Set Of Efficient Solutions Research Articles

A novel multi-objective scenario-based optimization model for sustainable reverse logistics supply chain network redesign considering facility reconstruction

With the increase of concern from environmental pollution and waste of resources, manufacturing firms have realized that the recovery of used products becomes an environment-friendly way to support sustainable development. However, many enterprises face a problem that is how to implement the recovery of used products into their existing forward logistics networks. In this case, it is necessary to redesign a novel sustainable reverse logistics supply chain network by reconstructing the existing facilities into hybrid processing facilities. To handle the foregoing problem, a multi-objective scenario-based optimization model is proposed. It aims to maximize the expected total monetary profits, minimize the expected total carbon emission costs, and maximize the expected total created job opportunities. To solve the proposed model, we develop a method to linearize the model and then apply the weighted-sum method to reformulate it as a single-objective one. In addition to the weighted-sum method, an augmented E-constraint method is used to obtain a set of efficient Pareto-optimal solutions and the trade-off among three conflicting objectives is presented. Finally, several numerical instances from a tire supply chain are performed to validate the proposed model and some managerial implications are also concluded.

A monotonic optimization approach for solving strictly quasiconvex multiobjective programming problems

In this article, we use the monotonic optimization approach to propose an outcome-space outer approximation by copolyblocks for solving strictly quasiconvex multiobjective programming problems and especially in the case that the objective functions are nonlinear fractional. After the algorithm is terminated, with any given tolerance, we obtain an approximation of the weakly efficient solution set, that contains the whole weakly efficient solution set of the problem. The algorithm is proved to be convergent and it is suitable to be implemented in parallel using standard convex programming tools. Some computational experiments are reported to show the accuracy and efficiency of the proposed algorithm.

An improved algorithm to compute the $$\omega $$-primality

In this paper, we present an improved methodology to compute the $$\omega $$ -primality of a numerical semigroup. The approach is based on exploiting the structure of the problem on a resolution method for optimizing a linear function over the set of efficient solutions of a multiple objective integer linear programming problem. The numerical experiments show the efficiency of the proposed technique compared to the existing methods.

Multiobjective particle swarm community discovery arithmetic based on representation learning

SummaryWith the continuous increase of the network scale, the structure of the network has also become complicated. The original community discovery algorithm based on small‐scale static networks has been unable to meet our needs. In order to improve the quality of community division, community discovery algorithms based on multiple optimization functions have been proposed. These multiobjective algorithms have continued to increase in time complexity as the optimization functions increase. The time complexity of the multiobjective community discovery algorithm is reduced, and the particle swarm algorithm has higher efficiency and accuracy in solving multiobjective optimization (MOO) problems. Based on the above background, the purpose of this article is to study a multiobjective particle swarm community discovery algorithm based on representation learning. This article uses the network representation learning method for static network community discovery, and designs an improved multiobjective particle swarm‐based community discovery algorithm (MOPSO‐CD). This randomness effectively prevents the algorithm from falling into a local optimum. At the same time, combined with the MOO algorithm, all the Pareto optimal solution sets are retained to adjust the population to correct the lack of accuracy caused by the randomness of the algorithm. In addition, in order to improve the efficiency of the algorithm, this article introduces an efficient Pareto optimal solution set method. Compared with the traditional MOO strategy, the time complexity of the MOO process is O(n2) Reduced to O(nlogn). Through experimental analysis, MOPSO‐CD has higher efficiency and community discovery quality.

Generalisation of A-equitable preference in multiobjective optimisation problems

The concept of A-equitable efficiency in solving the multiobjective optimisation problems have recently been introduced by Mut and Wiecek [Generalised equitable preference in multiobjective programming. Euro J Oper Res. 2011;212:535–551], where A is an arbitrary matrix with non-negative entries. The preference relation of this concept solution, , does not satisfy the strict monotonicity and strict principle of transfers axioms in general, therefore the set of A-equitably efficient solutions is not contained within the set of equitably efficient solutions and the set of Pareto-optimal solutions for the same problem. In this paper, we extend the work done by Mut and Wiecek and state the new conditions on the matrix A that guarantee to satisfy these axioms by the preference relation . The other contribution of this paper is the use of the preference relation to solve the multio objective optimisation problems instead of . This has the advantage that the decision-maker has more freedom to choose the preferences matrix A. The relation has become an equitable rational preference relation by imposing the weaker conditions on entries of A, in comparison to the relation .

