Abstract: Abstract Internet of things (IoT) covers various aspects of collecting and exchanging data between diverse entities. From IoT provider’s perspective, one of the most significant issues is how to set the price that maximizes its revenue while meeting users’ requirements. In this paper, we focus on revenue maximization of the IoT service provider by applying pay per use pricing within the combinatorial sealed-bid auction. Pay per use pricing option implies that each user is charged per unit of consumption according to the actual usage. We assume that a user pays a threshold price for a unit of consumption, which is determined based on the auction. The auction is conducted with bidding prices set up in advance within service level agreement (SLA). We use variable neighbourhood search (VNS) in order to derive the optimal threshold price that maximizes IoT provider’s revenue, and users’ satisfaction. In addition, the optimization within the auction mechanism is conducted using different metaheuristics, which are compared with two types of VNS algorithms. PubDate: 2020-10-01

Abstract: Abstract The capacitated vehicle routing problem (CVRP) is a well-known NP-hard combinatorial optimization problem with numerous real-world applications in logistics. In this work, we present a literature review with recent successful parallel implementations of variable neighborhood search regarding different variants of vehicle routing problems. We conduct an experimental study for the CVRP using well-known benchmark instances, and we present and investigate three parallelization strategies that coordinate the communication of the multiple processors. We experimentally evaluate a non-cooperative and two novel cooperation models, the managed cooperative and the parameterized cooperative strategies. Our results constitute a first proof-of-concept for the benefits of this new self-adaptive parameterized cooperative approach, especially in computationally hard instances. PubDate: 2020-10-01

Abstract: Abstract The quartet method is a novel hierarchical clustering approach where, given a set of n data objects and their pairwise dissimilarities, the aim is to construct an optimal tree from the total number of possible combinations of quartet topologies on n, where optimality means that the sum of the dissimilarities of the embedded (or consistent) quartet topologies is minimal. This corresponds to an NP-hard combinatorial optimization problem, also referred to as minimum quartet tree cost (MQTC) problem. We provide details and formulation of this challenging problem, and propose a basic greedy heuristic that is characterized by some appealing insights and findings for speeding up and simplifying the processes of solution generation and evaluation, such as the use of adjacency-like matrices to represent the topology structures of candidate solutions; fast calculation of coefficients and weights of the solution matrices; shortcuts in the enumeration of all solution permutations for a given configuration; and an iterative distance matrix reduction procedure, which greedily merges together highly connected objects which may bring lower values of the quartet cost function in a given partial solution. It will be shown that this basic greedy heuristic is able to improve consistently the performance of popular quartet clustering algorithms in the literature, namely a reduced variable neighbourhood search and a simulated annealing metaheuristic, producing novel efficient solution approaches to the MQTC problem. PubDate: 2020-10-01

Abstract: Abstract The continuous single-source capacitated multi-facility Weber problem (SSCMFWP) where setup cost of opening facilities is taken into account is investigated. The aim is to locate a set of facilities on the plane, to define their respective capacities which can be linked to the configuration of the processing machines used, and to allocate customers to exactly one facility with the objective being the minimisation of the total transportation and setup costs. A new nonlinear mathematical model based on the SSCMFWP is introduced where Rectilinear and Euclidean distances are used. Efficient metaheuristic approaches based on Variable Neighbourhood Search and Simulated Annealing are also developed. The proposed metaheuristics incorporate an exact method and the commonly used Cooper’s alternate location-allocation method. We also constructed a new data set to reflect the characteristic of this particular location problem as no data set is available in the literature. Computational experiments show that the proposed metaheuristics generate interesting results for this class of continuous location problems. PubDate: 2020-10-01

Abstract: Abstract In this work, we are interested in the multi-quays berth allocation and crane assignment problem under availability restrictions. Availability restrictions may arise due weather conditions, or when, for example, cranes must undergo planned maintenance in order to stay in good performance. This problem was inspired by a real-case of a bulk port in Morocco. To solve the problem we propose at first a mixed-integer programming model. Then, in view of the limitations of the proposed model, we investigate a set of heuristics based on general variable neighborhood search with three variants of variable neighborhood descent as a local search. To validate the proposed model and the proposed heuristic approach, real-world instances are used. The computational results reveal that CPLEX MIP solver consumes a lot of CPU time to solve this model, even sometimes failing to guarantee the optimality of the provided solution. On the other hand, the proposed GVNS heuristic turns out to be very efficient in solving the considered problem. PubDate: 2020-10-01

