A model of an urban transportation system formulated as a multiobjective mathematical programming problem under uncertainty

In this work, we propose a novel multiobjective optimization model for the sustainable design and operation of bioelectricity supply chain networks, which simultaneously accounts for the associated economic, environmental, and social impacts. The proposed model covers the cradle-to-gate life cycle of bioelectricity including biomass cultivation and harvesting, feedstock pretreatment, energy conversion, and biopower generation, as well as transportation and storage. We formulate the problem as a multiobjective mixed-integer linear fractional programming (MILFP) problem following the functional-unit-based life cycle optimization approach. The geographical dispersion and seasonality of biomass supply are captured and handled by the spatially explicit and multiperiod features of the model. The multiobjective optimization is accomplished via the ε-constraint method to obtain the approximate Pareto frontiers, which reveal the trade-off between economic performance and concerns about environmental and social impacts. Tailored solution methods are proposed for the effective global optimization of the resulting MILFP problem. An illustrative example and a county-level case study on the potential bioelectricity supply chain in the state of Illinois are provided to demonstrate the application of both the modeling framework and solution methods.

The massive growth of IoT devices and the need for digitization drive future wireless communication technologies intensively. The end-users are always demanding all kinds of network services including the time-critical and mission-critical ones. The Quality of Network Services (QoNS) of the future 5G and 6G networks are aiming to address all possible types of flexible user demands optimally. Telecom. Service Providers (TSPs) are rigorously looking for suitable network architectures that can assist them to realize such user-friendly systems. vSDN or virtualized Software Defined Network Architecture is the key technology enabler that makes such functionalities possible. In the recent paradigm shift where everything is being based on IoT, service availability and system stability are two major concerns. For keeping the quality index of the network services high, it is essential to orchestrate and deploy the network infrastructures that will provide additional and upgraded network services. Keeping these fundamental issues in mind, in this work, we have proposed a novel multi-instance deployment strategy for Controllers and Hypervisors over an actual network topology. While defining the work, our prime concern targets improving service availability within the ULL (Ultra-Low Latency) environment. Thus, we have developed a Multi-Objective Mixed Integer Linear Programming (MILP) problem for optimally placing the hypervisors and controllers over the network topology to minimize the H-plane service agreements along with propagation latency of network function demands. After analyzing the results, it can be claimed that our approach has a significant impact in improving the QoS of network parameters. The proposed model can be applied in similar time-critical relocation problems associated with UAV-assisted networks depending upon various application domains.

Multi-objective optimization for the deployment of carbon capture utilization and storage supply chain considering economic and environmental performance

This paper presents the use of a Taylor series for multiobjective integer linear fractional programming problem having grey parameters in the right-side of the constraints (GMOILFP).To deal with the grey parameters in the right-side of the constraints the positioned programming should be used.An equivalent grey multiobjective linear fractional programming problem (GMOLFP) is formulated using Gomory's cutting plane method.The Taylor series, which is a series expansion that a representation of a function, is applied to convert the fractional functions into polynomials.In the proposed approach a white value of each grey parameter is determined, Taylor series is applied and the functions are unified by using the nonnegative weighted sum method.Thus, the problem is reduced to a single linear objective with grey parameter in the right side of the constrains.An algorithm for solving GMOILGP problem with grey interval coefficients using positioned programming and Taylor series polynomials is proposed.A numerical example is provided to demonstrate the efficiency and feasibility of the proposed approach.A special case study for handling the environmental economic energy dispatch problem also is included in this paper, the main goal of this problem is how to schedule committed generators to meet the load required to minimize the pollution emissions and fuel cost.The model formulation for a special case study problem is presented, the mathematical model will be considered as (GMOLFP) and the problem is solved according to the proposed solution algorithm.

We describe an improvement of Chergui and Moulaï’s method (2008) that generates the whole efficient set of a multiobjective integer linear fractional program based on the branch and cut concept. The general step of this method consists in optimizing (maximizing without loss of generality) one of the fractional objective functions over a subset of the original continuous feasible set; then if necessary, a branching process is carried out until obtaining an integer feasible solution. At this stage, an efficient cut is built from the criteria’s growth directions in order to discard a part of the feasible domain containing only nonefficient solutions. Our contribution concerns firstly the optimization process where a linear program that we define later will be solved at each step rather than a fractional linear program. Secondly, local ideal and nadir points will be used as bounds to prune some branches leading to nonefficient solutions. The computational experiments show that the new method outperforms the old one in all the treated instances.

An algorithm is developed which ranks the feasible solutions of an integer linear and linear fractional programming problems with bounded variables in decreasing order of objective values. Numerical illustration is also included.

