mixed integer programming

One of the chief attractions of stochastic mixed-integer second-order cone programming is its diverse applications, especially in engineering (Alzalg and Alioui, {\em IEEE Access}, 10:3522-3547, 2022). The linear and nonlinear versions of this class of optimization problems are still unsolved yet. In this paper, we develop a hybrid optimization algorithm coupling branch-and-bound and primal-dual interior-point methods for solving two-stage stochastic mixed-integer nonlinear second-order cone programming. The adopted approach uses a branch-and-bound technique to handle the integer variables and an infeasible interior-point method to solve continuous relaxations of the resulting subproblems. The proposed hybrid algorithm is also implemented to data to show its efficiency.

A two-dimensional strip packing problem is the process of packing a set of rectangular items of given dimensions into a strip of bounded width and infinite height so that the used height of the strip is minimized. In the case that only guillotine packing is permitted, the problem is called the guillotine strip packing problem (GSPP). Guillotine packing commonly arises in different industries such as glass, steel, paper and wood. Nevertheless, there is a lack of explicit mathematical models for GSPP that can globally solve the problem. In this paper, a new mixed-integer programming model inspired by a so-called sequence sub-tour elimination technique for the traveling salesman problem (TSP) is presented as a relaxation of (non-staged) GSPP with orthogonal rotation. The proposed model is able to find good solutions (good upper bounds) for the optimal objective value and more importantly, it is a polynomial model of order $O(n^2)$, i.e. the number of decision variables (and constraints, as well) is a polynomial of order $O(n^2)$ in the number of the rectangular items ($n$). Numerical results show that the solutions obtained from the proposed model are superior to several existing heuristic algorithms in the literature.

This study proposes a method for solving mixed integer multi-objective fractional signomial geometric programming (MIMOFSGP) problems. A few methods have been applied in the recent past to convert a fractional signomial objective function into a non-fractional signomial objective function to find the optimal solution by use of some common mathematical programming techniques. In this paper, at first a multi-objective fractional signomial programming is converted into a non-fractional multi-objective signomial programming problem by a new convenient reformulation strategy. A convex relaxation is used to reach global solution and then fuzzy programming technique is applied to find the optimal compromise solution. A mixed integer compromise optimal solution of the convex programming problem can finally be found by use of nonlinear branch and bound algorithm. Then 0n using the Spacial branch and bound algorithm, we find a solution that has the shortest distance from the solution of original problem. Finally two illustrative examples are included to demonstrate the correctness and efficiency of the proposed strategy and compare the results with the other solutions obtained by the other methods.

One of the problems raised in software defined networks is to determine the number and installation location of controllers so that the cost of implementation reduced and survivability of the network against link or node failure increased. Current investigation in SDN imposes full mesh topology in order to connect controllers. This approach while incurring a huge installation cost, dose not carefully incorporate network survivability requirements. In this paper, we improve an existing integer programming approach to a novel model so as to effectively address user defined survivability requirements. Computational results reported also reveals that our models could be solved by state-of-the-art MIP solvers like CPLEX within a reasonable time limit.

Given the reduction of non-renewable energy resources and increase of energy costs during  recent years, developing an efficient scheduling model considering energy consumption is necessary in manufacturing systems. This paper is dedicated to flow shop scheduling problem under Time-Of-Use electricity tariffs. In this regard, a bi-objective mixed-integer programming model is formulated for the problem. Two objectives, namely, the minimization of the total electricity cost and the sum of earliness and tardiness of jobs, are considered simultaneously. The bi-objective model is converted into an equivalent single objective linear programming model using fuzzy multi-objective programming approach. The CPLEX solver in GAMS software is used to solve the proposed model for an instance. The numerical example shows that the proposed model is reasonable and applicable.

Data Envelopment Analysis (DEA) cannot provide adequate discrimination among efficient decision making units (DMUs). To discriminate these efficient DMUs is an interesting research subject. The purpose of this paper is to develop the mix integer linear model which was proposed by Foroughi (Foroughi A.A. A new mixed integer linear model for selecting the best decision making units in data envelopment analysis. Computers & Industrial Engineering 60 (2011) 550-554) to present new alternative mix integer programming DEA (MIP-DEA) models which can be used to improve discrimination power of DEA and select the most BCC-efficient decision making unit (DMU). We will demonstrate that proposed model is able to select DMU throughout the real data sets.