Abstract: Abstract The Online Order Batching Problem (OOBP) is a variant of the well-known Order Batching Problem (OBP). As in the OBP, the goal of this problem is to collect all the orders that arrive at a warehouse, following an order batching picking policy, while minimizing a particular objective function. Therefore, orders are grouped in batches, of a maximum predefined capacity, before being collected. Each batch is assigned to a single picker, who collects all the orders within the batch in a single route. Unlike the OBP, this variant presents the peculiarity that the orders considered in each instance are not fully available in the warehouse at the beginning of the day, but they can arrive at the system once the picking process has already begun. Then, batches have to be dynamically updated and, as a consequence, routes must too. In this paper, the maximum turnover time (maximum time that an order remains in the warehouse) and the maximum completion time (total collecting time of all orders received in the warehouse) are minimized. To that aim, we propose an algorithm based in the combination of a Greedy Randomized Adaptive Search Procedure and a Variable Neighborhood Descent. The best variant of our method has been tested over a large set of instances and it has been favorably compared with the best previous approach in the state of the art. PubDate: 2020-10-01

Abstract: Abstract When solving large-scale multiobjective optimization problems, solvers can get stuck because of memory and/or time limitations. In such cases, one is left with no information on the distance to the best feasible solution, found before the optimization process has stopped, to the true Pareto optimal solution. In this work, we show how to provide such information. To this aim we make use of the concept of lower shells and upper shells, developed in our earlier works. No specific assumptions about the problems to be solved are made. We illustrate the proposed approach on biobjective multidimensional knapsack problems derived from single-objective multidimensional knapsack problems in the Beasley OR Library. We address cases when a top-class commercial mixed-integer linear solver fails to provide Pareto optimal solutions attempted to be derived by scalarization. PubDate: 2020-09-19

Abstract: Abstract On the basis of the notion of approximating family of cones and a generalized type of Gerstewitz’s/Tammer’s nonlinear scalarization functional, we establish variants of the Ekeland variational principle (for short, EVP) involving set perturbations for a type of approximate proper solutions in the sense of Henig of a vector equilibrium problem. Initially, these results are obtained for both an unconstrained and a constrained vector equilibrium problem, where the objective function takes values in a real locally convex Hausdorff topological linear space. After that, we consider special cases when the objective function takes values in a normed space and in a finite-dimensional vector space. For the finite-dimensional objective space with a polyhedral ordering cone, we give the explicit representation of variants of EVP depending on matrices, and in such a way, some selected applications for multiobjective optimization problems and vector variational inequality problems are also derived. PubDate: 2020-09-18

Abstract: Abstract We consider the lower bounded inverse optimal value problem on minimum spanning tree under unit \(l_{\infty }\) norm. Given an edge weighted connected undirected network \(G=(V,E,\varvec{w})\) , a spanning tree \(T^0\) , a lower bound vector \(\varvec{l}\) and a value K, we aim to find a new weight vector \(\bar{\varvec{w}}\) respecting the lower bound such that \(T^0\) is a minimum spanning tree under the vector \(\bar{\varvec{w}}\) with weight K, and the objective is to minimize the modification cost under unit \(l_{\infty }\) norm. We present a mathematical model of the problem. After analyzing optimality conditions of the problem, we develop a strongly polynomial time algorithm with running time O( V E ). Finally, we give an example to demonstrate the algorithm and present the numerical experiments. PubDate: 2020-09-12

