Mixed-integer programming and multi-objective optimization techniques for the design of control augmented structures

In this paper a general framework is discussed within which a municipal authority can assess future needs for certain public services within its area and can develop a programme for land purchase within a fixed budget. Concentration is on developing an optimising model, using mixed integer programming techniques, to identify available plots of land and to earmark them for specific land uses. A range of constraints is discussed, and a set of subsidies and penalties arising out of a solution method due to Balas, explained with reference to the local municipality of Coimbra in central Portugal, is presented.

This article presents an overview and a flavour of almost two decades of MARKAL model developments and selected applications. The MARKAL family of models has been contributing to energy/environmental planning since the early J980’s. Under the auspices of the International Energy Agency’s (IEA) Energy Technology Systems Analysis Programme (ETSAP) the model started as a linear programming (LP) application focused strictly on the integrated assessment of energy systems. It was followed by a non-linear programming (NLP) formulation which combines the ‘bottom-up’ technology model with a ‘top-down’ simplified macro-economic model. In recent years, the family was enlarged by members to model material flows, to employ stochastic programming (SP) to address future uncertainties, to model endogenous technology learning using mixed integer programming (MIP) techniques, and to model multiple regions (NLP/LP).

Mixed-integer nonlinear programming techniques for process systems engineering

In a recent paper by Prodan et al. (J. Optim. Theory Appl. 154:549---572, 2012), a technique was presented to reduce the number of binary variables needed to represent not convex constraints in a mixed-integer programming (MIP) problem. The proposed technique employs tuples of binary variables, which are associated with feasible regions of the feature space. However, since the number of all possible tuples with a given number of bits is a power of two, there may be several unallocated tuples that must be rendered infeasible by imposing suitable constraints. We show in this paper that it is always possible to partition the tuples so that only one inequality is necessary to render all the unallocated tuples and only them infeasible. Moreover, we develop a systematic procedure to perform this partition and write the referred inequality.

A re-entrant shop describes a manufacturing environment in which a machine can process a job more than once. A re-entrant shop can be classified into a re-entrant job-shop (RJS) and a re-entrant flow-shop (RFS). This article presents the development of the mixed binary integer programming (BIP) technique for the RJS and the RFS scheduling problems. Eight mixed BIP models are proposed for solving re-entrant shop scheduling problems to minimize makespan. The models RJS-1, RJS-2, RJS-3, and RJS-4 are for the RJS problems, while the other four models (RFS-1, RFS-2, RFS-3, and RFS-4) are for the RFS problems. Computational results show that the RJS-4 model is the best of the RJS models, and the RFS-3 model is the best of the RFS models.

We provide the methods for searching for the unique Nash equilibrium using mixed integer programming techniques. We also simulate the model parameters using this technique and derive the numerical solution to show the characteristics of a key player providing both public goods as suggested by Bergstrom et al. (1986). We present two key results. First, when the number of players decreases, the appearance rate of the unique equilibrium accompanying a key player increases. Second, when the variance of the preference or price parameters decreases, the appearance rate of the unique equilibrium accompanying a key player increases.

This paper proposes a real time price based optimal scheduling mechanism for centralized air conditioning load. In residential context, air conditioners are the main reason for peak load in summers. The proposed mechanism aims to determine optimal operation of air conditioner such that it results in reduction in consumer's electricity bills. Mixed Integer Programming technique is used for obtaining optimal schedule. The results obtained are compared with a previously established Linear Sequential Algorithm for evaluating the effectiveness of the scheme. The results show that Mixed Integer Programming technique provides higher reduction in electricity bill as compared to Linear Sequential technique.

