Integer Programming Techniques Research Articles

Sequence of Control in S3PMR

Huang et al. propose a more permissive siphon-based algorithm for deadlock prevention of a subclass of Petri nets, S3PMR. It iteratively (based on a mixed integer programming (MIP) technique) adds two kinds of control places called ordinary control (OC) places and weighted control (WC) places to the original model to prevent siphons from becoming unmarked. Numerical experiments indicate that the proposed policy appears to be more permissive than closely related approaches in the literature. The presence of WC renders the net a generalized Petri net, which is harder to analyze, and it is unclear how the above traditional MIP must be modified. We show that all monitors with WC places in all cases presented are redundant and can be removed while maintaining the maximal number of good states. We also (1) show that OC places and WC places are associated with resource and mixture siphons, respectively; (2) identify the condition and examples for a WC places to be redundant; (3) explore different types of problematic siphons; and (4) identify the correct sequence of adding monitors to avoid redundant monitors.

Genetic algorithms for a supply management problem: MIP-recombination vs greedy decoder

Two variants of genetic algorithm (GA) for solving the Supply Management Problem with Lower-Bounded Demands (SMPLD) are proposed and experimentally tested. The SMPLD problem consists in planning the shipments from a set of suppliers to a set of customers minimizing the total cost, given lower and upper bounds on shipment sizes, lower-bounded consumption and linear costs for opened deliveries. The first variant of GA uses the standard binary representation of solutions and a new recombination operator based on the mixed integer programming (MIP) techniques. The second GA is based on the permutation representation and a greedy decoder. Our experiments indicate that the GA with MIP-recombination compares favorably to the other GA and to the MIP-solver CPLEX 9.0 in terms of cost of obtained solutions. The GA based on greedy decoder is shown to be the most robust in finding feasible solutions.

Heuristic method for multi‐project finance‐based scheduling

A heuristic method is proposed for scheduling multiple projects subject to cash constraints. The heuristic determines cash availability during a given period, identifies all possible activities' schedules, determines the cash requirements for each schedule, ranks schedules based on the contribution to minimizing the increase in the project duration, schedules all activities of the selected schedule and determines the impact of the scheduled activities on the project cash flow. The effectiveness of the heuristic method was validated by comparing the results with the optimum results obtained by using the integer programming (IP) technique for 15 networks comprising up to 60 activities. The comparison indicated that the solutions obtained using the proposed heuristic are very comparable to the optimum solutions. An example of two concurrent projects was presented to demonstrate the proposed heuristic method. The proposed heuristic offers the ultimate flexibility to enter cash outflows and inflows at the actual occurrence time, the ability to rationalize the scheduling process, the flexibility to either devise or update schedules, and the ability to schedule practical‐size multiple projects. Finally, this heuristic can be easily coded in software to help managers schedule projects under finance‐constrained conditions.

Algebraic Attacks Galore!

This is the first in a two-part survey of current techniques in algebraic cryptanalysis. After introducing the basic setup of algebraic attacks and discussing several attack scenarios for symmetric cryptosystems, public key cryptosystems, and stream ciphers, we discuss a number of individual methods. The XL, XSL, and MutantXL attacks are based on linearization techniques for multivariate polynomial systems. Then we look at Gröbner basis and border bases methods. In the last section we introduce attacks based on integer programming techniques and try them in some concrete cases.

A global constraint for nesting problems

Nesting problems are particularly hard combinatorial problems. They involve the positioning of a set of small arbitrarily-shaped pieces on a large stretch of material, without overlapping them. The problem constraints are bidimensional in nature and have to be imposed on each pair of pieces. This all-to-all pattern results in a quadratic number of constraints. Constraint programming has been proven applicable to this category of problems, particularly in what concerns exploring them to optimality. But it is not easy to get effective propagation of the bidimensional constraints represented via finite-domain variables. It is also not easy to achieve incrementality in the search for an improved solution: an available bound on the solution is not effective until very late in the positioning process. In the sequel of work on positioning non-convex polygonal pieces using a CLP model, this work is aimed at improving the expressiveness of constraints for this kind of problems and the effectiveness of their resolution using global constraints. A global constraint "outside" for the non-overlapping constraints at the core of nesting problems has been developed using the constraint programming interface provided by Sicstus Prolog. The global constraint has been applied together with a specialized backtracking mechanism to the resolution of instances of the problem where optimization by Integer Programming techniques is not considered viable. The use of a global constraint for nesting problems is also regarded as a first step in the direction of integrating Integer Programming techniques within a Constraint Programming model.

