The multi-facility location–allocation problem with polyhedral barriers

In this paper we consider the problem of locating N new facilities with respect to M existing facilities in the plane and in the presence of polyhedral barriers. We assume that a barrier is a region where neither facility location nor traveling is permitted. For the resulting multi-dimensional mixed-integer optimization problem two different alternate location and allocation procedures are developed. Numerical examples show the superiority of a joint treatment of all assignment variables, including those specifying the routes taken around the barrier polyhedra, over a separate iterative solution of the assignment problem and the single-facility location problems in the presence of barriers.     

Uncertain location–allocation decisions for a bi-objective two-stage supply chain network design problem with environmental impacts

In the cases that the historical data of an uncertain event is not available, belief degree-based uncertainty theory is a useful tool to reflect such uncertainty. This study focuses on uncertain bi-objective supply chain network design problem with cost and environmental impacts under uncertainty. As such network may be designed for the first time in a geographical region, this problem is modelled by the concepts of belief degree-based uncertainty theory. This article is almost the first study on belief degree-based uncertain supply chain network design problem with environmental impacts. Two approaches such as expected value model and chance-constrained model are applied to convert the proposed uncertain problem to its crisp form. The obtained crisp forms are solved by some multi-objective optimization approaches of the literature such as TH, Niroomand, MMNV. A deep computational study with several test problems are performed to study the performance of the crisp models and the solution approaches. According to the results, the obtained crisp formulations are highly sensitive to the changes in the value of the cost parameters. On the other hand, Niroomand and MMNV solution approaches perform better than other solution approaches from the solution quality point of view.     

FA–QABC–MRTA: a solution for solving the multi-robot task allocation problem

Intelligent Service Robotics - The problem of task allocation in a multi-robot system is the situation where we have a set of tasks and a number of robots; then each task is assigned to the...     

A multi-dimensional shooting algorithm for the two-facility location–allocation problem with dense demand

We develop an efficient allocation-based solution framework for a class of two-facility location–allocation problems with dense demand data. By formulating the problem as a multi-dimensional boundary value problem, we show that previous results for the discrete demand case can be extended to problems with highly dense demand data. Further, this approach can be generalized to non-convex allocation decisions. This formulation is illustrated for the Euclidean metric case by representing the affine bisector with two points. A specialized multi-dimensional shooting algorithm is presented and illustrated on an example. Comparisons with two alternative methods through a computational study confirm the efficiency of the proposed methodology.     

An integrated multi-objective Markowitz–DEA cross-efficiency model with fuzzy returns for portfolio selection problem

In this paper, a novel multi objective model is proposed for portfolio selection. The proposed model incorporates the DEA cross-efficiency into Markowitz mean–variance model and considers return, risk and efficiency of the portfolio. Also, in order to take uncertainty in proposed model, the asset returns are considered as trapezoidal fuzzy numbers. Due to the computational complication of the proposed model, the second version of non-dominated sorting genetic algorithm (NSGA-II) is applied. To illustrate the performance of our model, the model is implemented for 52 firms listed in stock exchange market of Iran and the results are analyzed. The results show that the proposed model is suitable in compared with Markowitz and DEA models due to considering return, risk and efficiency, simultaneously.     

A revised ant algorithm for solving location–allocation problem with risky demand in a multi-echelon supply chain network

This study addresses a capacitated facility location and task allocation problem of a multi-echelon supply chain against risky demands. Two and three-echelon networks are considered to maximize profit. The study represents the problem by a bi-level stochastic programming model. The revised ant algorithm proposed in the study improves the existing ant algorithm by using new design of heuristic desirability and efficient greedy heuristics to solve the problem. A set of computational experiments is reported to not only allow to fine-tune the parameters of the algorithm but also to evaluate its performance for solving the problem proposed. Experiments reveal that the proposed solution algorithm can reach 95–99% of the optimal solution against risky demands while consuming only 1000th of the computational time for large-sized problems as compared to an optimization-based tool.     

Discrete approximation heuristics for the capacitated continuous location–allocation problem with probabilistic customer locations

The capacitated continuous location–allocation problem, also called capacitated multisource Weber problem (CMWP), is concerned with locating m facilities in the Euclidean plane, and allocating their capacity to n customers at minimum total cost. The deterministic version of the problem, which assumes that customer locations and demands are known with certainty, is a nonconvex optimization problem. In this work, we focus on a probabilistic extension referred to as the probabilistic CMWP (PCMWP), and consider the situation in which customer locations are randomly distributed according to a bivariate probability distribution. We first formulate the discrete approximation of the problem as a mixed-integer linear programming model in which facilities can be located on a set of candidate points. Then we present three heuristics to solve the problem. Since optimal solutions cannot be found, we assess the performance of the heuristics using the results obtained by an alternate location–allocation heuristic that is originally developed for the deterministic version of the problem and tailored by us for the PCMWP. The new heuristics depend on the evaluation of the expected distances between facilities and customers, which is possible only for a few number of distance function and probability distribution combinations. We therefore propose approximation methods which make the heuristics applicable for any distance function and probability distribution of customer coordinates.     

