Multiobjective Programming Problems Research Articles

Site selection framework of rail transit photovoltaic power station under interval-valued Pythagorean fuzzy environment

Different from centralized and large-scale photovoltaic power station, the sites selection of rail transit photovoltaic power station (RTPPS) concerns more on sustainability rather than profit and there is a lack of selection index system for RTPPS sites selection. Besides that, the decision model cannot deal with the uncertainty, the independence assumption problem and the solving problem of multi-objective programming (MOP) model in scenarios with more goals. The contributions of this paper are as follows: ① a selection index system of RTPPS site selection is established based on RTPPS’s characteristics to provide the scientific decision-making direction; ② the interval-valued Pythagorean fuzzy number (IVPFN) is used to deal with uncertainty in decision information; ③ the fuzzy measure were used to avoid the assumption of independence, which make the decision model is more in line with the reality; ④ the IVPFN-TOPSIS was used to decrease the number of goals, so the MOP model can be solved in scenarios with more goals. The effectiveness of this framework is proved by a China case study. According to the sensitivity analysis and comparative analysis, the decision result calculated by the proposed decision model has good robustness and the site selection framework can better serve the enterprise.

A novel multi-objective bi-level programming problem under intuitionistic fuzzy environment and its application in production planning problem

This paper presents an optimization method to solve a multi-objective model of a bi-level linear programming problem with intuitionistic fuzzy coefficients. The idea is based on TOPSIS (technique for order preference by similarity to ideal solution) method. TOPSIS method is a multiple criteria method that identifies a satisfactory solution from a given set of alternatives based on the minimization of distance from an ideal point and maximization of distance from the nadir point simultaneously. A new model of multi-objective bi-level programming problem in an intuitionistic fuzzy environment has been considered. The problem is first reduced to a conventional multi-objective bi-level linear programming problem using accuracy function. Then the modified TOPSIS method is proposed to solve the problem at both the leader and the follower level where various linear/non-linear membership functions are used to represent the flexibility in the approach of decision-makers (DMs). The problem is solved hierarchically, i.e., first the problem at the leader level is solved and then the feasible region is extended by relaxing the decision variables controlled by the leader. The feasible region is extended to obtain a satisfactory solution for the DMs at both levels. Finally, the application of the proposed approach in the production planning of a company has been presented. An illustrative numerical example is also given to explain the methodology defined in this paper.

Robust optimality conditions and duality for nonsmooth multiobjective fractional semi-infinite programming problems with uncertain data

In this article, some Karush-Kuhn-Tucker type robust optimality conditions and duality for an uncertain nonsmooth multiobjective fractional semi-infinite programming problem ((UMFP), for short) are established. First, we provide, by combining robust optimization and the robust limiting constraint qualification, robust necessary optimality conditions in terms of Mordukhovich's subdifferentials. Under suitable assumptions on the generalized convexity/the strictly generalized convexity, robust necessary optimality condition becomes robust sufficient optimality condition. Second, we formulate types of Mond-Weir and Wolfe robust dual problem for (UMFP) via the Mordukhovich subdifferentials. Finally, as an application, we establish weak/strong/converse robust duality theorems for the problem (UMFP) and its Mond-Weir and Wolfe types dual problem. Some illustrative examples are also provided for our findings.

Optimal economic-emission planning of multi-energy systems integrated electric vehicles with modified group search optimization

