Constrained Programming Research Articles

SCWOA: an efficient hybrid algorithm for parameter optimization of multi-pass milling process

In order to minimize total production time in multi-pass milling process, selecting optimal values of the process parameters is of great importance. The parameter optimization model of multi-pass milling process is a Constrained Non-Linear Programming formulation. Due to nonlinearity and complexity of the mathematical model, developing new solution methodologies, which can provide efficient solutions, is essential. For this purpose, in this paper a novel hybrid algorithm called Sine–Cosine Whale Optimization Algorithm is proposed for parameter optimization problem of multi-pass milling process in order to minimize total production time. The SCWOA uses exploration and exploitation abilities of the two basic algorithms to achieve better solutions. To show efficiency of the proposed algorithm, an experimental study is carried out and the result of the proposed algorithm is compared to the ones in the literature. The findings revealed that SCWOA provides promising solutions which result in significantly lower production time.

Protection Coordination for Microgrids With Grid-Connected and Islanded Capabilities Using Communication Assisted Dual Setting Directional Overcurrent Relays

This paper proposes a communication assisted dual setting relay protection scheme for micro-grids with grid connected and islanded capability. Previous work on dual setting relays has been applied to grid connected distributed generation systems only, but one major shortcoming is the failure of the backup scheme to operate in a coordinated manner. The proposed scheme relies on the use of dual setting directional overcurrent relays that are capable of operating in both forward and reverse directions, with different settings, and with a low bandwidth communication to maintain proper protection coordination. The problem is formulated as a non-linear constrained programming problem where the relay settings are optimally determined to minimize the overall relay operating time for primary and backup operation. The scheme is tested on a modified version of the IEEE 30 bus test system equipped with distributed generation and with capability of operating in an islanded mode. The proposed scheme is compared against the conventional scheme and the results show that it is capable of overcoming the problem of infeasibility, experienced by the conventional method, without the need of installing fault current limiters. Furthermore, it achieves remarkable reduction in both the primary and backup relay operating times, which was reflected in a reduction in the total relay operating time.

An integrated chance-constrained stochastic model for efficient and sustainable supplier selection and order allocation

Effective allocation of scarce resources across supply chain environments is an emerging issue, as enterprises face shortfalls in raw materials, human labour, budgetary resources, equipment, energy and capacity. We consider these related objectives in designing efficient and sustainable supply networks using a multi-objective mixed-integer non-linear programming (MINLP) model for efficient and sustainable supplier selection and order allocation with stochastic demand. Our approach considers sustainability dimensions including economic, environmental and social responsibility, but also seeks to design the most efficient supply network given constraints of the supply market. Enterprise efficiency is assessed using a bi-objective data envelopment analysis (DEA) whose inputs include raw materials, current expenses and labour force capacity. The resulting model is non-convex because of the presence of bilinear terms in DEA-related constraints, so we introduce a multi-stage solution procedure that first uses piecewise McCormick envelopes (PCM) to linearise the bilinear terms. Next, we introduce a set of valid inequalities in order to improve solution time of the problem whose dimension significantly increases after being linearised. We then exploit chance constrained programming approaches to deal with stochastic demand. Finally, a single aggregated objective function is derived using a fuzzy multi-objective programming approach. A manufacturing case study demonstrates the validity of the proposed approach, and its effectiveness in designing a supply network that addresses the ‘triple bottom line’ of people, profit and planet that comprises many sustainability initiatives in an efficient manner.

Energy Management Problems Under Uncertainties for Grid-Connected Microgrids: A Chance Constrained Programming Approach

This paper studies two energy management problems under uncertainties for a grid-connected microgrid. The problems are motivated by practical microgrid applications such as peak power shaving and frequency regulation. These applications require constraints on the microgrid energy output, which is uncertain due to the integration with renewable resources and random loads. Both problems are formulated as chance constrained programming problems to systematically incorporate uncertainties. We also show that the resulting chance constrained programming problems can both be solved using linear programming. The proposed formulation and solution are verified by two case studies originated from real world applications.