Genotype–phenotype heuristic approaches for a cutting stock problem with circular patterns

The cutting stock problem has been studied in the context of different industrial applications inducing NP-hard problems in most instances. However, the application in sawmill has not received the same attention. In this paper, we deal with the problem of determining the number of logs to cut over a period of several days and the geometry of sawmill patterns in order to satisfy the demand while minimizing the loss of material. First, the problem is formulated as an integer programming problem of the form of a constrained set covering problem where the knowledge of a priori cutting patterns is necessary to generate its columns. In our implementation, these patterns are obtained using a genetic algorithm (GA) or a simulated annealing method (SA). Then, two different approaches are introduced to solve the problem. The first approach includes two methods that combine a metaheuristic to generate the number of logs and a constructive heuristic to generate the cutting patterns for each of the logs. In the second approach, we use an exact procedure CPLEX to solve the integer programming model where the cutting patterns are generated with the GA method (GA+CPLEX) or the SA method (SA+CPLEX). These four methods are compared numerically on 11 semi-randomly generated problems similar to those found in real life. The best results for the loss are obtained with the two-stage GA+CPLEX approach that finds the best values for 7 problems.     

Stochastic switching for partially observable dynamics and optimal asset allocation

In industrial applications, optimal control problems frequently appear in the context of decision-making under incomplete information. In such framework, decisions must be adapted dynamically to account for possible regime changes of the underlying dynamics. Using stochastic filtering theory, Markovian evolution can be modelled in terms of latent variables, which naturally leads to high-dimensional state space, making practical solutions to these control problems notoriously challenging. In our approach, we utilise a specific structure of this problem class to present a solution in terms of simple, reliable, and fast algorithms. The algorithms presented in this paper have already been implemented in an R package.     

Bang–bang property for an uncertain saddle point problem

In this paper, we propose a bang–bang control model for a saddle point problem using the optimistic value criterion. By using equation of optimality in uncertain optimal control, a bang–bang control problem is investigated. And then, an example is given to illustrate our results.     

A centre–free approach for resource allocation with lower bounds

Since complexity and scale of systems are continuously increasing, there is a growing interest in developing distributed algorithms that are capable to address information constraints, specially for solving optimisation and decision-making problems. In this paper, we propose a novel method to solve distributed resource allocation problems that include lower bound constraints. The optimisation process is carried out by a set of agents that use a communication network to coordinate their decisions. Convergence and optimality of the method are guaranteed under some mild assumptions related to the convexity of the problem and the connectivity of the underlying graph. Finally, we compare our approach with other techniques reported in the literature, and we present some engineering applications.     

Modelling and solving grid resource allocation problem with network resources for workflow applications

A problem of allocating resources of a grid to workflow applications is considered. The problem consists, generally, in allocating distributed grid resources to tasks of a workflow in such a way that the resource demands of each task are satisfied. Grid resources are divided into computational resources and network resources. Computational tasks and transmission tasks of a workflow are distinguished. We present a model of the problem, and an algorithm for finding feasible resource allocations. A numerical example is included, showing the importance of the resource allocation phase on a grid. Some conclusions and directions for future research are given.     

Optimal production scheduling for hybrid manufacturing–remanufacturing systems with setups

Hybrid systems that use both raw materials (manufacturing mode) and returned products (remanufacturing mode) in their production process are considered. The system consists of one facility and necessitates setup for switching from one production mode to another. Since the flow rate of returned products is limited (fixed percentage of the demand rate is considered), switching from one mode to another is unavoidable, and so production and setup scheduling becomes critical for meeting customer demand and manufacturing cost optimization. Analytical solutions for production and setup strategies are obtained, feasibility conditions are derived, and the sensitivity of obtained results over system parameters is investigated. It is demonstrated that there exist two types of systems: mainly manufacturing systems with a relatively low rate of return, and mainly remanufacturing systems with a relatively low use of raw materials. Quantitative criteria distinguishing these two types of systems are developed, and it is shown that systems of different types obey different feasibility conditions and exhibit different optimal behavior.     

Optimal resource allocation for transmission diversity in multi-radio access networks： a coevolutionary genetic algorithm approach

The next generation wireless communication systems aim at supporting enhanced diversified network access and data transmission abilities via the cooperative integration and unified management of various radio access technologies(RATs).The resource allocation is the core component leading the network system and mobile terminals to the service robustness and performance maximization.In this paper,a numeric optimization model for optimizing terminals’transmission power and allocated RAT bandwidth for maximizing system capacity is proposed with the focal consideration of the multi-radio transmission diversity for parallel transmission through multiple links from diferent RATs,and diferent terminal characteristics on RAT supports.Also,we design a centralized and periodic scheduling algorithm including an improved coevolutionary genetic algorithm for efciently solving the optimization problem.Simulation results demonstrate that our propose algorithm can distinctly enhance the system performance and improve the computational efciency.     

