Search results for "linear programming"
showing 7 items of 137 documents
Linear Programming Based Methods for Solving Arc Routing Problems
2000
From the pioneering works of Dantzig, Edmonds and others, polyhedral (i.e. linear programming based) methods have been successfully applied to the resolution of many combinatorial optimization problems. See Junger, Reinelt & Rinaldi (1995) for an excellent survey on this topic. Roughly speaking, the method consists of trying to formulate the problem as a Linear Program and using the existing powerful methods of Linear Programming to solve it.
A choice of bilevel linear programming solving parameters: factoraggregation approach
2013
Our paper deals with the problem of choosing correct parameters for the bilevel linear program- ming solving algorithm proposed by M. Sakawa and I. Nishizaki. We suggest an approach based on fac- toraggregation, which is a specially designed general aggregation operator. The idea of factoraggregation arises from factorization by the equivalence relation generated by the upper level objective function. We prove several important properties of the factorag- gregation result regarding the analysis of param- eters in order to find an optimal solution for the problem. We illustrate the proposed method with some numerical and graphical examples, in particu- lar we consider a modification of the m…
Identification of efficient equilibria in multiproduct trading with indivisibilities and non-monotonicity
2018
Abstract This paper focuses on multiproduct trading with indivisibilities and where a representative agent may have non-monotonic preferences. In this framework, the set of firms’ profits (which comes from efficient subgame perfect Nash equilibria) is the Pareto frontier of some projection of the core of the game. We show that under monotonicity efficient subgame perfect Nash equilibria are achieved by single offers and the equilibrium characterization is easy to obtain. When dealing with non-monotonic preferences the problem becomes more challenging. Then, we define a pair of primal–dual linear programming problems that fully identifies the core of the game. A set of modified versions of t…
Interactively Learning the Preferences of a Decision Maker in Multi-objective Optimization Utilizing Belief-rules
2020
Many real life problems can be modelled as multiobjective optimization problems. Such problems often consist of multiple conflicting objectives to be optimized simultaneously. Multiple optimal solutions exist to these problems, and a single solution cannot be said to be the best without preferences given by a domain expert. Preferences can be used to find satisfying solutions: optimal solutions, which best match the expert’s preferences. To model the preferences of the expert, and aid him/her in finding satisfying solutions, a novel method is proposed. The method utilizes machine learning combined with belief-rule based systems to adaptively train a belief rule based system to learn a domai…
A more efficient cutting planes approach for the green vehicle routing problem with capacitated alternative fuel stations
2021
AbstractThe Green Vehicle Routing Problem with Capacitated Alternative Fuel Stations assumes that, at each station, the number of vehicles simultaneously refueling cannot exceed the number of available pumps. The state-of-the-art solution method, based on the generation of all feasible non-dominated paths, performs well only with up to 2 pumps. In fact, it needs cloning the paths between every pair of pumps. To overcome this issue, in this paper, we propose new path-based MILP models without cloning paths, for both the scenario with private stations (i.e., owned by the fleet manager) and that with public stations. Then, a more efficient cutting plane approach is designed for addressing both…
Energy Management Systems and tertiary regulation in hierarchical control architectures for islanded microgrids
2015
In this paper, the structure of the highest level of a hierarchical control architecture for micro-grids is proposed. Such structure includes two sub-levels: the Energy Management System, EMS, and the tertiary regulation. The first devoted to energy resources allocation in each time slot based on marginal production costs, the latter aiming at finding the match between production and consumption satisfying the constraints set by the EMS level about the energy production in each time slot. Neglecting the efficiency of the different energy generation systems as well as that of the infrastructure for electrical energy distribution, the problem dealt with by the EMS sub-level is linear and can …
Shape optimization in contact problems based on penalization of the state inequality
1986
The paper deals with the approximation of optimal shape of elastic bodies, unilaterally supported by a rigid, frictionless foundation. Original state inequality, describing the behaviour of such a body is replaced by a family of penalized state problems. The relation between optimal shapes for the original state inequality and those for penalized state equations is established. peerReviewed