Two-phase algorithm for solving the preference-based multicriteria optimal path problem with reference points

The shortest path problem arises in several contexts like transportation, telecommunication or data analysis. New requirements in solving practical problems (e.g., efficient content delivery for information-centric networks, urban passenger transport system or social network) impose that more than one criterion should be considered. Since the objectives are in conflict, the solution is not unique, rather a set of (efficient) paths is defined as optimal. The most satisfactory path should be selected considering additional preference information. Generally, computing the entire set of efficient solutions is time consuming. In this paper, we apply the reference point method for finding the best path. In a reference point-based approach, non-additive scalarizing function is applied. In this case, the classical optimality principle for the shortest path problem is not valid. To overcome this issue, we propose an equivalent formulation dealing with the constrained shortest path (CSP) problem. The idea is to define a set of constraints guaranteeing that an optimal solution to the problem at hand lies in the feasible region of the defined CSP problem. We propose a two-phase method where, in the first phase, a bound on the optimal solution is computed and used to define the constraints, whereas, in the second phase a labelling algorithm is applied to search for an optimal solution to the defined CSP problem. The method is tested on instances generated from random and grid networks, considering several scenarios. The computational results show that, on average, the proposed solution strategy is competitive with the state-of-the-art approaches and behaves the best on grid networks.

New results on proper efficiency for a class of vector optimization problems

ABSTRACT This paper presents two new theorems on Geoffrion's properly efficient solutions and seven examples illustrating their applications to linear fractional vector optimization problems with unbounded constraint sets. Provided that all the components of the objective function are properly fractional, the first theorem gives sufficient conditions for the efficient solution set to coincide with the Geoffrion properly efficient solution set. Admitting that the objective function can have some affine components, in the second theorem we give sufficient conditions for an efficient solution to be a Geoffrion's properly efficient solution. The recession cone of the constraint set, the derivatives of the scalar objective functions, but no tangent cone to the constraint set at the efficient point, are used in the second theorem.

Multiobjective pseudo‐variable neighborhood descent for a bicriteria parallel machine scheduling problem with setup time

AbstractA multiobjective variable neighborhood descent (VND) based heuristic is developed to solve a bicriteria parallel machine scheduling problem. The problem considers two objectives, one related to the makespan and the other to the flow time, where the setup time depends on the sequence, and the machines are identical. The heuristic has a set of neighborhood structures based on swap, remove, and insertion moves. We propose changing the local search inside the VND to a sequential search through the neighborhoods to obtain nondominated points for the Pareto‐front quickly. In the numerical tests, we consider a single‐objective version of the heuristic, comparing the results on 510 benchmark instances to show that it is quite effective. Moreover, new instances are generated in accordance with the literature for the bicriteria problem, showing the ability of the proposed heuristic to return an efficient set of nondominate solutions compared with the well‐known nondominated sorting genetic algorithm II.

Designing a sustainable integrated forward/reverse logistics network

Purpose In recent years, governmental regulations and the pressure of non-governmental organizations have convinced corporations to consider sustainable issues in their decisions. A simultaneous design of forward and reverse logistics can keep us away from sub-optimality caused by tackling these two phases (forward and reverse logistics) separately. Design/methodology/approach Hence, this paper presents a new multi-objective mathematical model for integrated forward and reverse logistics regarding economic, environmental and social issues. A new hybrid multi-objective metaheuristic algorithm is developed to obtain a set of efficient solutions (Pareto solutions). The proposed algorithm hybridizes a well-known, non-dominated genetic algorithm (NSGA-II) with a simulated annealing algorithm. Findings To validate the algorithm, its results are compared to the obtained solutions from simple NSGA-II with respect to some comparison metrics. The numerical results show the efficiency of the proposed algorithm. Finally, concluding remarks and future research directions are provided. Originality/value By applying a model presented in this paper, one can reach to sustainable and integrated logistics network which considers forward and reverse flow of commodities simultaneously.

Connectedness and Path Connectedness of Weak Efficient Solution Sets of Vector Optimization Problems via Nonlinear Scalarization Methods

The connectedness and path connectedness of the solution sets to vector optimization problems is an important and interesting study in optimization theories and applications. Most papers involving the direction established the connectedness and connectedness for the solution sets of vector optimization problems or vector equilibrium problems by means of the linear scalarization method rather than the nonlinear scalarization method. The aim of the paper is to deal with the connectedness and the path connectedness for the weak efficient solution set to a vector optimization problem by using the nonlinear scalarization method. Firstly, the union relationship between the weak efficient solution set to the vector optimization problem and the solution sets to a series of parametric scalar minimization problems, is established. Then, some properties of the solution sets of scalar minimization problems are investigated. Finally, by using the union relationship, the connectedness and the path connectedness for the weak efficient solution set of the vector optimization problem are obtained.