A priori and a posteriori error analysis of an augmented mixed-FEM for the Navier–Stokes–Brinkman problem

We introduce and analyze an augmented mixed finite element method for the Navier–Stokes–Brinkman problem with nonsolenoidal velocity. We employ a technique previously applied to the stationary Navier–Stokes equation, which consists of the introduction of a modified pseudostress tensor relating the gradient of the velocity and the pressure with the convective term, and propose an augmented pseudostress–velocity formulation for the model problem. The resulting augmented scheme is then written equivalently as a fixed point equation, so that the well-known Banach fixed point theorem, combined with the Lax–Milgram lemma, are applied to prove the unique solvability of the continuous and discrete systems. We point out that no discrete inf–sup conditions are required for the solvability analysis, and hence, in particular for the Galerkin scheme, arbitrary finite element subspaces of the respective continuous spaces can be utilized. For instance, given an integer $k\ge 0$, the Raviart–Thomas spaces of order $k$ and continuous piecewise polynomials of degree $\le k+1$ constitute feasible choices of discrete spaces for the pseudostress and the velocity, respectively, yielding optimal convergence. We also emphasize that, since the Dirichlet boundary condition becomes a natural condition, the analysis for both the continuous an discrete problems can be derived without introducing any lifting of the velocity boundary datum. In addition, we derive a reliable and efficient residual-based a posteriori error estimator for the augmented mixed method. The proof of reliability makes use of a global inf–sup condition, a Helmholtz decomposition, and local approximation properties of the Clément interpolant and Raviart–Thomas operator. On the other hand, inverse inequalities, the localization technique based on element-bubble and edge-bubble functions, approximation properties of the $L^2$-orthogonal projector, and known results from previous works, are the main tools for proving the efficiency of the estimator. Finally, some numerical results illustrating the performance of the augmented mixed method, confirming the theoretical rate of convergence and properties of the estimator, and showing the behavior of the associated adaptive algorithms, are reported.     

Application of fixed point-collocation method for solving an optimal control problem of a parabolic–hyperbolic free boundary problem modeling the growth of tumor with drug application

In this paper, employing a fixed point-collocation method, we solve an optimal control problem for a model of tumor growth with drug application. This model is a free boundary problem and consists of five time-dependent partial differential equations including three different first-order hyperbolic equations describing the evolution of cells and two second-order parabolic equations describing the diffusion of nutrient and drug concentration. In the mentioned optimal control problem, the concentration of nutrient and drug is controlled using some control variables in order to destroy the tumor cells. In this study, applying the fixed point method, we construct a sequence converging to the solution of the optimal control problem. In each step of the fixed point iteration, the problem changes to a linear one and the parabolic equations are solved using the collocation method. The stability of the method is also proved. Some examples are considered to illustrate the efficiency of method.     

Algorithm for the discrete Weber’s problem with an accuracy estimate

We consider a relaxation of the quadratic assignment problem without the constraint on the number of objects assigned to a specific position. This problem is NP-hard in the general case. To solve the problem, we propose a polynomial algorithm with guaranteed posterior accuracy estimate; we distinguish a class of problems with special assignment cost functions where the algorithm is 2-approximate. We show that if the graph in question contains one simple loop, and the set of assignment positions is a metric space, the proposed algorithm is 2-approximate and guaranteed to be asymptotically exact. We conduct a computational experiment in order to analyze the algorithm’s errors and evaluate its accuracy.     

Penalty guided bees search for redundancy allocation problems with a mix of components in series–parallel systems

This paper uses a penalty guided strategy based on an artificial bee colony algorithm (PGBC) to solve the redundancy allocation problem (RAP) in reliability series–parallel systems. The penalty strategy was designed to eliminate the equalities in constraints and formulate new objective operators which guarantee feasibility within a reasonable execution time. The PGBC is used to deal with two kinds of RAPs with a mix of components. In the first example, the RAPs are designed to find the appropriate mix of components and redundancies within a system in order to either minimize the cost in the context of a minimum level of reliability, or maximize reliability subject to a maximum cost and weight. The second example involves RAPs of multi-state series–parallel reliability structures, wherein each subsystem can consist of a maximum of two types of redundant components. The objective is to minimize the total investment cost of system design while satisfying system reliability constraints and the consumer load demands. There are five multi-state system design problems which have been solved for illustration in this example. The experimental results show that the PGBC can significantly outperform other existing methods in the literature with less cost, higher reliability, and a significantly shorter computational time.     

Optimal replacement policy for a general geometric process model with δ-shock

In this article, a general geometric process model with δ-shock for a deteriorating system and an improving system is studied. A system will fail as soon as a shock arrives with interarrival time being inside a real set. Assume that a replacement policy N is adopted by which the system will be replaced by a new, identical one at the time following the N-th failure. Then the optimal replacement policy N* for minimising the long-run average cost per unit time is determined analytically. Finally, the sensitivity analysis is studied.