A decision support system for cyclic master surgery scheduling with multiple objectives

This paper presents a decision support system for cyclic master surgery scheduling and describes the results of an extensive case study applied in a medium-sized Belgian hospital. Three objectives are taken into account when building the master surgery schedule. First of all, the resulting bed occupancy at the hospitalization units should be leveled as much as possible. Second, a particular operating room is best allocated exclusively to one group of surgeons having the same speciality; i.e., operating rooms should be shared as little as possible between different surgeon groups. Third, the master surgery schedule is preferred to be as simple and repetitive as possible, with few changes from week to week. The system relies on mixed integer programming techniques involving the solution of multi-objective linear and quadratic optimization problems, and on a simulated annealing metaheuristic.

A Typical Case Study: Solid Waste Management in Petroleum Refineries

The current environmental concerns have forced developed and developing countries to reduce air, water and land pollution for sustainable growth. Solid refinery waste is cocktail of hydrocarbons, water, heavy metal and fine solids and is substantial in quantity. The principal processes of waste management focus mainly on waste source reduction, reusing, recycling, composting, incineration with or without energy recovery, fuel production and land filling. Waste management models have a common approach of assignment of generating sources to landfills, transfer stations sitting, site selection for landfills, etc. but recently new integrated models have been developed and applied. Waste management system in an industrial complexes uses multi-objective mixed integer programming approach for the running of existing facilities in dynamic net work flow models with nonlinear costs of management. The latest multi-objective mixed integer programming techniques are applied to resolve the potential conflict between environmental and economic goals and to evaluate sustainable strategies for waste management. In this approach, material recycling in an economic sense exhibits huge indirect benefits, although the emphasis of environmental quality as a major objective in decision-making drives the optimal solution toward pro-recycling programs. The use of grey and fuzzy system theories as uncertainty analysis tools as an enhancement of this modeling analysis proves to be highly profitable. A multi-objective optimization model based on the goal programming approach has been developed and tested in this study for passable management of solid waste generated by a typical petroleum refining industry in the state of Kuwait. The analytic hierarchy process, a decision-making approach, including qualitative and quantitative aspects of a problem, has been integrated in the model to prioritize the conflicting goals existing in the waste management problems of the petroleum industries. The optimization model is developed based on the goal programming technique that attempts to minimize the set of deviations from pre-specified multiple goals, which are considered simultaneously but are weighted according to their relative importance. A set of data from local petroleum refining industries is obtained and is analyzed using the unique presently developed multi-objective optimization model based on goal programming technique with all treatment options and economic constraints. The successful application of this model has provided the most economically viable solution to be applied for the specified objectives to be accomplished for the management of solid waste generated from petroleum industries.

Solid Waste Management in Petroleum Refineries

Waste management became focus of attention of many researchers and scientists in the last half century due to its vital importance. Waste management covered waste source reduction in general, by recycling, reusing, composting, incineration with or without energy recovery, fuel production and land filling. A common approach of waste management models were for specific problems with a limited scope (like assignment of generating sources to landfills, transfer stations sitting, site selection for landfills, etc.). Integrated models have been developed more recently. The latest dynamic network flow models with nonlinear costs for waste management used multi-objective mixed integer programming approach for the management of existing facilities in an industrial complex waste management system. The application of multi-objective mixed integer programming techniques was for reasoning the potential conflict between environmental and economic goals and for evaluating sustainable strategies for waste management. Material recycling exhibited huge indirect benefits in an economic sense, although the emphasis of environmental quality as one of the objectives in decision-making has been inevitably driven the optimal solution toward pro-recycling programs. The enhancement of this modeling analysis by using the grey and fuzzy system theories as uncertainty analysis tools could prove highly beneficial. A multi-objective optimization model based on the goal programming approach was applied for proper management of solid waste generated by the petroleum industries in the state of Kuwait. The analytic hierarchy process, a decision-making approach, incorporating qualitative and quantitative aspects of a problem, has been incorporated in the model to prioritize the conflicting goals usually encountered when addressing the waste management problems of the petroleum industries. An optimization model was formulated based on the goal programming technique to minimize the set of deviations from pre-specified multiple goals, which were considered simultaneously but were weighted according to their relative importance. Ten years of solid waste data have been collected from local petroleum industries and processed with different treatment options with economical constraints to provide the best possible solution to be implemented for the specified objectives to be accomplished.

