An Interactive Method of Linear Mixed Integer Multicriteria Optimization

The paper describes a learning-oriented interactive method for solving linear mixed integer problems of multicriteria optimization. The method increases the possibilities of the decision maker (DM) to describe his/her local preferences and at the same time it overcomes some computational difficulties, especially in problems of large dimension. The method is realized in an experimental decision support system for finding the solution of linear mixed integer multicriteria optimization problems.

Mixed-integer convex model for VAr expansion planning

This paper presents a mixed-integer convex-optimization-based approach for optimum investment reactive power sources in transmission systems. Unlike some convex-optimization techniques for the reactive power planning solution, in the proposed approach the taps settings of under-load tap-changing of transformers are modeled as a mixed-integer linear set equations. Are also considered the continuous and discrete variables for the existing and new capacitive and reactive power sources. The problem is solved for three significant demand scenarios (low demand, average demand and peak demand). Numerical results are presented for the CIGRE-32 electric power system.

A mixed-integer linear programming approach to the optimization of event-bus schedules: a scheduling application in the tourism sector

This paper deals with “The Enchanted Journey,” which is a daily event tour booked by Bollywood-film fans. During the tour, the participants visit original sites of famous Bollywood films at various locations in Switzerland; moreover, the tour includes stops for lunch and shopping. Each day, up to five buses operate the tour. For operational reasons, however, two or more buses cannot stay at the same location simultaneously. Further operative constraints include time windows for all activities and precedence constraints between some activities. The planning problem is how to compute a feasible schedule for each bus. We implement a two-step hierarchical approach. In the first step, we minimize the total waiting time; in the second step, we minimize the total travel time of all buses. We present a basic formulation of this problem as a mixed-integer linear program. We enhance this basic formulation by symmetry-breaking constraints, which reduces the search space without loss of generality. We report on computational results obtained with the Gurobi Solver. Our numerical results show that all relevant problem instances can be solved using the basic formulation within reasonable CPU time, and that the symmetry-breaking constraints reduce that CPU time considerably.

Mixed integer non linear programming and artificial neural network based approach to ancillary services dispatch in competitive electricity markets

Ancillary services represent a good business opportunity that must be considered by market players. This paper presents a new methodology for ancillary services market dispatch. The method considers the bids submitted to the market and includes a market clearing mechanism based on deterministic optimization. An Artificial Neural Network is used for day-ahead prediction of Regulation Down, regulation-up, Spin Reserve and Non-Spin Reserve requirements. Two test cases based on California Independent System Operator data concerning dispatch of Regulation Down, Regulation Up, Spin Reserve and Non-Spin Reserve services are included in this paper to illustrate the application of the proposed method: (1) dispatch considering simple bids; (2) dispatch considering complex bids.

A mixed-integer linear programming approach for optimal type, size and allocation of distributed generation in radial distribution systems

This paper presents a mixed-integer linear programming approach to solving the problem of optimal type, size and allocation of distributed generators (DGs) in radial distribution systems. In the proposed formulation, (a) the steady-state operation of the radial distribution system, considering different load levels, is modeled through linear expressions; (b) different types of DGs are represented by their capability curves; (c) the short-circuit current capacity of the circuits is modeled through linear expressions; and (d) different topologies of the radial distribution system are considered. The objective function minimizes the annualized investment and operation costs. The use of a mixed-integer linear formulation guarantees convergence to optimality using existing optimization software. The results of one test system are presented in order to show the accuracy as well as the efficiency of the proposed solution technique.© 2012 Elsevier B.V. All rights reserved.

Bilevel approach for optimal location and contract pricing of distributed generation in radial distribution systems using mixed-integer linear programming

In this study, a novel approach for the optimal location and contract pricing of distributed generation (DG) is presented. Such an approach is designed for a market environment in which the distribution company (DisCo) can buy energy either from the wholesale energy market or from the DG units within its network. The location and contract pricing of DG is determined by the interaction between the DisCo and the owner of the distributed generators. The DisCo intends to minimise the payments incurred in meeting the expected demand, whereas the owner of the DG intends to maximise the profits obtained from the energy sold to the DisCo. This two-agent relationship is modelled in a bilevel scheme. The upper-level optimisation is for determining the allocation and contract prices of the DG units, whereas the lower-level optimisation is for modelling the reaction of the DisCo. The bilevel programming problem is turned into an equivalent single-level mixed-integer linear optimisation problem using duality properties, which is then solved using commercially available software. Results show the robustness and efficiency of the proposed model compared with other existing models. As regards to contract pricing, the proposed approach allowed to find better solutions than those reported in previous works. © The Institution of Engineering and Technology 2013.

New Rigorous Decomposition Methods for Mixed-integer Linear and Nonlinear Programming

