A stopping rule while searching for optimal solution of facility-location

Solutions to combinatorial optimization, such as p-median problems of locating facilities, frequently rely on heuristics to minimize the objective function. The minimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. However, pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small branch of the literature suggests using statistical principles to estimate the minimum and use the estimate for either stopping or evaluating the quality of the solution. In this paper we use test-problems taken from Baesley's OR-library and apply Simulated Annealing on these p-median problems. We do this for the purpose of comparing suggested methods of minimum estimation and, eventually, provide a recommendation for practioners. An illustration ends the paper being a problem of locating some 70 distribution centers of the Swedish Post in a region.

Optimization heuristic solutions, how good can they be? : With empirical applications in location problems

Combinatorial optimization problems, are one of the most important types of problems in operational research. Heuristic and metaheuristics algorithms are widely applied to find a good solution. However, a common problem is that these algorithms do not guarantee that the solution will coincide with the optimum and, hence, many solutions to real world OR-problems are afflicted with an uncertainty about the quality of the solution. The main aim of this thesis is to investigate the usability of statistical bounds to evaluate the quality of heuristic solutions applied to large combinatorial problems. The contributions of this thesis are both methodological and empirical. From a methodological point of view, the usefulness of statistical bounds on p-median problems is thoroughly investigated. The statistical bounds have good performance in providing informative quality assessment under appropriate parameter settings. Also, they outperform the commonly used Lagrangian bounds. It is demonstrated that the statistical bounds are shown to be comparable with the deterministic bounds in quadratic assignment problems. As to empirical research, environment pollution has become a worldwide problem, and transportation can cause a great amount of pollution. A new method for calculating and comparing the CO2-emissions of online and brick-and-mortar retailing is proposed. It leads to the conclusion that online retailing has significantly lesser CO2-emissions. Another problem is that the Swedish regional division is under revision and the border effect to public service accessibility is concerned of both residents and politicians. After analysis, it is shown that borders hinder the optimal location of public services and consequently the highest achievable economic and social utility may not be attained.

How does the use of different road networks effect the optimal location of facilities in rural areas?

The p-median problem is often used to locate P service facilities in a geographically distributed population. Important for the performance of such a model is the distance measure. Distance measure can vary if the accuracy of the road network varies. The rst aim in this study is to analyze how the optimal location solutions vary, using the p-median model, when the road network is alternated. It is hard to nd an exact optimal solution for p-median problems. Therefore, in this study two heuristic solutions are applied, simulating annealing and a classic heuristic. The secondary aim is to compare the optimal location solutions using dierent algorithms for large p-median problem. The investigation is conducted by the means of a case study in a rural region with an asymmetrically distributed population, Dalecarlia. The study shows that the use of more accurate road networks gives better solutions for optimal location, regardless what algorithm that is used and regardless how many service facilities that is optimized for. It is also shown that the simulated annealing algorithm not just is much faster than the classic heuristic used here, but also in most cases gives better location solutions.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Security constrained optimal active power flow via network model and interior point method

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Efficient heuristic algorithm used for optimal capacitor placement in distribution systems

An efficient heuristic algorithm is presented in this work in order to solve the optimal capacitor placement problem in radial distribution systems. The proposal uses the solution from the mathematical model after relaxing the integrality of the discrete variables as a strategy to identify the most attractive bus to add capacitors to each step of the heuristic algorithm. The relaxed mathematical model is a nonlinear programming problem and is solved using a specialized interior point method, The algorithm still incorporates an additional strategy of local search that enables the finding of a group of quality solutions after small alterations in the optimization strategy. Proposed solution methodology has been implemented and tested in known electric systems getting a satisfactory outcome compared with metaheuristic methods.The tests carried out in electric systems known in specialized literature reveal the satisfactory outcome of the proposed algorithm compared with metaheuristic methods. (C) 2009 Elsevier Ltd. All rights reserved.

On the value function for nonautonomous optimal control problems with infinite horizon

In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by L-1-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic programming inequalities and Hamilton-Jacobi-Bellman (HJB) inequalities for proximal sub (super) gradients is proven. Using this result we show that the value function is a Dini solution of the HJB equation. We obtain a verification result for the class of Dini sub-solutions of the HJB equation and also prove a minimax property of the value function with respect to the sets of Dini semi-solutions of the HJB equation. We introduce the concept of viscosity solutions of the HJB equation in infinite horizon and prove the equivalence between this and the concept of Dini solutions. In the Appendix we provide an existence theorem. (c) 2006 Elsevier B.V. All rights reserved.

