In this work we consider a Transportation Location Routing Problem (TLRP) that can be seen as an extension of the two stage Location Routing Problem, in which the first stage corresponds to a transportation problem wi...
详细信息
In this work we consider a Transportation Location Routing Problem (TLRP) that can be seen as an extension of the two stage Location Routing Problem, in which the first stage corresponds to a transportation problem with truck capacity. Two objectives are considered in this research, reduction of distribution cost and balance of workloads for drivers in the routing stage. Here, we present a mathematical formulation for the bi-objective TLRP and propose a new representation for the TLRP based on priorities. This representation lets us manage the problem easily and reduces the computational effort, plus, it is suitable to be used with both local search based and evolutionary approaches. In order to demonstrate its efficiency, it was implemented in two metaheuristic solution algorithms based on the Scatter Tabu Search Procedure for Non-Linear Multiobjective Optimization (SSPMO) and on the Non-dominated Sorting Genetic Algorithm II (NSGA-II) strategies. Computational experiments showed efficient results in solution quality and computing time. (C) 2013 Elsevier B.V. All rights reserved.
Until now, in the literature, little attention has been paid to the storage and handling of populations of multiobjective evolutionary algorithms (MOEAs). In this work, we present a new tool for representing and manag...
详细信息
Until now, in the literature, little attention has been paid to the storage and handling of populations of multiobjective evolutionary algorithms (MOEAs). In this work, we present a new tool for representing and managing populations of MOEAs by means of the use of graphs that keep the information on the relations among the individuals of the population. In the paper, we establish the theoretical basis of this sort of graph. In addition, we develop algorithms for its construction and updating (addition and removal of individuals in the population), analyzing their theoretical complexities. We also study several aspects of their practical behaviour including storage requirements, time needed for the construction and the management of these graphs. Finally, we present a selection process time comparison with and without the proposed methodology. (C) 2003 Elsevier B.V. All rights reserved.
This paper investigates multi-objective solid transportation problems (MOSTP) under various uncertain environments. The unit transportation penalties/costs are taken as random, fuzzy and hybrid variables respectively,...
详细信息
This paper investigates multi-objective solid transportation problems (MOSTP) under various uncertain environments. The unit transportation penalties/costs are taken as random, fuzzy and hybrid variables respectively, in three different uncertain multi-objective solid transportation models and in each case, the supplies, demands and conveyance capacities are fuzzy. Also, apart from source, demand and capacity constraints, an extra constraint on the total budget at each destination is imposed. Chance-constrained programming technique has been used for the first two models to obtain crisp equivalent forms, whereas expected value model is formulated for the last. We provide an another approach using the interval approximation of fuzzy numbers for the first model to obtain its crisp form and compare numerically two approaches for this model. Fuzzy programming technique and a gradient based optimisation - generalised reduced gradient (GRG) method are applied to beget the optimal solutions. Three numerical examples are provided to illustrate the models and programming.
In this paper, we are interested in producing discrete and tractable representations of the set of non dominated points for multi-objective optimization problems, both in the continuous and discrete cases. These repre...
详细信息
In this paper, we are interested in producing discrete and tractable representations of the set of non dominated points for multi-objective optimization problems, both in the continuous and discrete cases. These representations must satisfy some conditions of coverage, i.e. providing a good approximation of the non-dominated set, spacing, i.e. without redundancies, and cardinality, i.e. with the smallest possible number of points. This leads us to introduce the new concept of (epsilon, epsilon')-kernels, or epsilon-kernels when epsilon' = epsilon is possible, which correspond to epsilon=Pareto sets satisfying an additional. condition, of epsilon'-stability. Among these, the kernels of small, or possibly optimal, cardinality are claimed to be good representations of the non-dominated set. We first establish some general properties on epsilon-kernels. Then, for the bi-objective case, we propose some generic algorithms computing in polynomial time either an epsilon-kernel of small size or, for a fixed size k, an epsilon-kernel with a nearly optimal approximation ratio 1 + epsilon. For more than two objectives, we show that epsilon-kernels do not necessarily exist but that (epsilon, epsilon' )-kernels with epsilon' <= root 1 + epsilon-1 always exist. Nevertheless, we show that the size of a smallest (epsilon, epsilon')-kernel can be very far from the size of a smallest epsilon-Pareto set. (C) 2016 Published by Elsevier B.V.
Natural grasslands provide important land resources in pastoral areas, and greatly contribute to ecological functioning. Overgrazing and other unreasonable exploitations have led to the degradation and desertification...
详细信息
Natural grasslands provide important land resources in pastoral areas, and greatly contribute to ecological functioning. Overgrazing and other unreasonable exploitations have led to the degradation and desertification of natural grasslands, exacerbating the forage-livestock imbalance. In areas suffering from water shortage, this imbalance gradually evolves into a water-land forage-livestock imbalance. In this study, a water-land forage-livestock balance-based model was developed to optimise the allocation of water, land, and forage resources in pastoral areas, while addressing economic and ecological benefits in a coupled manner. The model was applied in a case study of Otog Front Banner to simulate the comprehensive economic and ecological benefits to the development of water, land, and forage resources in different coupled allocations of artificial and natural grasslands. The results showed that as the duration of supplementary and barn feeding increased, local development was first constrained by the availability of natural grasslands and then by the availability of water resources. The optimal resource allocation in Otog Front Banner predicted for 2030 included a water consumption of 266,000,000 m(3), an irrigation area of 43,000 ha, a natural grassland utilisation area of 684,700 ha, and a livestock farming scale of 1,188,500 sheep units.
