Fábio Luiz Usberti

GRASP with evolutionary path-relinking for the capacitated arc routing problem

The Capacitated Arc Routing Problem (CARP) is a well-known NP-hard combinatorial optimization problem where, given an undirected graph, the objective is to find a minimum cost set of tours servicing a subset of required edges under vehicle capacity constraints. There are numerous applications for the CARP, such as street sweeping, garbage collection, mail delivery, school bus routing, and meter reading. A Greedy Randomized Adaptive Search Procedure (GRASP) with Path-Relinking (PR) is proposed and compared with other successful CARP metaheuristics. Some features of this GRASP with PR are (i) reactive parameter tuning, where the parameter value is stochastically selected biased in favor of those values which historically produced the best solutions in average; (ii) a statistical filter, which discard initial solutions if they are unlikely to improve the incumbent best solution; (iii) infeasible local search, where high-quality solutions, though infeasible, are used to explore the feasible/infeasible boundaries of the solution space; (iv) evolutionary PR, a recent trend where the pool of elite solutions is progressively improved by successive relinking of pairs of elite solutions. Computational tests were conducted using a set of 81 instances, and results reveal that the GRASP is very competitive, achieving the best overall deviation from lower bounds and the highest number of best solutions found.

Switch Allocation Problems in Power Distribution Systems

Reliability analysis of power systems has been attracting increasing attention. Regulatory agencies establish reliability standards that, if infringed, result in costly fines for the utility suppliers. A special concern pertains to the distribution networks on which most failures occur. The allocation of switches is a possible strategy to improve reliability, by allowing network reconfiguration to isolate contingencies and restore power to dark areas. This paper proposes an optimization methodology to allocate switches on radially operated distribution networks. The solution framework considers sectionalizing and tie switches of different capacities, with manual or automatic operation schemes. The approach minimizes the costs of allocation and energy not supplied, under reliability and flow capacity constraints. The solution framework is based on memetic algorithm concepts with a structured population. Case studies with a large network and real-world scenarios were used to evaluate the methodology. The results indicate that significant cost reductions can be achieved using the proposed solutions.

A redistricting problem applied to meter reading in power distribution networks

The capacitated redistricting problem (CRP) has the objective to redefine, under a given criterion, an initial set of districts of an urban area represented by a geographic network. Each node in the network has different types of demands and each district has a limited capacity. Real-world applications consider more than one criteria in the design of the districts, leading to a multicriteria CRP (MCRP). Examples are found in political districting, sales design, street sweeping, garbage collection and mail delivery. This work addresses the MCRP applied to power meter reading and two criteria are considered: compactness and homogeneity of districts. The proposed solution framework is based on a greedy randomized adaptive search procedure and multicriteria scalarization techniques to approximate the Pareto frontier. The computational experiments show the effectiveness of the method for a set of randomly generated networks and for a real-world network extracted from the city of Sao Paulo.

A pseudo-polynomial algorithm for optimal capacitor placement on electric power distribution networks

Allocation of shunt capacitor banks on radial electric power distribution networks allow reduction of energy losses and aggregated benefits. Four decades ago Duran proposed the use of dynamic programming to find optimal capacitor placement on these networks; however, with the restricting assumption of single-ended networks, which precluded its application to real capacitor allocation problems. Subsequently heuristic methods prevailed in the capacitor allocation literature. Here the Extended Dynamic Programming Approach (EDP) lifts Duran’s restricting assumption; a richer definition of state and the projection of multidimensional informations into equivalent one-dimensional representations are the supporting concepts. In addition to allow consideration of multi-ended networks, EDP deals with other requirements of capacitor allocation studies, including the use of both fixed and switched capacitors and representation of voltage drops along the networks. When switched capacitors are considered the optimization procedure also solves the capacitor control problem, obtaining the best tap adjustments for them. Case studies with real scale distribution networks put into perspective the benefits of the methodology; EDP has the appeal of providing global optimal solutions with pseudo-polynomial computational complexity in the worst-case, and with linear complexity for practical applications.