A maritime scheduling transportation-inventory problem with normally distributed demands and fully loaded/unloaded vessels

• Studying a scheduling transportation-inventory problem with stochastic demands. • Four types of penalties are imposed on the shortages/excesses in storage levels. • The goal is to schedule vessels to meet stochastic demands and minimize total cost. • Proposed stochastic model is converted to an exact mixed integer nonlinear program. • Comparing stochastic and deterministic models and performing sensitivity analyses. Uncertainties in oil demands have significant effects on the routing and scheduling of oil tankers and inevitably influence the pertinent fleet operational expenses, shortage and excess inventory penalties, and chartering costs. In this paper, we study a stochastic maritime scheduling transportation-inventory problem to transport crude oil from a source using a set of fully loaded heterogeneous vessels to be fully unloaded at a destination over a finite time horizon. Daily demands at the destination are normally distributed random variables and different penalties are imposed on the shortages/excesses in daily storage levels at the destination. The expected total cost of such a fleet operation, consists of the total vessels’ operational expenses, expected total penalties resulting from violating specified lower and upper bounds at the destination storage facility, and chartering expenses. We aim to simultaneously optimize the fleet schedules and maintain desirable daily storage levels to meet the stochastic demand requirements at the destination with acceptable reliability levels. We formulate the problem as a stochastic optimization model and then use chance constrained programming to convert it to an exact mixed-integer nonlinear program with a convex objective function and linear constraints. Solutions obtained via the proposed stochastic model and its deterministic counterpart are compared and analyzed to gain insights into the impact of the variations in demands and the probabilities of meeting demands on the overall operation and cost structure.

Portfolio Choice Based on Third-Degree Stochastic Dominance

We develop an optimization method for constructing investment portfolios that dominate a given benchmark portfolio in terms of third-degree stochastic dominance. Our approach relies on the properties of the semivariance function, a refinement of an existing “superconvex” dominance condition, and quadratic constrained programming. We apply our method to historical stock market data using an industry momentum strategy. Our enhanced portfolio generates important performance improvements compared with alternatives based on mean-variance dominance and second-degree stochastic dominance. Relative to the Center for Research in Security Prices all-share index, our portfolio increases average out-of-sample return by almost seven percentage points per annum without incurring more downside risk, using quarterly rebalancing and without short selling. This paper was accepted by Lauren Cohen, finance.

Minimizing Total Weighted Earliness and Tardiness for Parallel Batch-processing Machines with Incompatible Job Families

This paper considers the parallel batch-processing machines with incompatible job families, that is, jobs with the same recipe can be processed together as a batch, and the sizes of these jobs in a batch should not exceed the capacity limit of a machine. Additionally, setups are required between batches with different families on a machine. Jobs come from the same customer have identical due dates, and according to contracts, penalty occurs when orders are delivered early or late. Thus, in this paper we attempt to formulate a constrained programming model to find a schedule for minimizing the weighted earliness and tardiness. By examining the model using two instances, the results showed that it requires a lot of computation time to find the optimal solution for the given examples due to its inherent complexity. It leads us to develop some heuristic algorithms to obtain optimal or near-optimal solutions efficiently in the future.

Honey Bee Mating Optimization with Nelder-Mead for Constrained Optimization, Integer Programming and Minimax Problems

Honey Bee Mating Optimization with Nelder-Mead for Constrained Optimization, Integer Programming and Minimax Problems

A Multiobjective Fuzzy Chance Constrained Programming Model for Land Allocation in Agricultural Sector: A case study

In this article a fuzzy multiobjective chance constrained programming model is used for modeling and solving land allocation problems efficiently with the help of fuzzy goal programming. Optimal production of seasonal crops and related expenditures are considered from the viewpoint of proper utilization of total cultivating land and different farming resources. Some resource parameters associated with the probabilistic constraints are taken as normally distributed fuzzy random variables. The potential use of this methodology is illustrated by a case example.

Information Gap Decision Theory-Based Risk-Constrained Bidding Strategy of Price-Taker GenCo in Joint Energy and Reserve Markets

This paper presents an optimal bidding strategy for price-taker generation companies (GenCos), which participate in a day-ahead joint energy and reserve market. Moreover, this problem is formulated as a Mixed-Integer Quadratic Constrained Program (MIQCP) to maximize the profit. Also, the price uncertainties of energy and reserve markets prices have direct impacts on the expected profit and bidding curves. This optimization problem is modeled with utilization of information gap decision theory (IGDT) for optimizing robustness to failure—or opportunity to windfall—under uncertainty conditions. IGDT assesses the robustness/opportunity of bidding strategy in the face of price uncertainties to determine whether a decision is risk-averse or risk-taking. Correlations among the prices of energy and reserve markets are properly modeled based on the concept of weighted average squared error using a variance–covariance matrix. It is shown that the risk-averse decisions, as well as risk-taking decisions, will affect both expected profit and bidding curves. The proposed method is verified in simulation studies on a GenCo comprising 5-unit thermal that participates in a day-ahead joint energy and reserve markets. Also, the proposed model is applied to a 54-unit thermal GenCo of IEEE-118 bus to validate the computational effectiveness of the proposed model in large system.

