In this paper we present several algorithms which combine a partial enumeration with meta-heuristics for the solution of general mixed-integer programming problems. The enumeration is based on the primal values assignable to the integer variables of the problem. We develop some algorithms for this integration, and test them using a set of well-known benchmark problems. Key-words: Enumeration, L...

in this paper the real-world occurrence of the multiple-product multiple-constraint single period newsboy problem with two objectives, in which there is incremental discounts on the purchasing prices, is investigated. the constraints are the warehouse capacity and the batch forms of the order placements. the first objective of this problem is to find the order quantities such that the expected ...

This paper proposes a modified non-dominated sorting genetic algorithm (NSGA-II) for a bi-objective location-allocation model. The purpose is to define the best places and capacity of the distribution centers as well as to allocate consumers, in such a way that uncertain consumers demands are satisfied. The objectives of the mixed-integer non-linear programming (MINLP) model are to (1) minimize...

Linear programming problems with alternate solutions are challenging due to the choice of multiple strategiesresulting in the same optimal value of the objective function. However, searching for these solutions is atedious task, especially when using mixed integer linear programming (MILP), as previously applied tometabolic models. Therefore, judgment on plurality of optimal m...

Symmetry is mainly exploited in mathematical programming in order to reduce the computation times of enumerative algorithms. The most widespread approach rests on: (a) finding symmetries in the problem instance; (b) reformulating the problem so that it does not allow some of the symmetric optima; (c) solving the modified problem. Sometimes (b) and (c) are performed concurrently: the solution al...

This paper proposes a model transformation approach for model-based energy management in buildings. Indeed, energy management is a large area that covers a wide range of applications such as simulation, mixed integer linear programming optimization, simulated annealing optimization, model parameter estimation, diagnostic analysis,. . . Each application requires a model but in a specific formali...

Differential and linear cryptanalysis are two of the most powerful techniques to analyze symmetric-key primitives. For modern ciphers, resistance against these attacks is therefore a mandatory design criterion. In this paper, we propose a novel technique to prove security bounds against both differential and linear cryptanalysis. We use mixedinteger linear programming (MILP), a method that is f...

Current mixed-integer linear programming solvers are based on linear programming routines that use floating-point arithmetic. Occasionally, this leads to wrong solutions, even for problems where all coefficients and all solution components are small integers. An example is given where many state-of-the-art MILP solvers fail. It is then shown how, using directed rounding and interval arithmetic,...