The open capacitated arc routing problem

The Open Capacitated Arc Routing Problem (OCARP) is a NP-hard combinatorial optimization problem where, given an undirected graph, the objective is to find a minimum cost set of tours that services a subset of edges with positive demand under capacity constraints. This problem is related to the Capacitated Arc Routing Problem (CARP) but differs from it since OCARP does not consider a depot, and tours are not constrained to form cycles. Applications to OCARP from literature are discussed. A new integer linear programming formulation is given, followed by some properties of the problem. A reactive path-scanning heuristic, guided by a cost-demand edge-selection and ellipse rules, is proposed and compared with other successful CARP path-scanning heuristics from literature. Computational tests were conducted using a set of 411 instances, divided into three classes according to the tightness of the number of vehicles available; results reveal the first lower and upper bounds, allowing to prove optimality for 133 instances.

Optimal allocation of remote controlled switches in radial distribution systems

There is an increasing interest in the analysis of power distribution systems, including demands to improve the distribution networks reliability. Regulatory agencies define reliability indices to quantify and evaluate the electric quality. In order to improve system reliability and provide a good quality service, this work proposes to install a minimum amount of switch devices at appropriate locations in the distribution network. A methodology is presented to effectively evaluate, even for large real networks the impact on reliability following contigen-cies. Firstly, are propose a constructive heuristic that allocates sectionalizers and tie switches, automatic and non-automatic, in a radial distribution system. This procedure aims to minimize the unsupplied energy caused in the network by determining a proper number, location and type of switches. A genetic algorithm is designed to further improve the switches location suggested by the constructive heuristic. The good performance of the proposed approach is confirmed by some case studies with large real energy distribution network.

Flow-based formulation for the maximum leaf spanning tree problem

Abstract The maximum leaf spanning tree problem consists in finding a spanning tree of a given graph G with the maximum number of leaves. In this work we propose a flow-based mixed-integer linear programming model for this problem. Computational experiments are executed in two sets of instances from the literature. The results show that the model is competitive with alternative exact approaches.

Hybrid genetic algorithm for the open capacitated arc routing problem

A hybrid genetic algorithm is proposed for the open capacitated arc routing problem.Solutions are encoded as permutations of required arcs, ignoring vehicle capacity.Chromosomes are decoded into viable solutions by an optimal feasibilization method.The genetic algorithm outperforms state-of-the-art methods w.r.t. optimality gaps.Experiments show the feasibilization method had a substantial role on performance. The Open Capacitated Arc Routing Problem (OCARP) is an NP-hard arc routing problem where, given an undirected graph, the objective is to find the least cost set of routes that services all edges with positive demand (required edges). The routes are subjected to capacity constraints in relation to edge demands. The OCARP differs from the Capacitated Arc Routing Problem (CARP) since OCARP does not consider a depot and routes are not constrained to form cycles. A hybrid genetic algorithm with feasibilization and local search procedures is proposed for the OCARP. Computational experiments conducted on a set of benchmark instances reveal that the proposed hybrid genetic algorithm achieved the best upper bounds for almost all instances.

Hierarchical multiple criteria optimization of maintenance activities on power distribution networks

Power distribution utilities must transport quality and reliable electric energy to all of the customers in a given network within specified targets. Failure of one of the network components is the main factor that compromises a system’s reliability. Maintenance actions, such as repairs and component replacements, are employed to avoid power interruptions or to resume the healthy network operation. This paper reports the relationship between maintenance activities and reliability as an optimization problem with two criteria: cost of maintenance activities and the maximum value for a system average interruption frequency index planning period. Solving these problems for each network provides local efficient solutions and associated trade-off curves. These solutions are optimally combined to solve a global-level multiple criteria optimization problem, revealing the local efficient solutions and associated trade-off curves for a group of networks or for a whole company. The procedure solves the hierarchical multiple criteria maintenance resources allocation problem and provides information to assess the decisions on maintenance activities at all decision levels in the network management. This procedure is applied to one illustrative example and real-life case studies to demonstrate its benefits.

A dynamic programming approach for optimal allocation of maintenance resources on power distribution networks

A relevant research topic in optimization of power distribution networks is to find the best relationship between system reliability and the allocation of maintenance resources. This paper presents a mathematical formulation that seeks the optimal preventive maintenance budget regarding the system reliability constraints. A dynamic programming approach is proposed to deal with this optimization problem. Some reductions are applied to the dynamic programming approach in order to avoid the combinatorial explosion. Case studies are presented to compare the performance of the dynamic programming approach with a hybrid genetic algorithm previously developed.