A New Exact Algorithm to Optimize a Linear Function over the Set of Efficient Solutions for Biobjective Mixed Integer Linear Programs

We present the first (criterion space search) algorithm for optimizing a linear function over the set of efficient solutions of biobjective mixed integer linear programs. The proposed algorithm is developed based on the triangle splitting method [Boland N, Charkhgard H, Savelsbergh M (2015) A criterion space search algorithm for biobjective mixed integer programming: The triangle splitting method. INFORMS J. Comput. 27(4):597–618.], which can find a full representation of the nondominated frontier of any biobjective mixed integer linear program. The proposed algorithm is easy to implement and converges quickly to an optimal solution. An extensive computational study shows the efficacy of the algorithm. We numerically show that the proposed algorithm can be used to quickly generate a provably high-quality approximate solution because it maintains a lower and an upper bound on the optimal value of the linear function at any point in time.

Multiobjective Quadratic Fractional Programming using Iterative Parametric Function

The paper proposed the Model of multiobjective quadratic fractional optimisation problem with a set of quadratic constraints and a methodology for obtaining a set of solutions based on the approach of using iterative parametric functions. Firstly, each fractional objective function is transformed into non-fractional parametric objective function by assigning a vector of parameters to each objective function. In this approach, the Decision Maker(DM) predecides the desired tolerance levels of the objective functions in the form of termination constants. Then, by using ε-constraint method, a set of efficient solutions is obtained and termination conditions are checked for each parametric objective function. Also, a comparative study of the proposed method and fuzzy approach is given to reveal the validity of the method. A numerical for Multiobjective quadratic fractional programming Model (MOQFPM) is given in the end to check the applicability of the approach.

Life cycle cost reduction and market acceleration for new nearly zero-energy buildings

Cost optimal and nearly zero-energy performance levels are principles initiated by the European Union’s Energy Performance of Buildings Directive, which was recast in 2010. These will be significant drivers in the construction sector in the next few years because all new buildings in the EU from 2021 onwards have to be nearly zero energy buildings (nZEBs); public buildings need to achieve the standard already by 2019 [1].While nZEBs realised so far have clearly shown that the nearly zero-energy target can be achieved using existing technologies and practices, most experts agree that a broad-scale shift towards nearly zero-energy buildings requires significant adjustments to current building market structures. Cost-effective integration of efficient solution sets and renewable energy systems are the major challenges [2]. The EU Horizon project CRAVEzero focuses on proven and new approaches to reduce the costs of nZEBs at all stages of the life cycle. The primary goal is to identify and eliminate the extra costs for nZEBs related to processes, technologies, building operation and to promote innovative business models considering the cost-effectiveness for all stakeholders in the building’s lifecycle. As a result, an international database for benchmarking actual nZEB life cycle costs (LCC) including urban and building planning, construction, commissioning, operation, maintenance, management, end-of-life, has been developed. Furthermore, an operative methodology to achieve the best conditions towards optimal cost nZEBs has been set-up.

On single-source capacitated facility location with cost and fairness objectives

We consider a location problem where a planner has to decide where to open facilities which have to be reached by customers at their own cost. The planner has two objectives: cost minimization and customer satisfaction. We argue that performance and fairness, as structural components of customer satisfaction, are both captured by an equity measure called conditional β-mean. We thus formulate the Fair Single-Source Capacitated Facility Location (F-SSCFL) problem, where the cost minimization objective is paired with the conditional β-mean minimization objective. The resulting formulation is a bi-objective mixed-integer linear program. A weighted sum method is developed to generate a small representative set of efficient solutions to the F-SSCFL problem, and a Benders decomposition approach is implemented to handle large-scale instances. On small/medium-scale instances, we analyse the trade-off between cost and conditional β-mean, showing that the model may be used as a managerial tool to balance direct costs and customer service. We also compare the quality of the solutions obtained with those obtained using alternative equity measures. On large-scale instances, we test Benders decomposition, showing that it is able to find good quality solutions in a relatively short computing time.