Smart Charging of EVs in Residential Distribution Systems Using the Extended Iterative Method

Smart charging of electrical vehicles (EVs) is critical to provide the secure and cost-effective operation for distribution systems. Three model objective functions which are minimization of total supplied power, energy costs and maximization of profits are formulated. The conventional household load is modeled as a ZIP load that consists of constant power, constant current and constant impedance components. The imbalance of distribution system, constraints on nodal voltages and thermal loadings of lines and transformers are all taken into account. Utilizing the radial operation structure of distribution system, an extended iterative method is proposed to greatly reduce the dimensions of optimization variables and thus improve calculation speed. Impacts of the conventional household load model on the simulation results are also investigated. Case studies on three distribution systems with 2, 14, and 141 buses are performed and analyzed. It is found that the linear constrained convex quadratic programming model is applicable at each iteration, when the conventional household load is composed of constant power and constant impedance load. However, it is not applicable when the conventional household load consists of constant current load. The accuracy and computational efficiency of the proposed method are also validated.

A copula-based fuzzy chance-constrained programming model and its application to electric power generation systems planning

This study developed a copula-based fuzzy chance-constrained programming (CFCCP) model and applied it to electric power generation systems planning under multiple uncertainties. The CFCCP model was formulated by incorporating existing joint-probabilistic constrained programming and generalized fuzzy linear programming techniques within a general mixed-integer linear programming framework. The CFCCP model can not only effectively reflect uncertain interactions among random variables even when the random variables follow different probability distributions and have previously unknown correlations, but can also provide information about the membership grades for the decision variables and objective-function values. Thus, it would have a wider application scope than existing optimization models for power generation systems planning. Its applicability has been demonstrated through a case study of electric power generation planning within a region of North China. As a result, fuzzy interval solutions related to power generation and capacity expansion patterns of electricity-generation facilities, and primary energy supply structures were generated within six scenarios of constraint-violation levels under different α-cut levels. The results are helpful to investigate dynamic features of the regional power generation system, identify desired decision alternatives, and analyze the influences of interactions among multiple uncertainties on system outputs.

Constrained integer fractional programming problem with box constraints

This paper deals with constrained integer linear fractional programming problem with box constraints whose integer solution is required to satisfy any h out of given set of l constraints. An iterative algorithm has been proposed for ranking and scanning of all the integer points of this problem to find an optimal solution. Numerical illustration is included in support of theory.

Multi-choice probabilistic linear programming problem

In this paper, we present a linear programming model where the parameter space contains some multi-choice parameters. Alternative choices of multi-choice parameter are considered as random variables. Using interpolating polynomial for each multi-choice parameter, the model has been transformed into a non-linear mixed integer probabilistic programming problem. Then chance constrained programming technique is used to obtain an equivalent deterministic model of the transformed problem. To find the deterministic form of the objective function four different models namely, E-model, V-model, probability maximization model and fractile criterion model are used. Assuming the values of the multi-choice parameters as independent normal random variables, the methodology is presented. A numerical example is also presented to illustrate the methodology.

Transmit Precoding for Interference Exploitation in the Underlay Cognitive Radio Z-channel

This paper introduces novel transmit beamforming approaches for the cognitive radio (CR) Z-channel. The proposed transmission schemes exploit non-causal information about the interference at the SBS to re-design the CR beamforming optimization problem. This is done with the objective to improve the quality of service (QoS) of secondary users by taking advantage of constructive interference in the secondary link. The beamformers are designed to minimize the worst secondary user's symbol error probability (SEP) under constraints on the instantaneous total transmit power, and the power of the instantaneous interference in the primary link. The problem is formulated as a bivariate probabilistic constrained programming (BPCP) problem. We show that the BPCP problem can be transformed for practical SEPs into a convex optimization problem that can be solved, e.g., by the barrier method. A computationally efficient tight approximate approach is also developed to compute the near-optimal solutions. Simulation results and analysis show that the average computational complexity per downlink frame of the proposed approximate problem is comparable to that of the conventional CR downlink beamforming problem. In addition, both the proposed methods offer significant performance improvements as compared to the conventional CR downlink beamforming, while guaranteeing the QoS of primary users on an instantaneous basis, in contrast to the average QoS guarantees of conventional beamformers.