Development of transportation cost functions and optimization of transportation networks for solar-aided utilization of CO2

ABSTRACTThe main objectives in the management of energy systems are to reduce the operation costs and simultaneously increase the reliability indices. The achievement of these aims is among the key challenges that network operators encounter. To overcome this challenge, the current study presents a model in which the reliability criterion is calculated in addition to the well-established technical constraints for an energy hub. In this strategy, reliability evaluations are added to the classical model as new constraints. In other words, the energy hubs can be more appropriately and realistically operated by imposing these limitations. Moreover, in addition to the costs of different energy carriers, the objective function also includes the costs of “energy not supplied” (ENS) for different loads. This approach demonstrates a mixed-integer nonlinear programming (MINLP) technique implemented using the LINDOGlobal solver in GAMS. To examine the efficiency of the proposed method, modeling is performed on a sample energy hub, and the results assessed.

The development of new mixed-integer nonlinear programming (MINLP) algorithms, coupled with advances in computers and software, is opening promising possibilities to rigorously model, optimize, and automate the synthesis of engineering systems. A general overview of the MINLP approach and algorithms will be presented in this paper with the aim of gaining a basic understanding of these techniques. Strengths and weaknesses will be discussed, as well as difficulties and challenges which still need to be overcome. In particular, it will be shown how proper problem representations, effective modeling schemes, and solution strategies can play a crucial role in the successful application of these techniques. The application of MINLP algorithms in synthesis will be illustrated with several examples.

The sugarcane transport system is very complex and uses a daily schedule, consisting of a set of locomotives runs, to satisfy the requirements of the mill and harvesters. The total cost of sugarcane transport operations is very high; over 35% of the total cost of sugarcane production in Australia is incurred in cane transport. Producing efficient schedules for sugarcane transport can reduce the cost and limit the negative effects that this system can have on the raw sugar production system. In this paper, the sugarcane rail operations are formulated as a blocking job shop scheduling problem. A mixed integer programming approach is used to formulate the shop job scheduling problem. Mixed integer programming and constraint programming search techniques are integrated for solving the problem. A case study is solved to test the approach.

ABSTRACTRailway disturbance management is inherently a multi-objective optimization problem that concerns both the operators’ cost and passenger’s service level. This study proposes a multi-objective simulation-based optimization framework to effectively manage the train conflicts after the occurrences of a disturbance caused by a temporary line blockage. The simulation model enhanced with a dynamic priority dispatching rule in order to speed up the optimization procedure. A multi-objective variable neighborhood search meta-heuristic is proposed to solve the train rescheduling model. The obtained Pareto optimal solutions for disturbance management model support the decision maker to find a trade-off between both user and operator viewpoints. The proposed approach has been validated on a set of disruption scenarios covering a large part of the Iranian rail network. The computational results prove that the proposed model can generate good-quality timetables with the minimum passenger delay and deviation from the initial timetable. The outcomes indicate that the developed simulation-based optimization approach has substantial advantages in producing practical solution quickly when compared to currently accepted solutions.Abbreviation: MOVNS: multi-objective variable neighbourhood search; DES: discrete-event simulation; SO: simulation-optimization; AG: Alternative Graph; FCFS: First Come First Served; MIP: mixed integer programming; MILP: mixed-integer linear programming; B&B: branch and bound algorithm; VND: Variable Neighborhood Descent; NSGA-II: Non-dominated Sorting Genetic Algorithm–II; CD: crowding distance; DP: dynamic priority; EDD: earliest due date first; SRTT: shortest remaining traveling time; LST: least slack time first

PurposeResource capacity and product changeovers must be both considered in the preparation of a realistic production plan. The purpose of this paper is to present a heuristic for enforcing resource availability and the accompanying changeover realities into a continuous‐variable linear programming formulation that would otherwise require a mixed‐integer model. The results from both approaches are compared in terms of objective function values and computational requirements; the effectiveness of the heuristic approach is demonstrated.Design/methodology/approachA case study search was conducted to identify relevant data sets that could be used to exercise the optimization and heuristic models. The case studies found in the literature were too small and simple compared to the problem complexity desired. The authors developed a case study based on the development of a production plan for a typical flashlight. It includes two end‐products that differ in their bills of materials and process requirements. Basic processes include plastic part preparation and final assembly; various raw materials with pre‐defined lead times are purchased from external suppliers. The results of the LP‐based heuristic and the mixed‐integer programming (MIP) optimization algorithm are then compared through a statistical experiment. The experiment includes four factors: number of products, number of periods, number of machines, and percentage line capacity utilization.FindingsWhen a MIP algorithm is applied to obtain the results, most of the time the planner would have to wait days or even weeks for the algorithm to provide a solution. However, the authors' linear programming‐based procedure provides the same quality of solution in minutes and for some problems in seconds.Originality/valueThe originality of the heuristic approach resides on the avoidance of the lengthy MIP computer runs. At each iteration, the authors solve the LP production planning problem without changeover considerations, and then subtract from the original capacity the time associated with the changeovers resulting from the last LP solution. After a small number of iterations the heuristic always converges to the optimal MIP solution. The contribution of this research can be appreciated by someone who is using this tool to generate a production plan in a real world factory where setups are important and the results can immediately suggest changes to some of the assumptions or parameters used in the planning exercise.

