Revisiting lagrange relaxation (LR) for processing large-scale mixed integer programming (MIP) problems

Lagrangean Relaxation has been successfully applied to process many well known instances of NP-hard Mixed Integer Programming problems. In this paper we present a Lagrangean Relaxation based generic solver for processing Mixed Integer Programming problems. We choose the constraints, which are relaxed using a constraint classification scheme. The tactical issue of updating the Lagrange multiplier is addressed through sub-gradient optimisation; alternative rules for updating their values are investigated. The Lagrangean relaxation provides a lower bound to the original problem and the upper bound is calculated using a heuristic technique. The bounds obtained by the Lagrangean Relaxation based generic solver were used to warm-start the Branch and Bound algorithm; the performance of the generic solver and the effect of the alternative control settings are reported for a wide class of benchmark models. Finally, we present an alternative technique to calculate the upper bound, using a genetic algorithm that benefits from the mathematical structure of the constraints. The performance of the genetic algorithm is also presented

Designing B-ISDN network topologies using the genetic algorithm

In this paper, the topology design of B-ISDN networks is addressed. We model the topological planning as a non-linear mixed-integer programming problem. The genetic algorithm, an effective optimization method, is applied to this problem. Since the randomness of the genetic algorithm cannot guarantee the biconnectivity requirement in the topologies generated by the genetic algorithm, we propose an algorithm to make all topologies at least biconnected while increasing the overall cost of the topologies the least. The result for a 20-node test case is presented in the paper and it is shown that the algorithm we propose has a very good convergence property.published_or_final_versio

Application of Evolutionary Computation Techniques to the Optimal Short-Term Scheduling of the Electrical Energy Production

In this paper, an evolutionary technique applied to the optimal short-term scheduling (24 hours) of the electric energy production is presented. The equations that define the problem lead to a nonlinear mixed-integer programming problem with a high number of real and integer variables. Consequently, the resolution of the problem based on combinatorial methods is rather complex. The required heuristics, introduced to assure the feasibility of the constraints, are analyzed, along with a brief description of the proposed genetic algorithm. Finally, results from realistic cases based on the Spanish power system are reported, revealing the good performance of the proposed algorithm, taking into account the complexity and dimension of the problem

A two-stage approach to locate and size PV sources in distribution networks for annual grid operative costs minimization

This paper contributes with a new two-stage optimization methodology to solve the problem of the optimal placement and sizing of solar photovoltaic (PV) generation units in mediumvoltage distribution networks. The optimization problem is formulated with a mixed-integer nonlinear programming (MINLP) model, where it combines binary variables regarding the nodes where the PV generators will be located and continuous variables associated with the power flow solution. To solve the MINLP model a decoupled methodology is used where the binary problem is firstly solved with mixed-integer quadratic approximation; and once the nodes where the PV sources will be located are known, the dimensioning problem of the PV generators is secondly solved through an interior point method applied to the classical multi-period power flow formulation. Numerical results in the IEEE 33-bus and IEEE 85-bus systems demonstrate that the proposed approach improves the current literature results reached with combinatorial methods such as the Chu and Beasley genetic algorithm, the vortex search algorithm, the Newton-metaheuristic algorithm as well as the exact solution of the MINLP model with the GAMS software and the BONMIN solver. All the numerical simulations are implemented in the MATLAB programming environment and the convex equivalent models are solved with the CVX tool

Comparative study of different approaches to solve batch process scheduling and optimisation problems

Effective approaches are important to batch process scheduling problems, especially those with complex constraints. However, most research focus on improving optimisation techniques, and those concentrate on comparing their difference are inadequate. This study develops an optimisation model of batch process scheduling problems with complex constraints and investigates the performance of different optimisation techniques, such as Genetic Algorithm (GA) and Constraint Programming (CP). It finds that CP has a better capacity to handle batch process problems with complex constraints but it costs longer time

A new approach for cell formation and scheduling with assembly operations and product structure

In this paper, a new formulation model for cellular manufacturing system (CMS) design problem is proposed. The proposed model of this paper considers assembly operations and product structure so that it includes the scheduling problem with the formation of manufacturing cells, simultaneously. Since the proposed model is nonlinear, a linearization method is applied to gain optimal solution when the model is solved using direct implementation of mixed integer programming. A new genetic algorithm (GA) is also proposed to solve the resulted model for large-scale problems. We examine the performance of the proposed method using the direct implementation and the proposed GA method. The results indicate that the proposed GA approach could provide efficient assembly and product structure for real-world size problems