In this paper, we present a multi-objective fractional probabilistic programming problem where the parameters in the objective functions and right-hand side constraints are multi-choice in nature. Multi-choice multi-objective objective fractional probabilistic programming problem is formulated. The multi-choice parameters in the right-hand side of constraints are random variables following Cauchy distribution. Multi-choice multi-objective fractional probabilistic programming problem is transformed to deterministic equivalent multi-choice multi-objective fractional programming problem using chance-constrained programming problem. Lagrange interpolating polynomial approach is proposed to deal with multi-choice parameters. The multi-choice multi-objective fractional programming problem is transformed to non-linear mixed integer multi-objective programming problem. An \(\epsilon -\) constrained method is applied to find the compromise solutions of non-linear mixed integer multi-objective programming problem using different values of \(\epsilon \). LINGO software is applied to find the optimal solution of single objective non-linear mixed integer programming problem. Finally, a numerical example is given to illustrate the proposed programming problem.KeywordsMulti-choice programming problemMulti-objective programming problemProbabilistic programming problemFractional programming problem\(\epsilon \)-constraint method

The multi-objective linear fractional programming is an interesting topic with many applications in different fields. Until now, various algorithms have been proposed in order to solve the multi-objective linear fractional programming (MOLFP) problem. An important point in most of them is the use of non-linear programming with a high computational complexity or the use of linear programming with preferences of the objective functions which are assigned by the decision maker. The current paper, through combining goal programming and data envelopment analysis (DEA), proposes an iterative method to solve MOLFP problems using only linear programming. Moreover, the proposed method provides an efficient solution which fairly optimizes each objective function when the decision maker has no information about the preferences of the objective functions. In fact, along with normalization of the objective functions, their relative preferences are fairly determined using the DEA. The implementation of the proposed method is demonstrated using numerical examples.

Engineering human-centric urban transport systems should be carried out using information technology in forecasting traffic and passenger flows. One of the most important objects of urban transport systems’ progress is modeling patterns of transport flows and their distribution on the road network. These patterns are determined by the subjective choice of city residents of traffic routes using public and private transport. This study aimed to form a sequence of stages of modeling transport and passenger flows in human-centric urban transport systems and passenger flows in the human-centric urban intelligent transport systems and to determine the patterns of change to the gravity function of employees of municipal services. It was revealed that the trip distribution function of workers of urban service enterprises can be described by the attributes of the structure of the city, socio-economic data, and attributes characterizing the zones and its residents.

Globally convergent exact and inexact parametric algorithms for solving large-scale mixed-integer fractional programs and applications in process systems engineering

This article addresses a special class of non-linear programming problems, viz., linear fractional programming problems having multiple objectives. In solving the real-life linear fractional optimization problems, the ambiguity and hesitation in the decision are inherent and ever-present, therefore, it is perfectly viable to formulate and solve these optimization models using the intuitionistic fuzzy environment. The purpose of this study is to propose a simple and computationally efficient approach to obtain the solution of multiple objective linear fractional programming problems having all the decision variables and parameters expressed in terms of triangular intuitionistic fuzzy numbers. The proposed solution algorithm is primarily based on the goal programming approach, fuzzy-based linearization technique, and a membership function strategy. The original linear fractional programming problem is first converted to its equivalent deterministic/crisp multi-objective linear fractional optimization problem using the weighted goal programming methodology along with the linear membership technique to resolve the intuitionistic fuzzy constraints into the crisp one. Finally, the variable transformation technique for the under- and over-deviational variables of the goal programming model is employed to linearize all the fractions involved in the problem so as to convert the original problem to an equivalent linear optimization problem. Further, this linear programming problem can be solved using any available commercial packages. Moreover, a numerical illustration is provided to demonstrate the steps of the proposed technique followed by the analysis and solution of an E-education set-up problem. The discussion and comparisons of the practical case establish the relevancy and usefulness of the proposed model.

On computational methods for solutions of multiobjective linear production programming games

A neural network approach to multiobjective and multilevel programming problems

This chapter summarizes recent developments in Santiago’s urban public and private transport system and outlines perspectives for the year 2030. The analysis is conducted with a set of indicators: motorization rate, current and expected congestion levels, level of service, modal split and accessibility levels. For each indicator the expected values for 2030 are estimated and analysed to determine the feasibility of a more sustainable urban transport system in Santiago. Assumptions regarding economic and demographic growth for the Metropolitan Area of Santiago, as well as infrastructural projects and operational adjustments are considered. Indicator quantification is achieved with mathematical economic models for transport and land use. Based on the indicator values, conclusions are drawn about the perspectives on Santiago’s urban transport system. Finally, recommendations for further policy action in the field are discussed.

In this paper, we propose a linear programming based interactive method for multiobjective linear programming problems, in which fuzzy coefficients and random variable coefficients are involved in the objective functions simultaneously. In the proposed method, it is assumed that the decision maker has a fuzzy goal for each objective function, and such a fuzzy goal can be quantified by eliciting the membership function. Through the possibility measure and a fractile optimization model, the original problem is transformed to the well-defined multiobjective programming problem. Then, a generalized Pareto optimal concept is defined, and a linear programming based interactive algorithm is proposed to obtain a satisfactory solution from among a generalized Pareto optimal solution set.