Abstract: Abstract In this paper we consider the multiple geometrical object detection problem. On the basis of the set \(\mathcal {A}\) containing data points coming from and scattered among a number of geometrical objects not known in advance, we should reconstruct or detect those geometrical objects. A new efficient method for solving this problem based on the popular RANSAC method using parameters from the DBSCAN method is proposed. Thereby, instead of using classical indexes for recognizing the most appropriate partition, we use parameters from the DBSCAN method which define the necessary conditions proven to be far more efficient. Especially, the method is applied to solving multiple circle detection problem. In this case, we give both the conditions for the existence of the best circle as a representative of the data set and the explicit formulas for the parameters of the best circle. In the illustrative example, we consider the multiple circle detection problem for the data point set \(\mathcal {A}\) coming from 5 intersected circles not known in advance. The method is tested on numerous artificial data sets and it has shown high efficiency. The comparison of the proposed method with other well-known methods of circle detection in real-world images also indicates a significant advantage of our method. PubDate: 2020-09-12

Abstract: Abstract Deterministic global optimization algorithms like Piyavskii–Shubert, direct, ego and many more, have a recognized standing, for problems with many local optima. Although many single objective optimization algorithms have been extended to multiple objectives, completely deterministic algorithms for nonlinear problems with guarantees of convergence to global Pareto optimality are still missing. For instance, deterministic algorithms usually make use of some form of scalarization, which may lead to incomplete representations of the Pareto optimal set. Thus, all global Pareto optima may not be obtained, especially in nonconvex cases. On the other hand, algorithms attempting to produce representations of the globally Pareto optimal set are usually based on heuristics. We analyze the concept of global convergence for multiobjective optimization algorithms and propose a convergence criterion based on the Hausdorff distance in the decision space. Under this light, we consider the well-known global optimization algorithm direct, analyze the available algorithms in the literature that extend direct to multiple objectives and discuss possible alternatives. In particular, we propose a novel definition for the notion of potential Pareto optimality extending the notion of potential optimality defined in direct. We also discuss its advantages and disadvantages when compared with algorithms existing in the literature. PubDate: 2020-09-05

Abstract: Abstract The split feasibility problem is to find an element in the intersection of a closed set C and the linear preimage of another closed set D, assuming the projections onto C and D are easy to compute. This class of problems arises naturally in many contemporary applications such as compressed sensing. While the sets C and D are typically assumed to be convex in the literature, in this paper, we allow both sets to be possibly nonconvex. We observe that, in this setting, the split feasibility problem can be formulated as an optimization problem with a difference-of-convex objective so that standard majorization-minimization type algorithms can be applied. Here we focus on the nonmonotone proximal gradient algorithm with majorization studied in Liu et al. (Math Program, 2019. https://doi.org/10.1007/s10107-018-1327-8, Appendix A). We show that, when this algorithm is applied to a split feasibility problem, the sequence generated clusters at a stationary point of the problem under mild assumptions. We also study local convergence property of the sequence under suitable assumptions on the closed sets involved. Finally, we perform numerical experiments to illustrate the efficiency of our approach on solving split feasibility problems that arise in completely positive matrix factorization, (uniformly) sparse matrix factorization, and outlier detection. PubDate: 2020-09-01

Abstract: Abstract Recently, Kronqvist et al. (J Global Optim 64(2):249–272, 2016) rediscovered the supporting hyperplane algorithm of Veinott (Oper Res 15(1):147–152, 1967) and demonstrated its computational benefits for solving convex mixed integer nonlinear programs. In this paper we derive the algorithm from a geometric point of view. This enables us to show that the supporting hyperplane algorithm is equivalent to Kelley’s cutting plane algorithm (J Soc Ind Appl Math 8(4):703–712, 1960) applied to a particular reformulation of the problem. As a result, we extend the applicability of the supporting hyperplane algorithm to convex problems represented by a class of general, not necessarily convex nor differentiable, functions. PubDate: 2020-09-01

Abstract: Abstract Successive quadratic approximations (SQA) are numerically efficient for minimizing the sum of a smooth function and a convex function. The iteration complexity of inexact SQA methods has been analyzed recently. In this paper, we present an algorithmic framework of inexact SQA methods with four types of line searches, and analyze its global complexity under milder assumptions. First, we show its well-definedness and some decreasing properties. Second, under the quadratic growth condition and a uniform positive lower bound condition on stepsizes, we show that the function value sequence and the iterate sequence are linearly convergent. Moreover, we obtain a o(1/k) complexity without the quadratic growth condition, improving existing \({\mathcal {O}}(1/k)\) complexity results. At last, we show that a local gradient-Lipschitz-continuity condition could guarantee a uniform positive lower bound for the stepsizes. PubDate: 2020-09-01

