Much work has been published on the theoretical aspects of simulated annealing. This paper provides a brief overview of this theory and provides an introduction to the practical aspects of function optimization using this approach. Different implementations of the general simulated annealing algorithm are discussed, and two examples are used to illustrate the behaviour of the algorithm in low dimensions. A third example illustrates a hybrid approach, combining simulated annealing with traditional techniques.

Optimization Using Simulated Annealing

In this paper, sharp a posteriori error estimators are derived for a class of distributed elliptic optimal control problems. These error estimators are shown to be useful in adaptive finite element approximation for the optimal control problems and are implemented in the adaptive approach. Our numerical results indicate that the sharp error estimators work satisfactorily in guiding the mesh adjustments and can save substantial computational work.

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Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems

In this paper, we present an a posteriori error analysis for finite element approximation of distributed convex optimal control problems. We derive a posteriori error estimates for the coupled state and control approximations under some assumptions which hold in many applications. Such estimates, which are apparently not available in the literature, can be used to construct reliable adaptive finite element approximation schemes for control problems. Explicit estimates are obtained for some model problems which frequently appear in real-life applications.

A Posteriori Error Estimates for Distributed Convex Optimal Control Problems

HVDC systems are playing an increasingly significant role in energy transmission due to their technical and economic superiority over HVAC systems for long distance transmission. HVDC is preferable beyond 300–800 km for overhead point-to-point transmission projects and for the cable based interconnection or the grid integration of remote offshore wind farms beyond 50–100 km. Several HVDC review papers exist in literature but often focus on specific geographic locations or system components. In contrast, this paper presents a detailed, up-to-date, analysis and assessment of HVDC transmission systems on a global scale, targeting expert and general audience alike. The paper covers the following aspects: technical and economic comparison of HVAC and HVDC systems; investigation of international HVDC market size, conditions, geographic sparsity of the technology adoption, as well as the main suppliers landscape; and high-level comparisons and analysis of HVDC system components such as Voltage Source Converters (VSCs) and Line Commutated Converters (LCCs), etc. The presented analysis are supported by practical case studies from existing projects in an effort to reveal the complex technical and economic considerations, factors and rationale involved in the evaluation and selection of transmission system technology for a given project. The contemporary operational challenges such as the ownership of Multi-Terminal DC (MTDC) networks are also discussed. Subsequently, the required development factors, both technically and regulatory, for proper MTDC networks operation are highlighted, including a future outlook of different HVDC system components. Collectively, the role of HVDC transmission in achieving national renewable energy targets in light of the Paris agreement commitments is highlighted with relevant examples of potential HVDC corridors.

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HVDC Transmission: Technology Review, Market Trends and Future Outlook

Real-world optimization problems often require the minimization/maximization of more than one objective, which, in general, conflict with each other. These problems (multiobjective optimization problems, vector optimization problems) are usually treated by using weighted sums or other decision-making schemes. An alternative way is to look for the pareto-optimal front. In this paper, the particle swarm algorithm is modified to detect the pareto-optimal front.

Pareto optimality and particle swarm optimization

This paper gives an overview of some stochastic optimization strategies, namely, evolution strategies, genetic algorithms, and simulated annealing, and how these methods can be applied to problems in electrical engineering. Since these methods usually require a careful tuning of the parameters which control the behavior of the strategies (strategy parameters), significant features of the algorithms implemented by the authors are presented. An analytical comparison among them is performed. Finally, results are discussed on three optimization problems.

Stochastic algorithms in electromagnetic optimization

A combined strategy for optimization of electromagnetic devices based on a two-stage scheme is described Two different ways of implementing a simulated annealing algorithm, one for discrete and one for continuous variables, have been implemented and tested The second one proved to be more reliable and problem-independent than the other This technique was used in a combined optimization strategy in combination with a pattern search method The combined strategy was tested versus analytical and numerical objective functions and showed good behavior, saving, in the best case, up to 70% of the iterations needed for a complete simulated annealing run The combined strategy was also tested in magnet design problems, with both analytical objective functions and objective functions evaluated by means of finite element codes The results obtained were encouraging in terms of the objective function values obtained and in the computer time needed >

A combined strategy for optimization in nonlinear magnetic problems using simulated annealing and search techniques

The paper discusses the use of different, "design of experiment" and statistical theory based methods to improve and speed up the "generalised response surface method", using multiquadrics to describe the objective function in parameter space, for the optimization of multiminima design problems in magnetics. The effectiveness of the proposed approach to enhance the convergence of stochastic optimisation algorithms is tested on a couple of test problems and the results are discussed.

A "design of experiment" and statistical approach to enhance the "generalised response surface" method in the optimisation of multiminima problems

The problem of design optimization is of high industrial interest, and has been extensively studied for years, with excellent results. However, there is the well-known issue of a reasonable balance between the computational effort usually required by stochastic methods, and the fact that deterministic optimizers, even though much more efficient, are not guaranteed to localize a good minimum, as they can remain trapped in the first found local one. To overcome these problems, the authors developed a hybrid strategy, which gave good results in terms of speed and reliability of the obtained optima, especially when the objective function is obtained through a finite element analysis, due, for example, to the absence of an analytical solution of the problem, and the direct use of a stochastic method would be unfeasible for practical purposes, because of the intolerable processing time required. Copyright © 2001 John Wiley & Sons, Ltd.

M. Nervi

Papers

Stochastic algorithms in electromagnetic optimization

A combined strategy for optimization in nonlinear magnetic problems using simulated annealing and search techniques

A "design of experiment" and statistical approach to enhance the "generalised response surface" method in the optimisation of multiminima problems

An efficient hybrid algorithm for the optimization of problems with several local minima

Ground/sea return with electrode systems for HVDC transmission