On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

A cuckoo search optimization scheme for non-convex economic load dispatch

This paper presents a Cuckoo Search (CS) based algorithm to solve constrained economic load dispatch (ELD) problems. The proposed methodology easily deals with non-smoothness of cost function arising due to the use of valve point effects. The performance of the algorithm has been tested on systems possessing 13 and 40 generating units involving varying degrees of complexity. The findings affirm that the method outperforms the existing techniques, and can be a promising alternative approach for solving the ELD problems in practical power system

Chaos Firefly Algorithm With Self-Adaptation Mutation Mechanism for Solving Large-Scale Economic Dispatch With Valve-Point Effects and Multiple Fuel Options

This paper presents a new metaheuristic optimization algorithm, the firefly algorithm (FA), and an enhanced version of it, called chaos mutation FA (CMFA), for solving power economic dispatch problems while considering various power constraints, such as valve-point effects, ramp rate limits, prohibited operating zones, and multiple generator fuel options. The algorithm is enhanced by adding a new mutation strategy using self-adaptation parameter selection while replacing the parameters with fixed values. The proposed algorithm is also enhanced by a self-adaptation mechanism that avoids challenges associated with tuning the algorithm parameters directed against characteristics of the optimization problem to be solved. The effectiveness of the CMFA method to solve economic dispatch problems with high nonlinearities is demonstrated using five classic test power systems. The solutions obtained are compared with the results of the original algorithm and several methods of optimization proposed in the previous literature. The high performance of the CMFA algorithm is demonstrated by its ability to achieve search solution quality and reliability, which reflected in minimum total cost, convergence speed, and consistency

A review of optimal operation of microgrids

The term microgrid refers to small-scale power grid that can operate autonomously or in concurrence with the area’s main electrical grid. The intermittent characteristic of DGs which defies the power quality and voltage manifests the requirement for new planning and operation approaches for microgrids. Consequently, conventional optimization methods in new power systems have been critically biased all through the previous decade. One of the main technological and inexpensive tools in this regard is the optimal generation scheduling of microgrid. As a primary optimization tool in the planning and operation fields, optimal operation has an undeniable part in the power system. This paper reviews and evaluates the optimal operation approaches mostly related to microgrids. In this work, the foremost optimal generation scheduling approaches are compared in terms of their objective functions, techniques and constraints. To conclude, a few fundamental challenges occurring from the latest optimal generation scheduling techniques in microgrids are addressed

Optimal Control Design for Multiterminal HVDC

This thesis proposes an optimal-control based design for distributed frequency control in multi-terminal high voltage direct current (MTDC) systems. The current power grid has become overstressed by rapid growth in the demand for electric power and penetration of renewable energy. To address these challenges, MTDC technology has been developed, which has the potential to increase the flexibility and reliability of power transmission in the grid. Several control strategies have been proposed to regulate the MTDC system and its interaction with connected AC systems. However, all the existing control strategies are based on proportional and integral (PI) control with predetermined controller structures. The objective of the thesis is to first determine if existing control structures are optimal, and if improved controller structures can be developed.The thesis proposes a general framework to determine the optimal structure for the control system in MTDC transmission through optimal feedback control. The proposed method is validated and demonstrated using an example of frequency control in a MTDC system connecting five AC areas

Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems

Many areas in power systems require solving one or more nonlinear optimization problems. While analytical methods might suffer from slow convergence and the curse of dimensionality, heuristics-based swarm intelligence can be an efficient alternative. Particle swarm optimization (PSO), part of the swarm intelligence family, is known to effectively solve large-scale nonlinear optimization problems. This paper presents a detailed overview of the basic concepts of PSO and its variants. Also, it provides a comprehensive survey on the power system applications that have benefited from the powerful nature of PSO as an optimization technique. For each application, technical details that are required for applying PSO, such as its type, particle formulation (solution representation), and the most efficient fitness functions are also discussed