The present paper aims to present a comprehensive multi-objective optimization model for energy management in local multi-energy systems in the presence of plug-in electric vehicles (PEVs), seeking to achieve the maximized profit of the operators of the local multi-energy systems and minimized CO2 emission at the same time. This problem involves technology transfer in local multi-energy systems and finding the PEVs charge/discharge optimization strategies in order to maximize the operators' profit and, in the meantime, reduce the CO2 emission. It can be solved by formulating a multi-purpose objective and can be dealt with by formulating a multi-objective programming problem through accurate modeling of mutual dependencies between the energy carriers. To solve this problem, a Modified Group Search Optimization (MGSO) algorithm is used based on the decomposition system. By the proposed structure, the local and global search is improved significantly. As indicated by the results of the effectiveness test of the optimization framework for maximizing the operator's profit and, meanwhile, reducing the CO2 emission, this objective is achievable through optimal coordination of multiple energy carriers in local multi-energy systems and effective management of the flexibility collected at both supply and demand sides.The simulation has been investigated in different scenarios. Obtained numerical analysis shows that the base case signifies the best case in terms of maximization of the local multi-energy systems operator’s profit through the optimized charging and discharging approaches of the PEVs. Also, in all scenarios, the profit of operator reductions by 5%–15% as compared with the base case. On the other hand, the best case scenario from an environmental point of view is provided by a scenario categorized with electric vehicles excluding under environmental optimization. In fact, CO2 emissions are reduced 7% compared to the emissions of base case.

Fuzzy harmonic mean technique for solving fully fuzzy multilevel multiobjective linear programming problems

This paper illustrates how the fuzzy harmonic mean technique can efficiently solve fully fuzzy multilevel multiobjective linear programming (FFMMLP) problems. First, at each level, the FFMMLP problem can be converted into three crisp multiobjective linear programming (CMLP) problems using the crisp linear technique. Then, the fuzzy harmonic mean technique is utilized to aggregate each crisp problem's multiobjective into a single objective. Second, the ensuing final, single-objective problem is constructed using the harmonic mean for each level. Finally, it is solved to obtain a fuzzy compromise solution for the FFMMLP problem in general. Two examples are given to obtain the application of the proposed method. One example is applying the proposed approach to a multilevel multiobjective production planning model for a supply chain under a fully fuzzy environment.

Warm-starting lower bound set computations for branch-and-bound algorithms for multi objective integer linear programs

In this paper we propose a generic branch-and-bound algorithm for solving multi-objective integer linear programming problems. In the recent literature, competitive frameworks has been proposed for bi-objective 0–1 problems, and many of these frameworks rely on the use of the linear relaxation to obtain lower bound sets. When increasing the number of objective functions, however, the polyhedral structure of the linear relaxation becomes more complex, and consequently requires more computational effort to obtain. In this paper we overcome this obstacle by speeding up the computations. To do so, in each branching node we use information available from its father node to warm-start a Bensons-like algorithm. We show that the proposed algorithm significantly reduces the CPU time of the framework on several different problem classes with three, four and five objective functions. Moreover, we point out difficulties that arise when non-binary integer variables are introduced in the models, and test our algorithm on problem that contains non-binary integer variables too.

Sustainable partner selection and order allocation for strategic items: an integrated multi-stage decision-making model

ABSTRACT Current environmental issues and government requirements, together with pressure from the market and other stakeholders, emphasise the importance of partner selection in constructing and operating sustainable supply chains. Strategic items, which carry both high supply risk and high importance of purchase, are particularly important in sustainable supply chains. This paper presents an integrated decision-making model, which aims to solve the partner selection and order allocation problem for strategic items in sustainable supply chains. In the proposed model, weightings of different decision-makers are first calculated using Trapezoidal Fuzzy Numbers. Then, Taguchi loss function is used to evaluate the relative importance of potential partners, with the weighting results of criteria by Best-Worst Method. Finally, considering the weights of different potential partners, Particle Swarm Optimisation (PSO) is used to solve the multi-objective programming problem, and Technique of Order Preference Similarity to the Ideal Solution (TOPSIS) is applied to identify the most appropriate Pareto solution for sustainable partner selection and order allocation of strategic items. An illustrative application of the proposed model is undertaken in a leading Chinese LED lighting manufacturer to show its effectiveness and applicability.

A goal programming approach for multi-objective linear fractional programming problem with LR possibilistic variables

A goal programming approach for multi-objective linear fractional programming problem with LR possibilistic variables

Application of multi-objective probabilistic fractional programming problem in production planning

This paper presents the application of multi-objective probabilistic fractional programming problem in production planning. The production planning model for a manufacturing company that produce multiple products with a specified period is formulated by considering some of the parameters in the right hand sides of the constraints as random variables following continuous distribution namely gamma distribution. The formulated mathematical model is a multi-objective probabilistic fractional programming problem. In the solution procedure, the deterministic equivalent of the probabilistic programming problem has not been obtained. The analytical method for multi-objective fractional programming problem has also not been applied to solve the proposed model. A stochastic simulation-based genetic algorithm is applied to solve the proposed model directly. A set of Pareto optimal solutions is obtained for the formulated production planning problem.