An integrated approach to optimise sugarcane rail operations

In Australia, the railway system plays a vital role in transporting the sugarcane crop from farms to mills. The sugarcane transport system is complex as it routines a daily schedule, which consists of a set of train runs to satisfy the requirements of the mills and harvesters. A constrain programming approach is used to formulate this complicated system. Metaheuristic techniques and constraint programming are hybridised as an efficient solution approach. Thus, a better sugarcane transport scheduling system is achieved to maximise the throughput of sugarcane transport. A numerical investigation is presented and demonstrates that high-quality solutions are obtainable for industry-scale applications in a reasonable time.

An efficient interior-point algorithm with new non-monotone line search filter method for nonlinear constrained programming

ABSTRACTAn efficient primal-dual interior-point algorithm using a new non-monotone line search filter method is presented for nonlinear constrained programming, which is widely applied in engineering optimization. The new non-monotone line search technique is introduced to lead to relaxed step acceptance conditions and improved convergence performance. It can also avoid the choice of the upper bound on the memory, which brings obvious disadvantages to traditional techniques. Under mild assumptions, the global convergence of the new non-monotone line search filter method is analysed, and fast local convergence is ensured by second order corrections. The proposed algorithm is applied to the classical alkylation process optimization problem and the results illustrate its effectiveness. Some comprehensive comparisons to existing methods are also presented.

Integrated Optimization of Upstream and Downstream Processing in Biopharmaceutical Manufacturing under Uncertainty: A Chance Constrained Programming Approach

This work addresses the integrated optimization of upstream and downstream processing strategies of a monoclonal antibody (mAb) under uncertainty. In the upstream processing (USP), the bioreactor sizing strategies are optimized, while in the downstream processing (DSP), the chromatography sequencing and column sizing strategies, including the resin at each chromatography step, the number of columns, the column diameter and bed height, and the number of cycles per batch, are determined. Meanwhile, the product’s purity requirement is considered. Under the uncertainties of both upstream titer and chromatography resin yields, a stochastic mixed integer linear programming (MILP) model is developed, using chance constrained programming (CCP) techniques, to minimize the total cost of goods (COG). The model is applied to an industrially relevant example and the impact of different USP:DSP ratios is studied. The computational results of the stochastic optimization model illustrate its advantage over the determinis...

Equilibria in the competitive retail electricity market considering uncertainty and risk management

In a medium term planning horizon, a retailer should determine its forward contracting and pool participating strategies as well as the selling price to be offered to the customers. Considering a competitive retail electricity market, the number of clients being supplied by any retailer is a function of the selling prices and some other characteristics of all the retailers. This paper presents an equilibrium problem formulation to model the retailer's medium term decision making problem considering the strategy of other retailers. Decision making of any single retailer is formulated as a risk constraint stochastic programming problem. Uncertainty of pool prices and clients' demands is modeled with scenario generation method and CVaR (conditional value at risk) is used as the risk measure. The resulting single retailer planning problem is a quadratic constrained programming problem which is solved using the Lagrangian relaxation method and the Nash equilibrium point of the competitive retailers is achieved by successive solving of this problem for all the retailers. The performance of the proposed method is demonstrated using a realistic case study of Texas electricity market.

Penalty Function Based Detector for Generalized Space Shift Keying Massive MIMO Systems

Generalized space shift keying (GSSK) has recently attracted much interest in the study of emerging massive MIMO systems. The maximum likelihood (ML) detection of GSSK can be posed as a 0-1 quadratic program with an equality constraint. The penalty function method is a common way to transform a constrained programming into an unconstrained one. However, determining an ideal penalty factor is not a trivial problem and has not been addressed adequately. In this letter, we prove a lemma to show that the ML detection of GSSK can be converted into an equivalent 0-1 quadratic program if the penalty factor is greater than a small constant. Based on the proposed lemma, we also present an algorithm to determine the penalty factor and finally recover the transmitted signals of GSSK. Simulation results substantiate the performance of the proposed detector.