Multiobjective Programming Problems Research Articles

Stochastic optimal operation of flexible distribution networks for security improvement considering active management

This paper presents a stochastic optimal operation problem of gas turbine integrated distribution networks in the presence of active management schemes, which is formulated as a multi-objective chance-constrained mixed integer nonlinear programming problem. The control variables are the on-load tap-changer tap position, the power provided by the distributed generation (DG), the DG power factor angle, the load participating in demand side management and the switch status. The objectives defined in this paper are to simultaneously minimize the expectation cost and variation coefficient of security distance. Uncertainties related to DG output and load fluctuation and fault power restoration under contingencies are also considered in the optimization problem. The collaboration of normal boundary intersection and dynamic niche differential evolution algorithm is proposed to handle the optimal operation mode. Simulation results are presented and demonstrate the effectiveness of the proposed model. Compared with the operation result without the consideration of security, the security-constrained operation can reduce the expectation cost. So the proposed optimization is reasonable and valuable.

On sufficiency and duality for semi-infinite multiobjective optimisation problems involving V-invexity

In the present paper, we study a non-convex non-smooth semi-infinite multiobjective programming problem with a finite number of Lipschitz continuous objective functions and infinite number of inequality constraints which is applicable in economics, engineering, optimal control theory, robust optimisation, social work and in different fields of mathematics. We derive sufficient conditions for the optimality of a feasible point under V-invexity and generalised V-invexity assumptions in terms of Clarke subdifferential. We formulate Mond-Weir type dual model for the primal non-smooth semi-infinite multiobjective programming problem and establish weak, strong and strict converse duality results under the V-invexity and generalised V-invexity conditions. The results established in the paper extend and unify several similar results in the literature.

A decentralized coordination algorithm for multi-objective linear programming with block angular structure

ABSTRACT This article considers linear multi-objective programming problems with block angular structure, which are analogous to multi-disciplinary optimization environments where disciplines must collaborate to achieve a common overall goal. In this decentralized environment, a mechanism to guide locally optimized decision makers’ solutions to a Pareto-optimal solution without sharing the entire local information is developed. The mechanism is based on an augmented Lagrangian approach to generate a solution and is separated into two phases: phase I determines an ideal point for each of the single objectives and phase II searches for a compromise solution starting from a single ideal point. Theoretical results show that the algorithm converges and the solution generated is Pareto optimal. The algorithm’s effectiveness is demonstrated via an illustrative example and a real-world bi-objective re-entrant flow-shop production planning problem. The real-world experimental results showed that the decentralized method had an average 50% better performance compared to other centralized methods.

New conditions for testing necessarily/possibly efficiency of non-degenerate basic solutions based on the tolerance approach

In this paper, a specific type of multiobjective linear programming problem with interval objective function coefficients is studied. Usually, in such problems, it is not possible to obtain an optimal solution which optimizes simultaneously all objective functions in the interval multiobjective linear programming (IMOLP) problem, requiring the selection of a compromise solution. In conventional multiobjective programming problems these compromise solutions are called efficient solutions. However, the efficiency cannot be defined in a unique way in IMOLP problems. Necessary efficiency and possible efficiency have been considered as two natural extensions of efficiency to IMOLP problems. In this case, necessarily efficient solutions may not exist and the set of possibly efficient solutions usually has an infinite number of elements. Furthermore, it has been concluded that the problem of checking necessary efficiency is co-NP-complete even for the case of only one objective function. In this paper, we explore new conditions for testing necessarily/possibly efficiency of basic non-degenerate solutions in IMOLP problems. We show properties of the necessarily efficient solutions in connection with possibly and necessarily optimal solutions to the related single objective problems. Moreover, we utilize the tolerance approach and sensitivity analysis for testing the necessary efficiency.Finally, based on the new conditions, a procedure to obtain some necessarily efficient and strictly possibly efficient solutions to multiobjective problems with interval objective functions is suggested.