Abstract: Abstract The problem of minimizing the difference of two convex functions is called polyhedral d.c. optimization problem if at least one of the two component functions is polyhedral. We characterize the existence of global optimal solutions of polyhedral d.c. optimization problems. This result is used to show that, whenever the existence of an optimal solution can be certified, polyhedral d.c. optimization problems can be solved by certain concave minimization algorithms. No further assumptions are necessary in case of the first component being polyhedral and just some mild assumptions to the first component are required for the case where the second component is polyhedral. In case of both component functions being polyhedral, we obtain a primal and dual existence test and a primal and dual solution procedure. Numerical examples are discussed. PubDate: 2020-09-01

Abstract: Abstract The Data-driven Optimization of bi-level Mixed-Integer NOnlinear problems (DOMINO) framework is presented for addressing the optimization of bi-level mixed-integer nonlinear programming problems. In this framework, bi-level optimization problems are approximated as single-level optimization problems by collecting samples of the upper-level objective and solving the lower-level problem to global optimality at those sampling points. This process is done through the integration of the DOMINO framework with a grey-box optimization solver to perform design of experiments on the upper-level objective, and to consecutively approximate and optimize bi-level mixed-integer nonlinear programming problems that are challenging to solve using exact methods. The performance of DOMINO is assessed through solving numerous bi-level benchmark problems, a land allocation problem in Food-Energy-Water Nexus, and through employing different data-driven optimization methodologies, including both local and global methods. Although this data-driven approach cannot provide a theoretical guarantee to global optimality, we present an algorithmic advancement that can guarantee feasibility to large-scale bi-level optimization problems when the lower-level problem is solved to global optimality at convergence. PubDate: 2020-09-01

Abstract: Abstract In this paper, we discuss two modified extragradient methods for variational inequalities. The first one can be applied when the Lipschitz constant of the involving operator is unknown. In contrast to the work by Hieu and Thong (J Glob Optim 70:385–399, 2018) and by Khanh (Numer Funct Anal Optim 37:1131–1143, 2016), the new algorithm does not require its step-sizes tending to zero. This feature helps to speed up our method. The second algorithm solves variational inequalities with non-Lipschitz continuous operators. Under the pseudomonotonicity assumption, the proposed algorithm converges to a solution of the problem. In contrast to other solution methods for this class of problems, the new algorithm does not require the step sizes being square summable. Some numerical experiments show that the new algorithms are more effective than the existing ones. PubDate: 2020-09-01

Abstract: Relaxed constant positive linear dependence constraint qualification (RCPLD) for a system of smooth equalities and inequalities is a constraint qualification that is weaker than the usual constraint qualifications such as Mangasarian Fromovitz constraint qualification and the linear constraint qualification. Moreover RCPLD is known to induce an error bound property. In this paper we extend RCPLD to a very general feasibility system which may include Lipschitz continuous inequality constraints, complementarity constraints and abstract constraints. We show that this RCPLD for the general system is a constraint qualification for the optimality condition in terms of limiting subdifferential and limiting normal cone and it is a sufficient condition for the error bound property under the strict complementarity condition for the complementarity system and Clarke regularity conditions for the inequality constraints and the abstract constraint set. Moreover we introduce and study some sufficient conditions for RCPLD including the relaxed constant rank constraint qualification. Finally we apply our results to the bilevel program. PubDate: 2020-09-01

Abstract: Abstract We introduce a new concept of asymptotic functions which allows us to simultaneously study convex and concave functions as well as quasiconvex and quasiconcave functions. We provide some calculus rules and most relevant properties of the new asymptotic functions for application purpose. We also compare them with the classical asymptotic functions of convex analysis. By using the new concept of asymptotic functions we establish sufficient conditions for the nonemptiness and for the boundedness of the solution set of quasiconvex minimization problems and quasiconcave maximization problems. Applications are given for quadratic and fractional quadratic problems. PubDate: 2020-09-01