Hybrid particle swarm optimization with chaotic search for solving integer and mixed integer programming problems

A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems.The performances of CLSPSO are compared with those of other five hybrid algorithms combining PSO with chaotic search methods.Experimental results indicate that in terms of robustness and final convergence speed,CLSPSO is better than other five algorithms in solving many of these problems.Furthermore,CLSPSO exhibits good performance in solving two high-dimensional problems,and it finds better solutions than the known ones.A performance index(PI) is introduced to fairly compare the above six algorithms,and the obtained values of(PI) in three cases demonstrate that CLSPSO is superior to all the other five algorithms under the same conditions.

Scheduling Step-Deteriorating Jobs on Parallel Machines by Mixed Integer Programming

Production scheduling has a major impact on the productivity of the manufacturing process. Recently, scheduling problems with deteriorating jobs have attracted increasing attentions from researchers. In many practical situations,it is found that some jobs fail to be processed prior to the pre-specified thresholds,and they often consume extra deteriorating time for successful accomplishment. Their processing times can be characterized by a step-wise function. Such kinds of jobs are called step-deteriorating jobs. In this paper,parallel machine scheduling problem with stepdeteriorating jobs( PMSD) is considered. Due to its intractability,four different mixed integer programming( MIP) models are formulated for solving the problem under consideration. The study aims to investigate the performance of these models and find promising optimization formulation to solve the largest possible problem instances. The proposed four models are solved by commercial software CPLEX. Moreover,the near-optimal solutions can be obtained by black-box local-search solver LocalS olver with the fourth one. The computational results show that the efficiencies of different MIP models depend on the distribution intervals of deteriorating thresholds, and the performance of LocalS olver is clearly better than that of CPLEX in terms of the quality of the solutions and the computational time.

A mixed integer linear programming approach for municipal solid waste management

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Combining Geographic Information Systems for Transportation and Mixed Integer Linear Programming in Facility Location-Allocation Problems

In this study, we aimed to assess the solution quality for location-allocation problems from facilities generated by the software TransCAD®?, a Geographic Information System for Transportation (GIS-T). Such facilities were obtained after using two routines together: Facility Location and Transportation Problem, when compared with optimal solutions from exact mathematical models, based on Mixed Integer Linear Programming (MILP), developed externally for the GIS. The models were applied to three simulations: the first one proposes opening factories and customer allocation in the state of Sao Paulo, Brazil;the second involves a wholesaler and a study of location and allocation of distribution centres for retail customers;and the third one involves the location of day-care centers and allocation of demand (0 - 3 years old children). The results showed that when considering facility capacity, the MILP optimising model presents results up to 37% better than the GIS and proposes different locations to open new facilities.

Detection of gross errors using mixed integer optimization approach in process industry

A novel mixed integer linear programming (NMILP) model for detection of gross errors is presented in this paper. Yamamura et al.(1988) designed a model for detection of gross errors and data reconciliation based on Akaike information cri- terion (AIC). But much computational cost is needed due to its combinational nature. A mixed integer linear programming (MILP) approach was performed to reduce the computational cost and enhance the robustness. But it loses the super performance of maximum likelihood estimation. To reduce the computational cost and have the merit of maximum likelihood estimation, the simultaneous data reconciliation method in an MILP framework is decomposed and replaced by an NMILP subproblem and a quadratic programming (QP) or a least squares estimation (LSE) subproblem. Simulation result of an industrial case shows the high efficiency of the method.

Integrated Optimization of Timetable and Rolling Stock Circulation under Mixed Usages of Short-length and Full-length Services in Urban Rail Transit

The rapid growth of passenger flow in urban rail transit has led to great service pressures for metro companies in organizing train services to provide higher transportation capacities in order to satisfy passengers' travel demand, especially on those metro lines with insufficient rolling stock. In order to cope with high passenger flow service pressure, a mixed integer nonlinear programming(MINLP) model is proposed to optimize the line plan, timetable and rolling stock circulation simultaneously, to reduce the number of rolling stocks and increase the number of full-length services. A two-step algorithm strategy is proposed. In the first stage, the train timetable is optimized under the assumption that all the train services are the full-length services. In the second stage, the rolling stock plan is optimized based on the timetable optimized in the first stage. To ensure a feasible rolling stock circulation, certain full-length services are shortened to the short-length services due to the limited number of rolling stocks. Numerical experiments are performed based on the real-life data of Shanghai Metro Line 8. Results show that the proposed method can efficiently optimize the timetable and rolling stock circulation of the whole operation day. The optimized results are beneficial for both the service and the operational costs.