Fuzzy rough bi-level multi-objective nonlinear programming problems

Fuzzy rough bi-level multi-objective nonlinear programming problem (FRBMNPP) moved toward becoming rise normally in various real applications. In this article we develop bi-level multi-objective nonlinear programming problem (BMNPP), in which the objective functions have fuzzy nature and the constraints represented as a rough set. The fuzzy objective functions converted into deterministic ones by utilizing the α-cut methodology. Thus the FRBMNPP become a rough BMNPP which is transformed into two problems corresponding to the upper and lower approximation models. The Karush-Kuhn-Tucker (KKT) method and two models of technique of order preferences by similarity to ideal solution (TOPSIS) approach are developed to solve such problem. At last, applicability and efficiency of the two TOPSIS models and KKT method, suggested in this study, are presented through an algorithm and a numerical illustration.

Solving multi-objective probabilistic factional programming problem

This paper presents the solution methodology of a multi-objective probabilistic fractional programming problem. In the proposed model the parameters in the constraints coefficient and the right-hand sides of the constraints follow continuous random variables having known distribution. Since the programming problem consists of random variables, multi-objective function and fractional objective function, it is lengthy, time-consuming and clumsy to solve the proposed programming problem using analytical methods. Stochastic simulation-based genetic algorithm approach is directly applied to solve multi-objective probabilistic non-linear fractional programming problem involving beta distribution and chi-square distribution. In the proposed method, it is not necessary to find the deterministic equivalent of a probabilistic programming problem and applying any traditional methods of fractional programming problem. The stochastic simulation-based genetic algorithm is coded by Code block C++ 16.01 compiler. A set of Pareto optimal solutions are generated for a multi objective probabilistic non-linear fractional programming problem. A numerical example and case study on inventory problem are presented to validate the proposed method.

On solving fuzzy rough multiobjective integer linear fractional programming problem

On solving fuzzy rough multiobjective integer linear fractional programming problem

Optimality and duality results for E-differentiable multiobjective fractional programming problems under E-convexity

A new class of (not necessarily differentiable) multiobjective fractional programming problems with E-differentiable functions is considered. The so-called parametric E-Karush–Kuhn–Tucker necessary optimality conditions and, under E-convexity hypotheses, sufficient E-optimality conditions are established for such nonsmooth vector optimization problems. Further, various duality models are formulated for the considered E-differentiable multiobjective fractional programming problems and several E-duality results are derived also under appropriate E-convexity hypotheses.

Optimizing Diet Problem for Cardiovascular Disease in Fuzzy Environment by Using Multi-Objective Fuzzy Linear Programming

Our purpose in this paper is to present a proper diet model for cardiovascular patients in the fuzzy environment. In previous studies many efforts were made regarding preparation of a diet model appropriate for different age groups. But in most studies the daily nutrient intake decisions were made based on crisp data. By prescribing a diet based on crisp data, some of realities are neglected. For the same reason, we dealt with human diet problem through fuzzy approach. Also due to the importance of nutrition for individuals, especially patients with cardiovascular diseases, we have provided nutrition model as multi-objective fuzzy linear programming problem in which minimization of saturated fats, salt, monosaccharide and amount of received calery are considered as our objectives. First we review literature of fuzzy mathematics and then we will discuss nutrition model of cardiovascular patients in the fuzzy environment. Results indicated uncertainty about amount of nutrients and their intake affects diet quality making it more realistic.

An Algorithmic Model Building Scheme Based on Dynamic Programming Algorithms

Dynamic programming algorithm is a basic tool for solving multi-level decision-making problems, which is widely used in social economy, engineering technology and optimal control. Aiming at the incommensurability of multi-objective programming indices, the relative membership degree matrix of allocation schemes for quantitative and qualitative indices is established, and the analysis method of multi-objective and multi-stage dynamic programming problems is given by using vector and matrix unification. The decision maker determines the decision coefficients of each constraint indicator according to the specific problem and performs weighting processing. The weights of different state variables for different constraint indicators are integrated, the comprehensive weights of state variables are solved, and the original static constraint indicators are transformed into dynamic variables that can influence the decision results. The research shows that the algorithm transforms the multi-stage decision problem into a single-stage decision problem, and solves the optimal value of the expected value through the mixture of random expectation models in a single stage. As long as it is used properly, dynamic planning of this traditional method can be a better way to solve complex problems.

