are concerned with modeling of systems related to real-world problems. In machine learning (ML), the common practice is to use classical optimization techniques. However, due to massive and large-scale data sets faced in real world problems, optimization becomes a challenging task and traditional approaches cannot keep up with expectations. Accordingly, optimization methods adapted or integrated for machine learning tasks are needed to make ML more feasible for real world data sets. Another important challenging task is model selection. Because of the mathematical structure of the optimization model, there are parameters to be searched offline for the training data. Statistical model selection methods such as crossvalidation can be very time consuming when the size and the dimension of the training data is large. Thus, developing powerful model selection methods is an important factor for the feasibility of the algorithm solving the optimization problem. This special issue on “Model Selection and Optimization in ML” was inspired from the stream “Model Selection and Optimization Techniques in Machine Learning” organized by Kristiaan Pelckmans and Sureyya Ozogur-Akyuz at 23rd European Conference on Operational Research held in Bonn, Germany, July 5–8, 2009.

Real-parameter evolutionary multimodal optimization — A survey of the state-of-the-art

Multimodal optimization amounts to finding multiple global and local optima (as opposed to a single solution) of a function, so that the user can have a better knowledge about different optimal solutions in the search space and as and when needed, the current solution may be switched to another suitable one while still maintaining the optimal system performance. Evolutionary Algorithms (EAs), due to their population-based approaches, are able to detect multiple solutions within a population in a single simulation run and have a clear advantage over the classical optimization techniques, which need multiple restarts and multiple runs in the hope that a different solution may be discovered every run, with no guarantee however. Numerous evolutionary optimization techniques have been developed since late 1970s for locating multiple optima (global or local). These techniques are commonly referred to as “niching” methods. Niching can be incorporated into a standard EA to promote and maintain formation of multiple stable subpopulations within a single population, with an aim to locate multiple globally optimal or suboptimal solutions simultaneously. This article is the first of its kind to present a comprehensive review of the basic concepts related to real-parameter evolutionary multimodal optimization, a survey of the major niching techniques, a detailed account of the adaptation of EAs from diverse paradigms to tackle multimodal problems, benchmark problems and performance measures.

CUDA Memory Optimizations for Large Data-Structures in the Gravit Simulator

Modern GPUs open a completely new field to optimize embarrassingly parallel algorithms. Implementing an algorithm on a GPU confronts the programmer with a new set of challenges for program optimization. Especially tuning the program for the GPU memory hierarchy whose organization and performance implications are radically different from those of general purpose CPUs; and optimizing programs at the instruction-level for the GPU. In this paper we analyze different approaches for optimizing the memory usage and access patterns for GPUs and propose a class of memory layout optimizations that can take full advantage of the unique memory hierarchy of NVIDIA CUDA. Furthermore, we analyze some classical optimization techniques and how they effect the performance on a GPU. We used the Gravit gravity simulator to demonstrate these optimizations. The final optimized GPU version achieves a 87× speedup compared to the original CPU version. Almost 30% of this speedup are direct results of the optimizations discussed in this paper.

A Fully Distributed Lagrangean Solution for a Peer-to-Peer Overlay Network Design Problem

Peer-to-peer (P2P) computing already accounts for a large part of the traffic on the Internet, and it is likely to become as ubiquitous as current client/server architectures in next generation information systems. This paper addresses a central problem of P2P systems: the design of an optimal overlay communication network for a set of processes on the Internet. Such a network defines membership to the P2P group and allows for members to disseminate information within the group. The problem, named the membership overlay problem (MOP), can be formulated as a dynamic optimization problem where classical combinatorial optimization techniques must face the further challenge of time-varying input data. This paper proposes an innovative, fully distributed, and asynchronous subgradient optimization algorithm for the Lagrangean relaxation of the MOP, which can run online in fully decentralized P2P systems, and integrates it with a distributed heuristic that can achieve sound hot-start states for fast response to varying network structures.