Optimal capacitor placement in radial distribution networks

The capacitor placement (replacement) problem for radial distribution networks determines capacitor types, sizes, locations and control schemes. Optimal capacitor placement is a hard combinatorial problem that can be formulated as a mixed integer nonlinear program. Since this is a NP complete problem (Non Polynomial time) the solution approach uses a combinatorial search algorithm. The paper proposes a hybrid method drawn upon the Tabu Search approach, extended with features taken from other combinatorial approaches such as genetic algorithms and simulated annealing, and from practical heuristic approaches. The proposed method has been tested in a range of networks available in the literature with superior results regarding both quality and cost of solutions.

TIME-OPTIMAL GEOMAGNETIC ATTITUDE MANEUVERS OF AN AXISYMMETRICAL SPINNING SATELLITE

A formulation used to determine the time-optimal geomagnetic attitude maneuvers subject to dynamic and geometric constraints is proposed in this paper. This was obtained by a direct search procedure based on a control function parametrization method, using linear programming to obtain numerical suboptimal solutions by linear perturbation. Due to its characteristics it can be used in small computers and to generate computer programs of general application. The dynamic modeling, the magnetic torque model and the suboptimal control procedure are presented. Simulation runs have verified the feasibility of the formulation thus derived and have shown a notable improvement in performance.

Multi-areas optimal reactive power flow

This paper describes a method for the decentralized solution of the optimal reactive power flow (ORPF) problem in interconnected power systems. The ORPF model is solved in a decentralized framework, consisting of regions, where the transmission system operator in each area operates its system independently of the other areas, obtaining an optimal coordinated but decentralized solution. The proposed scheme is based on an augmented Lagrangian approach using the auxiliary problem principle (APP). An implementation of an interior point method is described to solve the decoupled problem in each area. The described method is successfully implemented and tested using the IEEE two area RTS 96 test system. Numerical results comparing the solutions obtained by the traditional and the proposed decentralized methods are presented for validation. ©2008 IEEE.

Multiarea optimal power flow using multiobjective evolutionary algorithm

In this work the multiarea optimal power flow (OPF) problem is decoupled into areas creating a set of regional OPF subproblems. The objective is to solve the optimal dispatch of active and reactive power for a determined area, without interfering in the neighboring areas. The regional OPF subproblems are modeled as a large-scale nonlinear constrained optimization problem, with both continuous and discrete variables. Constraints violated are handled as objective functions of the problem. In this way the original problem is converted to a multiobjective optimization problem, and a specifically-designed multiobjective evolutionary algorithm is proposed for solving the regional OPF subproblems. The proposed approach has been examined and tested on the RTS-96 and IEEE 354-bus test systems. Good quality suboptimal solutions were obtained, proving the effectiveness and robustness of the proposed approach. ©2009 IEEE.

Optimal contract pricing of distributed generation under a competitive framework

A bilevel programming approach for the optimal contract pricing of distributed generation (DG) in distribution networks is presented. The outer optimization problem corresponds to the owner of the DG who must decide the contract price that would maximize his profits. The inner optimization problem corresponds to the distribution company (DisCo), which procures the minimization of the payments incurred in attending the expected demand while satisfying network constraints. The meet the expected demand the DisCo can purchase energy either form the transmission network through the substations or form the DG units within its network. The inner optimization problem is substituted by its Karush- Kuhn-Tucker optimality conditions, turning the bilevel programming problem into an equivalent single-level nonlinear programming problem which is solved using commercially available software. © 2010 IEEE.

Optimal energy generation with biomass of sugarcane harvest

The aim of this work is the application of the Interior Point and Branch and Bound methods in multiobjective optimization models related to sugarcane harvest residual biomass. These methods showed their viability to help on choosing the sugarcane planting varieties, searching to optimize cost and energy balance of harvest residual biomass, which have conflitant objectives. These methods provide satisfactory results, with fair computing performance and reliable and consistent solutions to the analyzed models. © 2011 IEEE.

A new sufficient condition for optimal impulsive control problems

In this article we introduce the concept of MP-pseudoinvexity for general nonlinear impulsive optimal control problems whose dynamics are specified by measure driven control equations. This is a general paradigm in that, both the absolutely continuous and singular components of the dynamics depend on both the state and the control variables. The key result consists in showing the sufficiency for optimality of the MP-pseudoinvexity. It is proved that, if this property holds, then every process satisfying the maximum principle is an optimal one. This result is obtained in the context of a proper solution concept that will be presented and discussed. © 2012 IEEE.

Optimal conductor size selection and reconductoring in radial distribution systems using a mixed-integer LP approach

This paper presents a mixed-integer linear programming model to solve the conductor size selection and reconductoring problem in radial distribution systems. In the proposed model, the steady-state operation of the radial distribution system is modeled through linear expressions. The use of a mixed-integer linear model guarantees convergence to optimality using existing optimization software. The proposed model and a heuristic are used to obtain the Pareto front of the conductor size selection and reconductoring problem considering two different objective functions. The results of one test system and two real distribution systems are presented in order to show the accuracy as well as the efficiency of the proposed solution technique. © 1969-2012 IEEE.