ε-Constraint method for bi-objective competitive facility location problem with uncertain demand scenario

We consider a model of two parties’ competition organized as a Stackelberg game. The parties open their facilities intending to maximize profit from serving the customers that behave following a binary rule. The set of customers is unknown to the party which opens its facilities first and is called the Leader. Instead, a finite list of possible scenarios specifying this set is provided to the Leader. One of the scenarios is to be realized in the future before the second party, called the Follower, would make their own decision. The scenarios are supplied with known probabilities of realization, and the Leader aims to maximize both the probability to get a profit not less than a specific value, called a guaranteed profit, and the value of a guaranteed profit itself. We formulate the Leader’s problem as a bi-objective bi-level mathematical program. To approximate the set of efficient solutions of this problem, we develop an ε -constraint method where a branch-and-bound algorithm solves a sequence of bi-level problems with a single objective. Based on the properties of feasible solutions of a bi-level program and mathematical programming techniques, we developed three upper bound procedures for the branch-and-bound method mentioned. In numerical experiments, we compare these procedures with each other. Besides that, we discuss relations of the model under investigation and the stochastic competitive location model with uncertain profit values.

Toward an Efficient Resolution for a Single-machine Bi-objective Scheduling Problem with Rejection

Abstract We consider a single-machine bi-objective scheduling problem with rejection. In this problem, it is possible to reject some jobs. Four algorithms are provided to solve this scheduling problem. The two objectives are the total weighted completion time and the total rejection cost. The aim is to determine the set of efficient solutions. Four heuristics are described; they are implicit enumeration algorithms forming a branching tree, each one having two versions according to the root of the tree corresponding either to acceptance or rejection of all the jobs. The algorithms are first illustrated by a didactic example. Then they are compared on a large set of instances of various dimension and their respective performances are analysed.

A novel algorithm for solving bi-objective fractional transportation problems with fuzzy numbers

A new method is proposed for finding a set of efficient solutions to bi-objective fractional transportation problems with fuzzy numbers using ranking function. This method is an important tool for the decision makers to obtain efficient solutions and select the preferred optimal solution from the satisfaction level. The procedure allows the user to identify next efficient solution to the problem from the current efficient solution. This new approach enables the decision makers to evaluate the economic activities and make satisfactory managerial decisions when they are handling a variety of logistic problems involving two objectives. An illustrative example is presented to clarify the idea of the proposed approach.

Flexible multi-manned assembly line balancing problem: Model, heuristic procedure, and lower bounds for line length minimization

Assembly lines dedicated to the production of large products often allow multiple workers to perform tasks simultaneously on the product. Previous works on such multi-manned lines define workstations with fixed, discrete, and restrictive frontiers, despite commonly considering continuous paced line control. This paper proposes flexible station frontiers for multi-manned lines and shows that such innovation allows significantly shorter line lengths. A new Mixed Integer Linear Programming model and a novel model-based heuristic procedure are presented to describe and optimize lines. Algorithmic lower bounds are also introduced for the problem. The formulation was compared to a literature benchmark of regular multi-manned solutions. These experiments showed that flexible multi-manned formulations can lead to line length reductions of up to 42%. Such reductions were obtained for most instances (81 out of 88), with an average value of 18%. The relationship between cycle time and minimal line length is also analyzed, demonstrating that efficient solution sets can be continuous or discrete, depending on the instance.

Evaluation and development of sustainable urban land use plans through spatial optimization

AbstractAlong with rapid global urbanization, cities are challenged by environmental risks and resource scarcity. Sustainable urban planning is central to address the dilemma of economic growth and ecosystem protection, where the use of land is critical. Sustainable land use patterns are spatially explicit in nature, and can be structured and addressed using spatial optimization integrating GIS and mathematical models. This research discusses prominent sustainability concerns in land use planning and suggests a generalized multi‐objective spatial optimization model to facilitate conventional planning. The model is structured to meet land use demand while satisfying the requirements of the physical environment, society and economy. Unlike existing work relying on raster data, due to its simple data structure and ease of spatial relationship evaluation, this research develops an approach for identifying land use solutions based on vector data that better reflects the actual shape and spatial layout of land parcels as well as the ways land use information is managed in practice. An evolutionary algorithm is developed to find the set of efficient (Pareto) solutions given the complexity of vector‐based representations of space. The proposed approach is applied in an empirical study of Dafeng, China in order to support local urban growth and development. The results demonstrate that spatial optimization can be a powerful tool for deriving effective and efficient land use planning strategies. A comparison to results using a raster data approach supports the superiority of land use optimization using vector data as part of planning practice.

A Network Approach to Public Goods

Suppose that agents can exert costly effort that creates nonrival, heterogeneous benefits for each other. At each possible outcome, a weighted, directed network describing marginal externalities is defined. We show that Pareto efficient outcomes are those at which the largest eigenvalue of the network is 1. An important set of efficient solutions—Lindahl outcomes—are characterized by contributions being proportional to agents’ eigenvector centralities in the network. The outcomes we focus on are motivated by negotiations. We apply the results to identify who is essential for Pareto improvements, how to efficiently subdivide negotiations, and whom to optimally add to a team.