Pareto Efficient Solutions Research Articles

Multi-objective optimization of waste and resource management in industrial networks – Part I: Model description

This article presents a general multi-objective mixed-integer linear programming (MILP) optimization model aimed at providing decision support for waste and resources management in industrial networks. The MILP model combines material flow analysis, process models of waste treatments and other industrial processes, life cycle assessment, and mathematical optimization techniques within a unified framework. The optimization is based on a simplified representation of industrial networks that makes use of linear process models to describe the flows of mass and energy. Waste-specific characteristics, e.g. heating value or heavy metal contamination, are considered explicitly along with potential technologies or process configurations. The systems perspective, including both provision of waste treatment and industrial production, enables constraints imposed upon the systems, e.g. available treatment capacities, to be explicitly considered in the model. The model output is a set of alternative system configurations in terms of distribution of waste and resources that optimize environmental and economic performance. The MILP also enables quantification of the improvement potential compared to a given reference state. Trade-offs between conflicting objectives are identified through the generation of a set of Pareto-efficient solutions. This information supports the decision making process by revealing the quantified performance of the efficient trade-offs without relying on weighting being expressed prior to the analysis. Key features of the modeling approach are illustrated in a hypothetical case. The optimization model described in this article is applied in a subsequent paper (Part II) to assess and optimize the thermal treatment of sewage sludge in a region in Switzerland.

Population Dynamics and Regional Social Security Sustainability in Italy

Bonasia M. and De Siano R. Population dynamics and regional social security sustainability in Italy, Regional Studies. Making due allowances for differences in demographics, the labour market and internal migration dynamics, this study analyses the sustainability of the Italian pension balance at a regional level. A worsening of the elderly dependency ratio and a decline in birth and employment rates have generated a negative trend, particularly for regions in southern Italy, characterized by early retirement and an increase in migration outflows. The suggestion is that a decentralized pension policy is not a Pareto-efficient solution because it would favour the sustainability of the pension balance in northern regions over those in the South.

A new approach for uncertain multiobjective programming problem based on $\mathcal{P}_{E}$ principle

On the basis of the uncertainty theory, this paper is devoted to the uncertain multiobjective programming problem. Firstly, several principles are provided to define the relationship between uncertain variables. Then a new approach is proposed for obtaining Pareto efficient solutions in uncertain multiobjective programming problem based on $\mathcal{P}_{E}$ principle, which involves transforming the uncertain multiobjective problem into a problem with only one uncertain objective function, and its validity has been proved. Due to the complexity of this problem, it is very suitable for the use of genetic algorithm. Finally, a numerical example is presented to illustrate the novel approach proposed, and the genetic algorithm is adopted to solve it.

Strict vector variational inequalities and strict Pareto efficiency in nonconvex vector optimization

In this paper, we consider a vector optimization problem involving the difference of two cone convex functions in Banach spaces. In terms of Clarke subdifferential, we formulate strict Minty vector variational inequality problem and strict Stampacchia vector variational inequality problem. We mainly study the relationships between the solutions of these vector variational inequality problems and the strict Pareto efficient solution of the vector optimization problem.

Variable and large neighborhood search to solve the multiobjective set covering problem

In this paper, we study the multiobjective version of the set covering problem. To our knowledge, this problem has only been addressed in two papers before, and with two objectives and heuristic methods. We propose a new heuristic, based on the two-phase Pareto local search, with the aim of generating a good approximation of the Pareto efficient solutions. In the first phase of this method, the supported efficient solutions or a good approximation of these solutions is generated. Then, a neighborhood embedded in the Pareto local search is applied to generate non-supported efficient solutions. In order to get high quality results, two elaborate local search techniques are considered: a large neighborhood search and a variable neighborhood search. We intensively study the parameters of these two techniques. We compare our results with state-of-the-art results and we show that with our method, better results are obtained for different indicators.

A Penalty Function Algorithm with Objective Parameters and Constraint Penalty Parameter for Multi-Objective Programming

In this paper, we present an algorithm to solve the inequality constrained multi-objective programming (MP) by using a penalty function with objective parameters and constraint penalty parameter. First, the penalty function with objective parameters and constraint penalty parameter for MP and the corresponding unconstraint penalty optimization problem (UPOP) is defined. Under some conditions, a Pareto efficient solution (or a weakly-efficient solution) to UPOP is proved to be a Pareto efficient solution (or a weakly-efficient solution) to MP. The penalty function is proved to be exact under a stable condition. Then, we design an algorithm to solve MP and prove its convergence. Finally, numerical examples show that the algorithm may help decision makers to find a satisfactory solution to MP.

