The generic denomination of ‘Memetic Algorithms’ (MAs) is used to encompass a broad class of metaheuristics (i.e. general purpose methods aimed to guide an underlying heuristic). The method is based on a population of agents and proved to be of practical success in a variety of problem domains and in particular for the approximate solution of NP Optimization problems. Unlike traditional Evolutionary Computation (EC) methods, MAs are intrinsically concerned with exploiting all available knowledge about the problem under study. The incorporation of problem domain knowledge is not an optional mechanism, but a fundamental feature that characterizes MAs. This functioning philosophy is perfectly illustrated by the term “memetic”. Coined by R. Dawkins [52], the word ‘meme’ denotes an analogous to the gene in the context of cultural evolution [154]. In Dawkins’ words:

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A Gentle Introduction to Memetic Algorithms

Distribution systems commonly operate with a radial topology, so all models of optimization problems in these distribution systems should consider radiality in their formulation. This work presents a literature review, a critical analysis, and a proposal for incorporating the radiality constraints in mathematical models of optimization problems for radial distribution systems. The objective is to show that the radiality constraints on such optimization problems can be considered in a simple and efficient way. The reconfiguration and expansion planning problems of distribution systems are used to test and verify the proposed radiality constraints. A generalization of radiality constraints is also examined.

Imposing Radiality Constraints in Distribution System Optimization Problems

The directional overcurrent relays (DOCRs) coordination problem is usually studied based on a fixed network topology in an interconnected power system, and is formulated as an optimization problem. In practice, the system may be operated in different topologies due to outage of the transmission lines, transformers, and generating units. There are some situations for which the changes in the network topology of a system could cause the protective system to operate without selectivity. The aim of this paper is to study DOCRs coordination considering the effects of the different network topologies in the optimization problem. Corresponding to each network topology, a large number of coordination constraints should be taken into account in the problem formulation. In this situation, in addition to nonlinearity and nonconvexity, the optimization problem experiences many coordination constraints. The genetic algorithm (GA) is selected as a powerful tool in solving this complex and nonconvex optimization problem. In this paper, in order to improve the convergence of the GA, a new hybrid method is introduced. The results show a robust and optimal solution can be efficiently obtained by implementing the proposed hybrid GA method.

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Considering Different Network Topologies in Optimal Overcurrent Relay Coordination Using a Hybrid GA

This paper presents a model for use in the problem of multistage planning of energy distribution systems including distributed generation. The expansion model allows alternatives to be considered for increasing the capacity of existing substations, for installing new ones, for using distributed generation, and for the possible change to feeders in terms of addition and removing feeders sections; combining, subdividing, and load transfer between feeders; and replacement of conductors. The objective function to be minimized is the present value of total installation costs (feeders and substations), of operating and maintaining the network, and of distributed generation. The model takes operational constraints on equipment capacities and voltage limits together into account with logical constraints, aimed at reducing the search space. This paper presents: (1) an extension to the linear disjunctive formulation to represent the inclusion, exclusion, and replacement of branches and (2) a generalization of constraints related to the creation of new paths which can be applied in more complex topologies. The resulting mixed integer linear model allows the optimal solution to be found using mathematical programming methods, such as the branch-and-bound algorithm. The validity and efficiency of the model are demonstrated in Part II of this paper.

Multistage Model for Distribution Expansion Planning With Distributed Generation—Part I: Problem Formulation

Distributed generation, with respect to its ability in utilizing the alternative resources of energy, provides a promising future for power generation in electric networks. Distributed generators contribution to power systems include improvement in energy efficiency and power quality to reliability and security. These benefits are only achievable with optimal allocation of distributed resources that considers the objective function, constraints, and employs suitable optimization algorithm. In this paper, a comprehensive review on the optimal allocation of distributed generators was carried out for different objectives, constraints, and algorithms. Current review highlights how the methods and algorithms for optimal distributed generation allocation play an important role in improving the accuracy and efficiency of the results.

A review of the optimal allocation of distributed generation: Objectives, constraints, methods, and algorithms

The planning problem of electrical power distribution networks, stated as a mixed nonlinear integer optimization problem, is solved using the ant colony system algorithm (ACS). The behavior of real ants has inspired the development of the ACS algorithm, an improved version of the ant system (AS) algorithm, which reproduces the technique used by ants to construct their food recollection routes from their nest, and where a set of artificial ants cooperate to find the best solution through the interchange of the information contained in the pheromone deposits of the different trajectories. This metaheuristic approach has proven to be very robust when applied to global optimization problems of a combinatorial nature, such as the traveling salesman and the quadratic assignment problem, and is favorably compared to other solution approaches such as genetic algorithms (GAs) and simulated annealing techniques. In this work, the ACS methodology is coupled with a conventional distribution system load-flow algorithm and adapted to solve the primary distribution system planning problem. The application of the proposed methodology to two real cases is presented: a 34.5-kV system with 23 nodes from the oil industry and a more complex 10-kV electrical distribution system with 201 nodes that feeds an urban area. The performance of the proposed approach outstands positively when compared to GAs, obtaining improved results with significant reductions in the solution time. The technique is shown as a flexible and powerful tool for the distribution system planning engineers.

Ant colony system algorithm for the planning of primary distribution circuits

A hybrid methodology is presented for the solution of the problem of the optimal allocation of reactive power sources. The technique is based upon a modified genetic algorithm, which is applied at an upper level stage, and a successive linear program at a lower level stage. The objective is the minimization of the total cost associated to the installation of the new sources. The genetic algorithm is devoted to defining the location of the new reactive power sources, and therefore to handle the combinatorial nature of the fixed costs problem. At the lower level, the variable cost problem is solved by calculating the magnitude of the sources to be installed at the previously determined locations by means of a linear program iterated successively with a fast decoupled load flow. Results are presented for the application of the proposed methodology when applied to the Venezuelan electric network.

A hybrid genetic algorithm for optimal reactive power planning based upon successive linear programming

Presolve analysis and interior point solutions of the linear programming coordination problem of directional overcurrent relays

The capacitated dispersion problem is a variant of the maximum diversity problem in which a set of elements in a network must be determined. These elements might represent, for instance, facilities in a logistics network or transmission devices in a telecommunication network. Usually, it is considered that each element is limited in its servicing capacity. Hence, given a set of possible locations, the capacitated dispersion problem consists of selecting a subset that maximizes the minimum distance between any pair of elements while reaching an aggregated servicing capacity. Since this servicing capacity is a highly usual constraint in real-world problems, the capacitated dispersion problem is often a more realistic approach than is the traditional maximum diversity problem. Given that the capacitated dispersion problem is an NP-hard problem, whenever large-sized instances are considered, we need to use heuristic-based algorithms to obtain high-quality solutions in reasonable computational times. Accordingly, this work proposes a multi-start biased-randomized algorithm to efficiently solve the capacitated dispersion problem. A series of computational experiments is conducted employing small-, medium-, and large-sized instances. Our results are compared with the best-known solutions reported in the literature, some of which have been proven to be optimal. Our proposed approach is proven to be highly competitive, as it achieves either optimal or near-optimal solutions and outperforms the non-optimal best-known solutions in many cases. Finally, a sensitive analysis considering different levels of the minimum aggregate capacity is performed as well to complete our study.

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J.F. Gomez

Papers

Ant colony system algorithm for the planning of primary distribution circuits

A hybrid genetic algorithm for optimal reactive power planning based upon successive linear programming

Presolve analysis and interior point solutions of the linear programming coordination problem of directional overcurrent relays

A Multi-Start Biased-Randomized Algorithm for the Capacitated Dispersion Problem