Process systems design, operation and synthesis problems under uncertainty can readily be formulated as two-stage stochastic mixed-integer linear and nonlinear (nonconvex) programming (MILP and MINLP) problems. These problems, with a scenario based formulation, lead to large-scale MILPs/MINLPs that are well structured. The first part of the thesis proposes a new finitely convergent cross decomposition method (CD), where Benders decomposition (BD) and Dantzig-Wolfe decomposition (DWD) are combined in a unified framework to improve the solution of scenario based two-stage stochastic MILPs. This method alternates between DWD iterations and BD iterations, where DWD restricted master problems and BD primal problems yield a sequence of upper bounds, and BD relaxed master problems yield a sequence of lower bounds. A variant of CD, which includes multiple columns per iteration of DW restricted master problem and multiple cuts per iteration of BD relaxed master problem, called multicolumn-multicut CD is then developed to improve solution time. Finally, an extended cross decomposition method (ECD) for solving two-stage stochastic programs with risk constraints is proposed. In this approach, a CD approach at the first level and DWD at a second level is used to solve the original problem to optimality. ECD has a computational advantage over a bilevel decomposition strategy or solving the monolith problem using an MILP solver. The second part of the thesis develops a joint decomposition approach combining Lagrangian decomposition (LD) and generalized Benders decomposition (GBD), to efficiently solve stochastic mixed-integer nonlinear nonconvex programming problems to global optimality, without the need for explicit branch and bound search. In this approach, LD subproblems and GBD subproblems are systematically solved in a single framework. The relaxed master problem obtained from the reformulation of the original problem, is solved only when necessary. A convexification of the relaxed master problem and a domain reduction procedure are integrated into the decomposition framework to improve solution efficiency. Using case studies taken from renewable resource and fossil-fuel based application in process systems engineering, it can be seen that these novel decomposition approaches have significant benefit over classical decomposition methods and state-of-the-art MILP/MINLP global optimization solvers.

Distributed Large-scale Mixed-Integer Optimization with Application to Energy and Multi-robot Networks

Several decision and control tasks in cyber-physical networks can be formulated as large- scale optimization problems with coupling constraints. In these "constraint-coupled" problems, each agent is associated to a local decision variable, subject to individual constraints. This thesis explores the use of primal decomposition techniques to develop tailored distributed algorithms for this challenging set-up over graphs. We first develop a distributed scheme for convex problems over random time-varying graphs with non-uniform edge probabilities. The approach is then extended to unknown cost functions estimated online. Subsequently, we consider Mixed-Integer Linear Programs (MILPs), which are of great interest in smart grid control and cooperative robotics. We propose a distributed methodological framework to compute a feasible solution to the original MILP, with guaranteed suboptimality bounds, and extend it to general nonconvex problems. Monte Carlo simulations highlight that the approach represents a substantial breakthrough with respect to the state of the art, thus representing a valuable solution for new toolboxes addressing large-scale MILPs. We then propose a distributed Benders decomposition algorithm for asynchronous unreliable networks. The framework has been then used as starting point to develop distributed methodologies for a microgrid optimal control scenario. We develop an ad-hoc distributed strategy for a stochastic set-up with renewable energy sources, and show a case study with samples generated using Generative Adversarial Networks (GANs). We then introduce a software toolbox named ChoiRbot, based on the novel Robot Operating System 2, and show how it facilitates simulations and experiments in distributed multi-robot scenarios. Finally, we consider a Pickup-and-Delivery Vehicle Routing Problem for which we design a distributed method inspired to the approach of general MILPs, and show the efficacy through simulations and experiments in ChoiRbot with ground and aerial robots.

Optimal scheduling of a renewable micro-grid in an isolated load area using mixed-integer linear programming

In the energy management of the isolated operation of small power system, the economic scheduling of the generation units is a crucial problem. Applying right timing can maximize the performance of the supply. The optimal operation of a wind turbine, a solar unit, a fuel cell and a storage battery is searched by a mixed-integer linear programming implemented in General Algebraic Modeling Systems (GAMS). A Virtual Power Producer (VPP) can optimal operate the generation units, assured the good functioning of equipment, including the maintenance, operation cost and the generation measurement and control. A central control at system allows a VPP to manage the optimal generation and their load control. The application of methodology to a real case study in Budapest Tech, demonstrates the effectiveness of this method to solve the optimal isolated dispatch of the DC micro-grid renewable energy park. The problem has been converged in 0.09 s and 30 iterations.

Non emergency patients transport - a mixed integer linear programming

This work presents a model and a heuristic to solve the non-emergency patients transport (NEPT) service issues given the new rules recently established in Portugal. The model follows the same principle of the Team Orienteering Problem by selecting the patients to be included in the routes attending the maximum reduction in costs when compared with individual transportation. This model establishes the best sets of patients to be transported together. The model was implemented in AMPL and a compact formulation was solved using NEOS Server. A heuristic procedure based on iteratively solving problems with one vehicle was presented, and this heuristic provides good results in terms of accuracy and computation time.

Synthesis of plantwide control strategies using mixed integer optimization

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2012

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.

A mixed-integer LP model for the reconfiguration of radial electric distribution systems considering distributed generation

The problem of reconfiguration of distribution systems considering the presence of distributed generation is modeled as a mixed-integer linear programming (MILP) problem in this paper. The demands of the electric distribution system are modeled through linear approximations in terms of real and imaginary parts of the voltage, taking into account typical operating conditions of the electric distribution system. The use of an MILP formulation has the following benefits: (a) a robust mathematical model that is equivalent to the mixed-integer non-linear programming model; (b) an efficient computational behavior with exiting MILP solvers; and (c) guarantees convergence to optimality using classical optimization techniques. Results from one test system and two real systems show the excellent performance of the proposed methodology compared with conventional methods. © 2012 Published by Elsevier B.V. All rights reserved.

A mixed-integer LP model for the optimal allocation of voltage regulators and capacitors in radial distribution systems

This paper presents a mixed-integer linear programming model to solve the problem of allocating voltage regulators and fixed or switched capacitors (VRCs) in radial distribution systems. The use of a mixed-integer linear model guarantees convergence to optimality using existing optimization software. In the proposed model, the steady-state operation of the radial distribution system is modeled through linear expressions. The results of one test system and one real distribution system are presented in order to show the accuracy as well as the efficiency of the proposed solution technique. An heuristic to obtain the Pareto front for the multiobjective VRCs allocation problem is also presented. © 2012 Elsevier Ltd. All rights reserved.