Parallel genetic algorithm with fading selection

This work presents a novel approach to designing the parallel genetic algorithm (GA) with fading selection for the solving of the problem of the shareholder value maximisation of an oil company. The algorithm based on the dynamical interaction of synchronised processes, which are interdependent GAs having own separate evolutions of their populations. The developed system allows users to find a set of non-dominated investment projects (Pareto-efficient solutions), allowing to pick a particular solution in accordance with their utility function.

The Application of Stochastic Order to Stochastic Multiobjective Programming Problems

This paper is devoted to the application of stochastic order to the with stochastic multiobjective programming problem. A new method, called stochastic approach, is originally presented based on stochastic order. The partial Pareto efficient solution is defined first, and then several types of stochastic order from the viewpoint of practical problems are proposed. The results obtained can provide theoretical basis for dealing with the stochastic problems in field of civil engineering and transportation.

Problems to Reselect Optimization to Pareto efficient solution for Linear Multi-objective Decision-making

Problems to Reselect Optimization to Pareto efficient solution for Linear Multi-objective Decision-making

Towards a multi-objective performance assessment and optimization model of a two-echelon supply chain using SCOR metrics

This paper aims at multi-objective performance assessment and optimization of a multi-period two-echelon supply chain consisting of a supplier and a manufacturer. On the basis of the assessment system of the supply-chain operations reference model, the supply chain’s performance is investigated with respect to costs, assets, agility, reliability and responsiveness. First, methods to quantify these five performance attributes are put forward. Then a multi-objective mathematical programming model is developed for production decision making of components and products so that the supply chain’s performance frontier formed with Pareto efficient performance values can be achieved. Thereafter a simple augmented $$\epsilon $$ -constraint method is proposed for searching for all Pareto efficient solutions of the multi-objective mathematical programming problem. Finally, efficiency of the method is demonstrated with a numerical example and a sensitivity analysis is implemented to reveal effects of capacity expansion on supply chains’ performance.

Problems with resource allocation constraints and optimization over the efficient set

The paper studies a nonlinear optimization problem under resource allocation constraints. Using quasi-gradient duality it is shown that the feasible set of the problem is a singleton (in the case of a single resource) or the set of Pareto efficient solutions of an associated vector maximization problem (in the case of $$k>1$$ resources). As a result, a nonlinear optimization problem under resource allocation constraints reduces to an optimization over the efficient set. The latter problem can further be converted into a quasiconvex maximization over a compact convex subset of $$\mathbb{R }^k_+.$$ Alternatively, it can be approached as a bilevel program and converted into a monotonic optimization problem in $$\mathbb{R }^k_+.$$ In either approach the converted problem falls into a common class of global optimization problems for which several practical solution methods exist when the number $$k$$ of resources is relatively small, as it often occurs.

The output estimation of a DMU to preserve and improvement of the relative efficiency

In this paper, we consider the inverse BCC model is used to estimate output levels of the Decision Making Units (DMUs), when the input levels are changed and maintain the efficiency index for all DMUs. Since the inverse BCC problem is in the form of a multi objective nonlinear programming model (MONLP), which is not easy to solve. Therefore, we propose a linear programming model, which gives a Pareto-efficient solution to the inverse BCC problem. So far, we propose a model for improvement of the current efficiency value for considered DMU. Numerical examples are, also, used to illustrate the proposed approaches.

Seller – Buyer Supply Chain Games Where Shortage Are Permitted

In the area of seller-buyer supply chain management, researchers have been very active in seeking optimal policies for both players to achieve a favorable outcome. Most studies are based on somewhat unrealistic assumptions such as deterministic demand and unpermitted shortages. In reality, due to factors such as irregular production capacity or unanticipated demands, shortages will occur, and it will influence both players’ decisions. In this paper, we include shortage as a decision variable determined by the seller, and demand is assumed sensitive to both selling price and marketing expenditure. The interaction between seller and buyer will be investigated as non-cooperative Stackelberg game, and the cooperation between seller and buyer will be explored based on Pareto-efficient solution concept. Consequences of the non–cooperative and cooperative aspects of these games will be compared and finally, numerical examples and sensitivity analysis will be presented to compare between models with and without shortages.

A comparison of representations for discrete multi-criteria decision problems

Discrete multi-criteria decision problems with numerous Pareto-efficient solution candidates place a significant cognitive burden on the decision maker. An interactive, aspiration-based search process that iteratively progresses toward the most preferred solution can alleviate this task. In this paper, we study three ways of representing such problems in a DSS, and compare them in a laboratory experiment using subjective and objective measures of the decision process as well as solution quality and problem understanding. In addition to an immediate user evaluation, we performed a re-evaluation several weeks later. Furthermore, we consider several levels of problem complexity and user characteristics. Results indicate that different problem representations have a considerable influence on search behavior, although long-term consistency appears to remain unaffected. We also found interesting discrepancies between subjective evaluations and objective measures. Conclusions from our experiments can help designers of DSS for large multi-criteria decision problems to fit problem representations to the goals of their system and the specific task at hand.