The Football Pool Polytope

Abstract The football pool problem asks for the minimun number of bets on the result on n football matches ensuring that some bet correctly predicts the outcome of at least n − 1 of them. This combinatorial problem has proven to be extremely difficult, and is open for n ⩾ 6 . Integer programming techniques have been applied to this problem in the past but, in order to tackle the open cases, a deep knowledge of the polytopes associated with the integer programs modeling this problem is required. In this work we address this issue, by defining and studying the football pool polytope in connection with a natural integer programming formulation of the football pool problem. We explore the basic properties of this polytope and present several classes of facet-inducing valid inequalities over natural combinatorial structures in the original problem.

Solving large double digestion problems for DNA restriction mapping by using branch-and-bound integer linear programming

The double digestion problem for DNA restriction mapping has been proved to be NP-complete and intractable if the numbers of the DNA fragments become large. Several approaches to the problem have been tested and proved to be effective only for small problems. In this paper, we formulate the problem as a mixed-integer linear program (MIP) by following (Waterman, 1995) in a slightly different form. With this formulation and using state-of-the-art integer programming techniques, we can solve randomly generated problems whose search space sizes are many-magnitude larger than previously reported testing sizes.

A prototype of a hierarchical global logistics network planning model

In this article, we present a prototype Global Logistics (GL) networks planning model in which the GL facilities such as hubs and depots are hierarchically characterised. The proposed method is developed based on the fundamentals of hierarchical cluster analysis and integer programming techniques to determine the corresponding types, locations and numbers of service areas of facilities involved in the proposed GL networks with the goal of minimising the corresponding costs and risks of network configurations. Particularly, the potential risk-oriented costs such as macro-environmental-risk and micro-operational-risk costs are taken into account in the proposal model. In addition, a case study aiming at air express delivery enterprises is conducted to demonstrate the applicability of the proposed methodology.

A Method for Voltage Sag State Estimation in Power Systems

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper presents a new technique for voltage sag state estimation. The proposed method is based on estimating the number of voltage sags occurring at nonmonitored buses from the number of sags recorded at a limited number of monitored buses. This problem, contrary to the traditional state estimation where redundant measurements are available, is formulated as an underdetermined system of equations. In this paper, linear integer programming techniques are employed to solve this estimation problem. The performance of the proposed method is tested by means of several case studies applied in the IEEE 24-bus Reliability Test System (RTS) and in the IEEE 118-bus Test System. </para>

Liveness-enforcing supervisor design for a class of generalised petri net models of flexible manufacturing systems

The importance of siphons is well recognised in the analysis and control of deadlocks in Petri nets. Deadlock prevention problems are considered for S4PR, a class of generalised Petri nets, that can model well a large class of flexible manufacturing systems (FMS). Siphons in a plant net model are divided into elementary and dependent ones. Deadlock prevention is achieved by adding monitors (control places) to make every elementary siphon satisfy the maximal controlled-siphon property. Conditions are developed under which a dependent siphon is maximally controlled when its elementary siphons are so. The max-controllability of a dependent siphon is ensured by properly supervising the control depth variables of its elementary siphons via linear integer programming techniques. Compared with existing methods, this policy requires a much smaller number of supervisory monitors. Finally, the application of this approach is illustrated by an FMS example.

A note on single-machine makespan scheduling with deteriorating jobs and scheduled maintenance

A single-machine scheduling problem with simple linear deteriorating jobs is considered in this paper. The objective is to minimize the makespan when the machine is not always available. We study the scheduling problem under a deterministic environment; specifically, the availability periods are known in advance and jobs are non-resumable. It is shown that the problem is NP-hard even with a single maintenance period. Thus, the 0–1 integer programming technique is utilized to solve the simple linear deterioration model.