A NEW GLOBAL OPTIMIZATION ALGORITHM FOR MIXED-INTEGER QUADRATICALLY CONSTRAINED QUADRATIC FRACTIONAL PROGRAMMING PROBLEM

The mixed-integer quadratically constrained quadratic fractional programming(MIQCQFP)problem often appears in various fields such as engineering practice,management science and network communication.However,most of the solutions to such problems are often designed for their unique circumstances.This paper puts forward a new global optimization algorithm for solving the problem MIQCQFP.We first convert the MIQCQFP into an equivalent generalized bilinear fractional programming(EIGBFP)problem with integer variables.Secondly,we linearly underestimate and linearly overestimate the quadratic functions in the numerator and the denominator respectively,and then give a linear fractional relaxation technique for EIGBFP on the basis of non-negative numerator.After that,combining rectangular adjustment-segmentation technique and midpointsampling strategy with the branch-and-bound procedure,an efficient algorithm for solving MIQCQFP globally is proposed.Finally,a series of test problems are given to illustrate the effectiveness,feasibility and other performance of this algorithm.

Hierarchical On-line Scheduling of Multiproduct Batch Plants with a Combined Approach of Mathematical Programming and Genetic Algorithm

In this contribution we present an online scheduling algorithm for a real world multiproduct batch plant. The overall mixed integer nonlinear programming (MINLP) problem is hierarchically structured into a mixed integer linear programming (MILP) problem first and then a reduced dimensional MINLP problem, which are optimized by mathematical programming (MP) and genetic algorithm (GA) respectively. The basis idea relies on combining MP with GA to exploit their complementary capacity. The key features of the hierarchical model are explained and illustrated with some real world cases from the multiproduct batch plants.

Stochastic Programming For Order Allocation And Production Planning

Stochastic demand is an important factor that heavily affects production planning.It influences activities such as purchasing,manufacturing,and selling,and quick adaption is required.In production planning,for reasons such as reducing costs and obtaining supplier discounts,many decisions must be made in the initial stage when demand has not been realized.The effects of non-optimal decisions will propagate to later stages,which can lead to losses due to overstocks or out-of-stocks.To find the optimal solutions for the initial and later stage regarding demand realization,this study proposes a stochastic two-stage linear program-ming model for a multi-supplier,multi-material,and multi-product purchasing and production planning process.The objective function is the expected total cost after two stages,and the results include detailed plans for purchasing and production in each demand scenario.Small-scale problems are solved through a deterministic equivalent transformation technique.To solve the problems in the large scale,an algorithm combining metaheuristic and sample average approximation is suggested.This algorithm can be implemented in parallel to utilize the power of the solver.The algorithm based on the observation that if the remaining quantity of materials and number of units of products at the end of the initial stage are given,then the problems of the first and second stages can be decomposed.

Evaluation of Integer Programming Solvers to Improve the Efficiency of Individual Work Planning

This study proposes a novel approach to optimizing individual work schedules for book digitization using mixed-integer programming (MIP). By leveraging the power of MIP solvers, we aimed to minimize the overall digitization time while considering various constraints and process dependencies. The book digitization process involves three key steps: cutting, scanning, and binding. Each step has specific requirements and limitations such as the number of pages that can be processed simultaneously and potential bottlenecks. To address these complexities, we formulate the problem as a one-machine job shop scheduling problem with additional constraints to capture the unique characteristics of book digitization. We conducted a series of experiments to evaluate the performance of our proposed approach. By comparing the optimized schedules with the baseline approach, we demonstrated significant reductions in the overall processing time. In addition, we analyzed the impact of different weighting schemes on the optimization results, highlighting the importance of identifying and prioritizing critical processes. Our findings suggest that MIP-based optimization can be a valuable tool for improving the efficiency of individual work schedules, even in seemingly simple tasks, such as book digitization. By carefully considering specific constraints and objectives, we can save time and leverage resources by carefully considering specific constraints and objectives.

A Green Mixed Integer Linear Programming Model for Optimization of Byproduct Gases in Iron and Steel Industry

Byproduct gas is an important secondary energy in iron and steel industry, and its optimization is vital to cost reduction. With the development of iron and steel industry to be more eco-friendly, it is necessary to construct an integrated optimized system, taking economics, energy consumption and environment into consideration. Therefore, the environmental cost caused by pollutants discharge should be factored in total cost when optimizing byproduct gas distribution. A green mixed integer linear programming （MILP） model for the optimization of byproduct gases was established to reduce total cost, including both operation cost and environmental cost. The operation cost included penalty for gas deviation, costs of fuel and water consumption, holder booster trip penalty, and so forth; while the environmental cost consisted of penalties for both direct and indirect pollutants discharge. Case study showed that the proposed model brought an optimum solution and 2.2% of the total cost could be reduced compared with previous one.

Joint optimization of electric bus charging and energy storage system scheduling

The widespread use of energy storage systems in electric bus transit centers presents new opportunities and challenges for bus charging and transit center energy management.A unified optimization model is proposed to jointly optimize the bus charging plan and energy storage system power profile.The model optimizes overall costs by considering battery aging,time-of-use tariffs,and capacity service charges.The model is linearized by a series of relaxations of the nonlinear constraints.This means that we can obtain the exact solution of the model quickly with a commercial solver that is fully adapted to the time scale of day-ahead scheduling.The numerical simulations demonstrate that the proposed method can optimize the bus charging time,charging power,and power profile of energy storage systems in seconds.Monte Carlo simulations reveal that the proposed method significantly reduces the cost and has sufficient robustness to uncertain fluctuations in photovoltaics and office loads.