Economic and Environmental Optimisation Framework for Carbon Capture Utilisation and Storage Supply Chain

Carbon capture utilisation and storage (CCUS) is widely recognised as a key mitigation technology that can significantly reduce carbon dioxide (CO2) emission. This study develops an optimisation framework focused on the economic and environmental aspects of Northeast China CCUS supply chain. The overall network is economically optimised over a 20 years’ time horizon to provide the geographic location and scale of capture and sequestration sites as well as the most convenient transport routes. The resulting problem is a multi-objective mixed integer linear programming (MILP) problem, whose objectives include minimising its total annual cost and minimising life cycle greenhouse gas (GHG) emission. The economic and environmental performances are optimised by e-constraint method. To demonstrate the application of the proposed model, a realistic case study from Northeast China involving 16 sources and 3 sinks is illustrated. The results provide valuable insights to adopt more sustainable strategic alternatives in the design of CCUS supply chain.

On generating the set of nondominated solutions of a linear programming problem with parameterized fuzzy numbers

The paper presents a new method for solving fully fuzzy linear programming problems with inequality constraints and parameterized fuzzy numbers, by means of solving multiobjective linear programming problems. The equivalence is proven between the set of nondominated solutions of the fully fuzzy linear programming problem and the set of weakly efficient solutions of the considered and related multiobjective linear problem. The whole set of nondominated solutions for a fully fuzzy linear programming problem is explicitly obtained by means of a finite generator set.

Wiretap Code Design by Neural Network Autoencoders

In industrial machine type communications, an increasing number of wireless devices communicate under reliability, latency, and confidentiality constraints, simultaneously. From information theory, it is known that wiretap codes can asymptotically achieve reliability (vanishing block error rate (BLER) at the legitimate receiver Bob) while also achieving secrecy (vanishing information leakage (IL) to an eavesdropper Eve). However, under finite block length, there exists a tradeoff between the BLER at Bob and the IL at Eve. In this work, we propose a flexible wiretap code design for degraded Gaussian wiretap channels under finite block length, which can change the operating point on the Pareto boundary of the tradeoff between BLER and IL given specific code parameters. To attain this goal, we formulate a multi-objective programming problem, which takes the BLER at Bob and the IL at Eve into account. During training, we approximate the BLER by the mean square error and the IL by schemes based on Jensen's inequality and the Taylor expansion and then solve the optimization problem by neural network autoencoders. Simulation results show that the proposed scheme can find codes outperforming polar wiretap codes (PWC) with respect to both BLER and IL simultaneously. We show that the codes found by the autoencoders could be implemented with real modulation schemes with only small losses in performance.

On multi-level multi-objective linear fractional programming problem with interval parameters

This paper develops a method to solve multi-level multi-objective linear fractional programming problem (ML-MOLFPP) with interval parameters as the coefficients of decision variables and the constants involved in both the objectives and constraints. The objectives at each level are transformed into interval-valued fractional functions and approximated by intervals of linear functions using variable transformation and Taylor series expansion. Interval analysis and weighting sum method with analytic hierarchy process (AHP), are used to determine the non-dominated solutions at each level from which the aspiration values of the controlled decision variables are ascertained and linear fuzzy membership functions are constructed for all the objectives. Two multi-objective linear problems are equivalently formulated for the ML-MOLFPP with interval parameters and fuzzy goal programming is used to compute the optimal lower and upper bounds of all the objective values. A numerical example is solved to demonstrate the proposed solution approach.