A parallel multistart algorithm for the closest string problem

In this paper we describe and implement a parallel algorithm to find approximate solutions for the Closest String Problem (CSP). The CSP, also known as Motif Finding problem, has applications in Coding Theory and Computational Biology. The CSP is NP-hard which motivates us to think about heuristics to solve large instances. Several approximation algorithms have been designed for the CSP, but all of them have a poor performance guarantee. Recently some researchers have shown empirically that integer programming techniques can be successfully used to solve moderate-size instances (10–30 strings each of which is 300–800 characters long) of the CSP. However, real-world instances are larger than those tested. In this paper we show how a simple heuristic can be used to find near-optimal solutions to that problem. We implemented a parallel version of this heuristic and report computational experiments on large-scale instances. These results show the effectiveness of our approach.

Identification of switched linear systems using subspace and integer programming techniques

We consider the identification of a switched linear system which consists of linear sub-models, with a rule that orchestrates the switching mechanism between the sub-models. Taking a set of switched linear systems and using a state space framework, we show that it is possible to combine subspace methods with mixed integer programming for system identification. The states of the system are first extracted from input–output data using sub-space methods. Once the state variables are known, the switched system is re-written as a mixed logical dynamical (MLD) system and the model parameters are calculated for via mixed integer programming. We report an example at the end of this paper together with simulation results in the presence of noise.

Hybrid tabu search for re-entrant permutation flow-shop scheduling problem

A re-entrant flow-shop (RFS) refers to situations in which every job must be processed on machines in the order, M1, M2, … , Mm, M1, M2, … , Mm, … , and M1, M2 , … , Mm. Every job can be decomposed into several layers each of which starts on M1 and finishes on Mm. In the RFS case, if the job ordering is the same on any machine at each layer, then no passing is said to be allowed, since no job is allowed to pass any former job. The RFS scheduling problem in which no passing is allowed, is called a re-entrant permutation flow-shop (RPFS) problem. This study considers RPFS scheduling, and applies hybrid tabu search (HTS) to minimize the makespan of jobs. The hybridization method is used to improve pure tabu search (TS) performance. The HTS is compared to the optimal solutions generated using the integer programming technique, and to the near optimal solutions generated by pure TS and heuristic NEH. The experimental results show that HTS has better performance than the others tested.

Improving the Robustness of a Supply Chain Tactical Plan

Based on linear and linear integer programming techniques, Advanced Planning Systems (APS) enable a tactical plan to be established each time the plan deviates from reality. Thus, planning is more reactive but may lead to a loss of robustness when making a decision.This article presents a specific approach to increase robustness and stability for tactical plans. Several methods have already been discussed to achieve this robustness target. This proposed new policy is called the “reference plan”.

Intelligent parking systems

The basic concepts of the parking reservation system and parking revenue management system are discussed in this paper. The proposed “intelligent” parking space inventory control system that is based on a combination of fuzzy logic and integer programming techniques makes “on line” decisions whether to accept or reject a new driver’s request for parking. In the first step of the proposed model, the best parking strategies are developed for many different patterns of vehicle arrivals. These parking strategies are developed using integer programming approach. In the second step, learning from the best strategies, specific rules are defined. The uniqueness of the proposed approach is that the rules are derived from the set of chosen examples assuming that the future traffic arrival patterns are known. The results were found to be close to the best solution assuming that the future arrival pattern is known.

A hybrid genetic algorithm for the re-entrant flow-shop scheduling problem

This study considers the production environment of the re-entrant flow-shop (RFS). In a RFS, all jobs have the same routing over the machines of the shop and the same sequence is traversed several times to complete the jobs. The aim of this study is to minimize makespan by using the genetic algorithm (GA) to move from local optimal solution to near optimal solution for RFS scheduling problems. In addition, hybrid genetic algorithms (HGA) are proposed to enhance the performance of pure GA. The HGA is compared to the optimal solutions generated by the integer programming technique, and to the near optimal solutions generated by pure GA and the non-delay schedule generation procedure. Computational experiments are performed to illustrate the effectiveness and efficiency of the proposed HGA algorithm.