On sufficiency and duality for multiobjective programming problems using convexificators

In this paper, we consider a multiobjective programming problem with inequality and set constraints. We derive sufficient conditions for the optimality of a feasible point under generalized invexity assumptions in terms of convexificators. We give an example to illustrate that the concept of invexity in terms of convexificators is weaker than invexity in terms of other subdifferentials. We formulateWolfe and Mond-Weir type duals for the nonsmooth multiobjective programming problem with inequality and set constraints in terms of convexificators. We establish weak, strong, converse, restricted converse and strict converse duality results under the assumptions of invexity and strict invexity using convexificators between the primal and the Wolfe dual. We derive the respective results between the primal and the Mond-Weir dual under the assumptions of generalized pseudoinvexity, strict pseudoinvexity and quasiinvexity in terms of convexificators. We also derive the relationship between a weak vector saddle-point and a weakly efficient solution of the multiobjective programming problem.

Solving Fuzzy Multi-Objective Linear Programming Problem by Applying Statistical Method

In this paper, the statistical averaging method and the new statistical averaging methods have been used to solve the fuzzy multi-objective linear programming problems. These methods have been applied to form a single objective function from the fuzzy multi-objective linear programming problems. At first, a numerical example of solving fuzzy multi-objective linear programming problem has been provided to validate the maximum risk reduction by the proposed method. The proposed method has been applied to assess the risk of damage due to natural calamities like flood, cyclone, sidor, and storms at the coastal areas in Bangladesh. The proposed method of solving the fuzzy multi-objective linear programming problems by the statistical method has been compared with the Chandra Sen’s method. The numerical results show that the proposed method maximizes the risk reduction capacity better than Chandra Sen’s method.

Karush-Kuhn-Tucker optimality conditions and duality for nonsmooth multiobjective semi-infinite programming problems with vanishing constraints

Karush-Kuhn-Tucker optimality conditions and duality for nonsmooth multiobjective semi-infinite programming problems with vanishing constraints

Profit and Satisfaction Aware Order Assignment for Online Food Delivery Systems Exploiting Water Wave Optimization

Online Food delivery, a specialized application of mobile crowdsourcing, has accelerated its popularity due to rushed urban lifestyle in recent times. The food delivery order assignment to workers that maximizes the service qualities, such as maximization of workers’ profit and minimization of order completion time to enhance the customer satisfaction at the same time, is a challenging problem. Existing works in the literature are limited either by focusing solely on minimizing order completion time or reduction of cost incurred in delivery of orders. In this paper, we develop a framework for optimal assignment of food delivery orders to workers as a multi-objective linear programming (MOLP) problem that makes a trade-off in between the worker profit and customer satisfaction. Due to NP-hardness of the above MOLP, a polynomial time solution of the food delivery problem has been developed, namely WWOFooD, exploiting Water Wave Optimization, a meta-heuristic algorithm. The WWOFooD not only explores ways of enhancing service quality of the customers, but also ensures giving additional incentives to the workers providing faster and reliable food delivery services. The results of simulation experiments depict that the WWOFooD offers competitive workers’ profit as well as significantly enhances customer satisfaction compared to the state-of-the-art works.