A mixed-integer linear programming approach for robust state estimation

In this paper,a mixed integer linear programming(MILP)formulation for robust state estimation(RSE)is proposed.By using the exactly linearized measurement equations instead of the original nonlinear ones,the existingmixed integer nonlinear programming formulation for RSE is converted to a MILP problem.The proposed approach not only guarantees to find the global optimum,but also does not have convergence problems.Simulation results on a rudimentary 3-bus system and several IEEE standard test systems fully illustrate that the proposed methodology is effective with high efficiency.

Passive shimming based on mixed integer programming for MRI magnet

A mathematical model based on mixed integer programming is presented in this paper for the passive shimming of magnet in magnetic resonance imaging(MRI) scanner.In this model,the magnetic field inhomogeneity tolerance and the central value of the magnetic field after shimming are programmed together with the volume of each shim piece as the variables,which increases the degree of freedom and guarantees a better solution.The magnetic field inhomogeneity tolerance after shimming with a weighting coefficient and the total volume of shim pieces are both contained in the objective function of the model.By assigning different values to the weighting coefficient in the objective function,different shimming plans with different emphases can be obtained.A simulation test has been carried out on a small permanent magnet with frame structure.Several solutions are given and compared in this paper,which indicates that a practical shimming plan can be obtained quickly by solving this model.

Reserve Constrained Dynamic Economic Dispatch with Valve-point Effect:A Two-stage Mixed Integer Linear Programming Approach

This paper proposes a deterministic two-stage mixed integer linear programming(TSMILP)approach to solve the reserve constrained dynamic economic dispatch(DED)problem considering valve-point effect(VPE).In stage one,the nonsmooth cost function and the transmission loss are piecewise linearized and consequently the DED problem is formulated as a mixed integer linear programming(MILP)problem,which can be solved by commercial solvers.In stage two,based on the solution obtained in stage one,a range compression technique is proposed to make a further exploitation in the subspace of the whole solution domain.Due to the linear approximation of the transmission loss,the solution obtained in stage two dose not strictly satisfies the power balance constraint.Hence,a forward procedure is employed to eliminate the error.The simulation results on four test systems show that TSMILP makes satisfactory performances,in comparison with the existing methods.

Deleting Outliers in Robust Regression with Mixed Integer Programming

In robust regression we often have to decide how many are the unusualobservations, which should be removed from the sample in order to obtain better fitting for the restof the observations. Generally, we use the basic principle of LTS, which is to fit the majority ofthe data, identifying as outliers those points that cause the biggest damage to the robust fit.However, in the LTS regression method the choice of default values for high break down-point affectsseriously the efficiency of the estimator. In the proposed approach we introduce penalty cost fordiscarding an outlier, consequently, the best fit for the majority of the data is obtained bydiscarding only catastrophic observations. This penalty cost is based on robust design weights andhigh break down-point residual scale taken from the LTS estimator. The robust estimation is obtainedby solving a convex quadratic mixed integer programming problem, where in the objective functionthe sum of the squared residuals and penalties for discarding observations is minimized. Theproposed mathematical programming formula is suitable for small-sample data. Moreover, we conduct asimulation study to compare other robust estimators with our approach in terms of their efficiencyand robustness.

AN EXTRACTION ALGORITHM FOR A SET OF ELEMENTARY SIPHONS BASED ON MIXED-INTEGER PROGRAMMING

Elementary siphons are useful in the development of a deadlock prevention policy for a discrete event system modeled with Petri nets. This paper proposes an algorithm to iteratively extract a set of elementary siphons in a class of Petri nets, called system of simple sequential processes with resources （S3pR）. At each iteration, by a mixed-integer programming （MIP） method, the proposed algorithm finds a maximal unmarked siphon, classifies the places in it, extracts an elementary siphon from the classified places, and adds a new constraint in order to extract the next elementary siphon. This algorithm iteratively executes until no new unmarked siphons can be found. It finally obtains a unique set of elementary siphons and avoids a complete siphon enumeration. A theoretical analysis and examples are given to demonstrate its efficiency and practical potentials.

A Linear Mixed Integer Programming Model for N-Vehicle Exploration Problem

Finding the accurate solution for N-vehicle exploration problem is NP-hard in strong sense.In this paper,authors build a linear mixed integer programming model for N-vehicle exploration problem based on its properties.The model is then proved equivalent to the original problem.Given the model,one can apply the already existed methods and algorithms for mixed integer linear programming on N-vehicle exploration problem,which helps to enrich methods for solving N-vehicle exploration problem.

Optimization Methods for Mixed Integer Weakly Concave Programming Problems

In this paper,we consider a class of mixed integer weakly concave programming problems(MIWCPP)consisting of minimizing a difference of a quadratic function and a convex function.A new necessary global optimality conditions for MIWCPP is presented in this paper.A new local optimization method for MIWCPP is designed based on the necessary global optimality conditions,which is different from the traditional local optimization method.A global optimization method is proposed by combining some auxiliary functions and the new local optimization method.Furthermore,numerical examples are also presented to show that the proposed global optimization method for MIWCPP is efficient.