The impact of user heterogeneity on road franchising

A model is presented for analyzing Pareto-efficient build-operate-transfer toll road contracts. The formulation simultaneously allows maximizing social welfare and private profit when road users vary in their value-of-time (VOT). The failure rate and mean residual functions of the VOT distribution are used to characterize Pareto-efficient solutions. Service quality, measured in terms of the volume-to-capacity ratio, is shown to be better than, identical to, or lower than the socially optimal level depending on the curvature of the mean residual VOT function. The outcomes of various regulatory regimes are examined as well.

An Exact Method for Balancing Efficiency and Equity in the Liver Allocation Hierarchy

We study the problem of (re)designing the regional network by which cadaveric livers are allocated. Whereas prior research focused mainly on maximizing a measure of efficiency of the network that was based on aggregate patient survival, we explicitly account for the trade-off between efficiency and a measure of geographical equity in the allocation process. To this end, we extend earlier optimization models to incorporate both objectives and develop an exact branch-and-price approach to solve this problem, generalizing a solution approach studied for the case where only efficiency is taken into account. In addition, we propose an effective solution algorithm that approximates the (generally nonconcave) frontier of Pareto-efficient solutions with respect to the two objectives by simultaneously generating and successively improving upper and lower bounds on this frontier. We implement and test our approach on observed data and show that solutions significantly dominating the current configuration in both efficiency and equity can be found. Of course, other subjective criteria are needed to choose among the different Pareto-efficient candidate solutions.

Mediation with Incomplete Information: Approaches to Suggest Potential Agreements

In bilateral Negotiation Analysis, the literature often considers the case of complete information. In this context, since the negotiators know the value functions of both parties, it is not difficult to calculate the Pareto efficient solutions for the negotiation. Thus rational negotiators can reach agreement on this frontier. However, these approaches are not applied in practice when complete information is not available. The research question of our work is “It is possible to help negotiators achieving an efficient solution in the absence of complete information regarding the different parameters of the model?”. We propose to derive incomplete information about the preferences of negotiators from the statements they make and the offers they exchange during the negotiation process. We present and discuss three approaches that use this information in order to help a mediator proposing a better solution than the compromise the negotiators have reached or are close to reach.

Linking objective and subjective modeling in engineering design through arc-elastic dominance

Engineering design in mechanics is a complex activity taking into account both objective modeling processes derived from physical analysis and designers’ subjective reasoning. This paper introduces arc-elastic dominance as a suitable concept for ranking design solutions according to a combination of objective and subjective models. Objective models lead to the aggregation of information derived from physics, economics or eco-environmental analysis into a performance indicator. Subjective models result in a confidence indicator for the solutions’ feasibility. Arc-elastic dominant design solutions achieve an optimal compromise between gain in performance and degradation in confidence. Due to the definition of arc-elasticity, this compromise value is expressive and easy for designers to interpret despite the difference in the nature of the objective and subjective models. From the investigation of arc-elasticity mathematical properties, a filtering algorithm of Pareto-efficient solutions is proposed and illustrated through a design knowledge modeling framework. This framework notably takes into account Harrington’s desirability functions and Derringer’s aggregation method. It is carried out through the re-design of a geothermal air conditioning system.

Game Theoretic Approach for Global Manufacturing Planning Under Risk and Uncertainty

In this paper, we present a game theoretic model in which one manufacturer and its suppliers are coordinated. Quality levels of products from suppliers are considered. Due to fluctuation of demand resulting from varying quality levels, manufacturers are subject to demand-side risks. The objective of the research is to help decision making between manufacturers and suppliers in order to improve level of quality. Stackelberg game is applied to coordinate the manufacturer and suppliers Then, Pareto efficient solutions are utilized to generate supplier's optimal response functions. Computational experiments are conducted to demonstrate the effectiveness of the proposed method.

Multicriteria Steiner tree with the cost of Steiner vertices

The multicriteria problem of constructing the Steiner tree with consideration for the cost of additional Steiner vertices is studied. Formulations of the problems of constructing the covering Steiner trees and algorithmic approaches are described. The engineering formulation of the problem is aimed at constructing a telecommunications network with allowance for the spatial distribution of radio interferences. An approach to solving the formulated milticriterion problem on the basis of combination of two solving schemes is proposed: (1) the basic scheme for constructing a covering Steiner tree on the basis of clustering the vertices of the initial graph and (2) the general scheme for constructing the covering Steiner trees with allowance for the number of additional vertices and calculation of the Pareto-efficient solutions. A module based on the modified Prim’s algorithm for constructing a multicriteria covering tree is additionally used. The vertices of the initial graph are clustered on the basis of a hierarchical algorithm. Examples of a computational experiment on constructing the multicriteria Steiner trees are given.