A constructive method for solving a multi-objective linear program with bounded variables

The search for an optimal solution remains a central objective in optimisation, but in many situations the optimal solution cannot be obtained in polynomial time. For this, it would sometimes be necessary to find a good solution close to the optimum that can be obtained in a reasonable time. The aim of this paper is to find an ε-efficient or efficient solution for a multi-objective linear programming problem with polyhedral constraints and bounded decision variables. For this, we define an ε-efficient solution for which a characterisation theorem is proved, and where the ε-optimality criterion is formulated simultaneously for all the objectives of the problem. By using this concept of ε-efficiency, we develop an algorithm that combines the well known Benson's procedure in multi-objective linear programming and the adaptive method elaborated for finding ε-optimal solutions in mono-objective linear programming, based on the diminution of the suboptimality estimate. The proposed algorithm is illustrated by a numerical example and finally, it is implemented in MATLAB to solve a set of generated test problems. The efficient solutions found are located on the Pareto fronts of the same test problems treated by using the well-known Gamultiobj algorithm of MATLAB optimisation tool.

Uncertain multi-objective dynamic weapon-target allocation problem based on uncertainty theory

<abstract><p>The weapon-target allocation (WTA) problem is a fundamental subject of defense-related applications research, and previous studies assume that the parameters in the model are determinate. For the real battlefield, asymmetric information usually leads to the failure of the above assumption, and there are uncertain factors whose frequency is hard to pinpoint. Based on uncertainty theory, we study a WTA problem in indeterminate battlefield in this paper. First, we analyze the uncertain factors in indeterminate battlefield and their influence on WTA problem. Then, considering the target threat value, the protected asset value and the extra cost of interception as uncertain variables, the uncertain multi-objective dynamic WTA (UMDWTA) model is established, where three indices including the value of destruction of targets, the value of surviving assets and the cost of operation are regarded as objective functions, and on this basis, an equivalent transformation is presented to convert the UMDWTA model into a determinate multi-objective programming (MOP) problem by expected value and standard deviation principle. To solve the proposed model efficiently, an improved multi-objective evolutionary algorithm based on decomposition (MOEA/D) is designed, which employs three new evolutionary operators and the weight vectors adaptation mechanism to improve the convergence and uniformity of the Pareto front obtained. Finally, a case of the UMDWTA problem is carried out to be solved by the designed algorithm, and the results verify the feasibility of the proposed model.</p></abstract>

Correction: On robust weakly $ \varepsilon $-efficient solutions for multi-objective fractional programming problems under data uncertainty

Correction: On robust weakly $ \varepsilon $-efficient solutions for multi-objective fractional programming problems under data uncertainty

Optimality and duality for complex multi-objective programming

<p style='text-indent:20px;'>We consider a complex multi-objective programming problem (CMP). In order to establish the optimality conditions of problem (CMP), we introduce several properties of optimal efficient solutions and scalarization techniques. Furthermore, a certain parametric dual model is discussed, and their duality theorems are proved.</p>

Solving binary semidefinite programming problems and binary linear programming problems via multi-objective programming

‎In recent years the binary quadratic program has grown in‎ ‎combinatorial optimization‎. ‎Quadratic programming can‎ ‎be formulated as a semidefinite programming problem‎. ‎In this paper‎, ‎we consider the general form of‎ ‎binary semidefinite programming problems (BSDP)‎.‎ ‎We show the optimal solutions of the BSDP belong to the efficient set of a semidefinite multiobjective programming problem (SDMOP)‎. ‎Although‎ ‎finding all efficient points for multiobjective is not an easy problem‎, ‎but‎ ‎solving a continuous problem would be easier than a discrete variable problem‎. ‎In this paper‎, ‎we solve an SDMOP‎, ‎as an auxiliary‎, ‎instead of BSDP‎. We show the performance of our method by generating and solving random problems.

Optimality and duality results for (h,φ)-nondifferentiable multiobjective programming problems with (h,φ) – (b,f,ρ) -convex functions

Generalized algebraic operations introduced by Ben-Tal [5] are used to define new classes of generalized convex functions, namely (h,?)?(b,F,?) -convex functions and generalized (h,?)?(b,F,?)-convex functions in the vectorial case. Further, optimality and duality results are proved for the considered (h,?)- nondifferentiable multiobjective programming problem under assumptions that the functions involved are (generalized) (h,?)- (b,F,?)-convex.

Optimality and duality for semidefinite multiobjective programming problems using convexificators

Optimality and duality for semidefinite multiobjective programming problems using convexificators