The lack of discrimination power and the inappropriate multipliers schemes remain major issues in data envelopment analysis (DEA). To overcome these problems, the multiple criteria DEA (MCDEA) model was introduced in ...
详细信息
The lack of discrimination power and the inappropriate multipliers schemes remain major issues in data envelopment analysis (DEA). To overcome these problems, the multiple criteria DEA (MCDEA) model was introduced in the late 1990s, drawing from a multipleobjective perspective. However, because the objectives of the MCDEA model are generally conflicting, an optimal solution satisfying all objectives simultaneously often does not exist. Within this context, goal programming (GP) approaches were proposed to solve the MCDEA model. This paper focuses specifically on the GP formulation, known as GPDEA. However, recently, the GPDEA models were found to be invalid, and no alternative formulation, under a GP framework, was proposed. Therefore, the aim here is to develop a formulation for adequately solving the MCDEA model using weighted GP. In order to do so, we point out inconsistencies in the existing GPDEA models, and we present the WGP-MCDEA model. (C) 2016 Elsevier B.V. All rights reserved.
This paper suggests an iterative parametric approach for solving multiobjective linear fractional programming (MOLFP) problems which only uses linear programming to obtain efficient solutions and always converges to a...
详细信息
This paper suggests an iterative parametric approach for solving multiobjective linear fractional programming (MOLFP) problems which only uses linear programming to obtain efficient solutions and always converges to an efficient solution. A numerical example shows that this approach performs better than some existing algorithms. Randomly generated MOLFP problems are also solved to demonstrate the performance of new introduced algorithm. (C) 2013 Elsevier Inc. All rights reserved.
In the maritime industry, the stakeholders comprising the port authorities, shipping companies, and port operators often compete and collaborate within an ecological system. This paper investigates the competition and...
详细信息
In the maritime industry, the stakeholders comprising the port authorities, shipping companies, and port operators often compete and collaborate within an ecological system. This paper investigates the competition and cooperation strategies amongst three parties: two major container hub ports and the shipping companies. This research develops a game theoretic network design model which considers three scenarios: (i) perfect competition between the hub ports, (ii) perfect cooperation between the hub ports, and (iii) cooperation between the shipping companies and the hub ports as a whole. The scenarios are tested using empirical data from two leading Asian hub ports: Singapore and Hong Kong. An interval branch and bound is designed to solve the models. Crown Copyright (C) 2012 Published by Elsevier Ltd. All rights reserved.
We develop a multi-objective model for resource allocation problem in PERT networks with exponentially or Erlang distributed activity durations, where the mean duration of each activity is a non-increasing function an...
详细信息
We develop a multi-objective model for resource allocation problem in PERT networks with exponentially or Erlang distributed activity durations, where the mean duration of each activity is a non-increasing function and the direct cost of each activity is a non-decreasing function of the amount of resource allocated to it. The decision variables of the model are the allocated resource quantities. The problem is formulated as a multi-objective optimal control problem that involves four conflicting objective functions. The objective functions are the total direct costs of the project (to be minimized), the mean of project completion time (min), the variance of project completion time (min), and the probability that the project completion time does not exceed a certain threshold (max). The surrogate worth trade-off method is used to solve a discrete-time approximation of the original problem. (c) 2005 Elsevier B.V. All rights reserved.
Development of microwave components is an inherently multi-objective task. This is especially pertinent to the design closure stage, i.e., final adjustment of geometry and/or material parameters carried out to improve...
详细信息
Development of microwave components is an inherently multi-objective task. This is especially pertinent to the design closure stage, i.e., final adjustment of geometry and/or material parameters carried out to improve the electrical performance of the system. The design goals are often conflicting so that the improvement of one normally leads to a degradation of others. Compact microwave passives constitute a representative case: reduction of the circuit footprint area is detrimental to electrical figures of merit (e.g., the operating bandwidth). Identification of the best available trade-off designs requires multiobjective optimization (MO). This is a computationally expensive task, especially when executed at the level of full-wave electromagnetic (EM) simulation. The computational complexity issue can be mitigated through the employment of surrogate modeling methods, yet their application is limited by a typically high nonlinearity of system responses, and the curse of dimensionality. In this paper, a novel technique for fast MO of compact microwave components is proposed, which allows for sequential rendition of the trade-off designs using triangulation of the already available Pareto front as well as rapid refinement algorithms. Our methodology is purely deterministic;in particular, it does not rely on population-based nature-inspired procedures. The three major benefits are low computational cost, possibility of handling explicit design constraints, and a capability of producing a visually uniform representation of the Pareto front. The algorithm is demonstrated using a compact branch-line coupler and a three-section impedance matching transformer. In both cases, considerable savings are obtained over the benchmark, here, the state-of-the-art surrogate-assisted MO technique.
暂无评论