Optimal Selection of Crowdsourcing Workers Balancing Their Utilities and Platform Profit

In a mobile crowdsourcing system (MCS), a platform outsources sensing tasks to numerous mobile worker devices. The collected data are analyzed and the processed information is shared among many other interested users. The platform pays the workers for the sensing data and earns money from the users receiving processed information services. Distributing the sensing workloads among the potential workers so as to maintain the required data quality and to make a reasonable amount of profit is a challenging problem for such a platform. In this paper, we develop a workload allocation policy that makes a reasonable tradeoff between worker utilities and platform profit. It quantifies the utility (i.e., the quality of sensed data) of a worker as a function of worker mobility, current location, and past sensing records. The workload allocation problem is formulated as a multiobjective nonlinear programming (MONLP) problem which aims to make the desired tradeoff between worker utilities and platform profit. The allocation problem is shown to be NP-hard and thus we develop two greedy algorithms with relaxed constraints to achieve polynomial time solutions. Performance of the proposed workload allocation policy is evaluated in a distributed computation environment using MATLAB. The results show its effectiveness compared to state-of-the-art methods in terms of platform profit, quality of sensing data, and request service satisfaction.

Duality for higher-order (F,η)-invexity multiobjective fractional programming

In this paper, we define a new class of generalized higher-order (F,η)-invexity functions, higher-order (F,η)-pseudo invexity functions and higher-order (F,η)-quasi invexity functions. Under the new generalized invexity, the Wolfe dual model for a class of multiobjective fractional programming problem is established, and several weak duality, strong duality and strict converse duality theorems are obtained and proved.

Sufficient optimality conditions for nondifferentiable multiobjective programming problem with generalized uniform invexity

In this paper, a new class of generalized invex functions named generalized uniform pseudoinvex (C, q) – type I, generalized uniform pseudoquasi-invex (C, q) – type I and generalized uniform quasipseudo-invex (C, q) – type I are defined by utilizing the Clarke subdifferential, where C is sublinear in the third argument. Then some sufficient optimality conditions are derived and proved for a class of nondifferentiable multiobjective programming problems involving the new generalized uniform invexity.

Biobjective optimization over the efficient set of multiobjective integer programming problem

<p style='text-indent:20px;'>In this article, an exact method is proposed to optimize two preference functions over the efficient set of a multiobjective integer linear program (MOILP). This kind of problems arises whenever two associated decision-makers have to optimize their respective preference functions over many efficient solutions. For this purpose, we develop a branch-and-cut algorithm based on linear programming, for finding efficient solutions in terms of both preference functions and MOILP problem, without explicitly enumerating all efficient solutions of MOILP problem. The branch and bound process, strengthened by efficient cuts and tests, allows us to prune a large number of nodes in the tree to avoid many solutions. An illustrative example and an experimental study are reported.

Optimal strategies for the yard truck scheduling in container terminal with the consideration of container clusters

In container loading and unloading operations, container clusters are more suitable for large-scale operation and coupling scheduling of loading and unloading equipment. Taking a container cluster as a work unit, this study analyzes the multi-vessel large container clusters operation and researches the optimal scheduling strategy of the yard truck. A multi-objective mathematical programming model is developed through the pre-distribution of inbound container clusters and outbound container clusters, where the objectives are to minimize the non-loaded traveling distance and obtain the shortest completion time to finish the loading and unloading of containers in multiple vessels. The modeled problem is analyzed and solved by a heuristic-adaptive genetic algorithm. Fuzzy membership function and Pareto optimal solution are used to transform the multi-objective mathematical model into a single objective. The two methods are compared with results from the multi-objective programming problem of the model proposed. The result from the experimental case proved that the result of the Pareto optimal solution is better than that of the fuzzy membership function with regard to the problems of minimizing the distance of non-loaded traveling and finding the shortest completion time to finish the loading and unloading of containers in multiple vessels.

Multiobjective Integer Programming: Synergistic Parallel Approaches

Exactly solving multiobjective integer programming (MOIP) problems is often a very time-consuming process, especially for large and complex problems. Parallel computing has the potential to signifi...