In this paper, we present a method incorporating axiomatic design, TRIZ, and mixed integer programming (MIP) to solve engineering design problems. Axiomatic design decomposes the problem into several mutually independent sub-problems, TRIZ generates all feasible design concepts, and MIP optimizes cost and the numerical configuration among available design options. The method is illustrated on a locomotive ballast arrangement case study. Ballast arrangement is a key process for a locomotive assembly, which determines the carrying capacity. Due to the unsophisticated technology requirements, the ballast arrangement process has received little attention. The trend of mass customization, however, demands locomotive manufacturers to provide diverse products with affordable cost and reduced time. Thus, a flexible and easy to implement ballast arrangement process design is sought. The proposed method determines what material combinations, in what quantity, and where in the limited cavities should the ballast be allocated to minimize cost. Using the case study, we demonstrate the advantages in cost reduction and time savings. The synergy of these improvements not only can enhance productivity and agility but also competitive advantage.

Centralized algorithms are widely used for optimization and control in power system applications. These algorithms require all the measurements and data to be accumulated at central location and hence suffer from single-point-of-failure. Additionally, these algorithms lack scalability with an increasing number of sensors and actuators, specially with the increasing integration of distributed energy resources (DERs). As the power system becomes a confluence of a diverse set of decision-making entities with a multitude of objectives, the preservation of privacy and operation of the system with limited information has been a growing concern. Distributed optimization techniques solve these challenges while also ensuring resilient computational solutions for the power system operation in the presence of both natural and man-made adversaries. A detailed discussion of possible applications of distributed optimization in power systems is provided in this work. However, there exist multiple challenges for accurate and computationally efficient distributed solutions. Commonly-used distributed optimization approaches include Lagrange relaxation, augmented Lagrangian, approximate network directions in conjunction with standard Lagrangian, auxiliary problem principle, alternating directions method of multipliers, optimality condition decomposition, proximal atomic coordination, and optimal feedback-based voltage control. A comprehensive classification of the distributed optimization problems has been discussed and detailed in this work. All of these algorithms have displayed efficient identification of global optimum solutions for convex continuous distributed optimization problems. The algorithms discussed so far are predominantly used to manage continuous state variables. Inclusion of integer variables in the decision support are needed for specific power system problems. Mixed integer programming (MIP) problem arises in a power system operation and control due to tap changing transformers, capacitors and switches. The global optimization techniques for MIPs are Branch and Bound, Branch and Cut, Cutting planes, Adaptive coordinate search, Nelder-Mead, Genetic algorithm etc. Although the above optimization techniques are able to solve NP-hard convexified MIP problems centrally, but are time consuming and do not scale well for large scale distributed problems. Decomposition and solution approach of distributed coordination can resolve the scalability issue. Despite the fact that a large body of work is present on the centralized solution methods for convexified MIP problems, the literature on distributed MIPs is relatively limited. The distributed optimization algorithms applied in power network to solve MIPs are reported here. ML based solutions can help to get faster convergence for distributed optimization or can replace optimization techniques depending on the problem as discussed in this work. Finally, a summary and path forward are provided, and the advancement needed in distributed optimization for the power grid is also presented.