Abstract: Abstract
In a Hilbert space, the problem of terminal control with linear dynamics and fixed ends of the trajectory is considered. The integral objective functional has a quadratic form. In contrast to the traditional approach, the problem of terminal control is interpreted not as an optimization problem, but as a saddle-point problem. The solution to this problem is a saddle point of the Lagrange function with components in the form of controls, phase and conjugate trajectories. A saddle-point method is proposed, the convergence of the method in all components of the solution is proved. PubDate: 2016-05-01

Abstract: Abstract
Previous research has analyzed deterministic and stochastic models of lateral transhipments between different retailers in a supply chain. In these models the analysis assumes given fixed transhipment costs and determines under which situations (magnitudes of excess supply and demand at various retailers) the transhipment is profitable. However, in reality, these depend on aspects like the distance between retailers or the transportation mode chosen. In many situations, combining the transhipments may save transportation costs. For instance, one or more vehicle routes may be used to redistribute the inventory of the potential pickup and delivery stations. This can be done in any sequence as long as the vehicle capacity is not violated and there is enough load on the vehicle to satisfy demand. The corresponding problem is an extension of the one-commodity pickup and delivery traveling salesman and the pickup and delivery vehicle routing problem. When ignoring the routing aspect and assuming given fixed costs, transhipment is only profitable if the quantities are higher than a certain threshold. In contrast to that, the selection of visited retailers is dependent on the transportation costs of the tour and therefore the selected retailers are interrelated. Hence the problem also has aspects of a (team) orienteering problem. The main contribution is the discussion of the tour planning aspects for lateral transhipments which may be valuable for in-house planning but also for price negotiations with external contractors. A mixed integer linear program for the single route and single commodity version is presented and an improved LNS framework to heuristically solve the problem is introduced. Furthermore, the effect of very small load capacity on the structure of optimal solutions is discussed. PubDate: 2016-05-01

Abstract: Abstract
Close connections existing among sequence-dependent tasks should be emphasized while assembling products within automotive or electronic industries. This paper addresses the mixed-model assembly line balancing problem with sequence-dependent tasks with two objectives, the minimization of cycle time and workload variance. A hybrid genetic algorithm with novel logic strings was proposed to address the problem. First, both the sequence-dependent connections and precedence relations are integrated into the combined precedence graph so as to transform the original problem into the single-model assembly line balancing problem and to decrease the computational complexity. Second, three heuristic factors are hybridized into the process of initialization with the purpose of improving the quality of initial solution population. Third, considering sequence-dependent tasks, logic strings are designed to ensure the feasibility of chromosomes during two-point crossover and insertion mutation operations. Computational studies have demonstrated that the proposed algorithm can solve problems to near-optimality and even optimality with less computational effort. PubDate: 2016-05-01

Abstract: Abstract
In the present paper, we propose a preconditioned Newton–Block Arnoldi method for solving large continuous time algebraic Riccati equations. Such equations appear in control theory, model reduction, circuit simulation amongst other problems. At each step of the Newton process, we solve a large Lyapunov matrix equation with a low rank right hand side. These equations are solved by using the block Arnoldi process associated with a preconditioner based on the alternating direction implicit iteration method. We give some theoretical results and report numerical tests to show the effectiveness of the proposed approach. PubDate: 2016-05-01

Abstract: Abstract
The counting function on binary values is extended to the signed case in order to count the number of transitions between contiguous locations. A generalized subdifferential for this sign change counting function is given where classical subdifferentials remain intractable. An attempt to prove global optimality at some point, for the 4-dimensional first non trivial example, is made by using a sufficient condition specially tailored among all the cases for this subdifferential. PubDate: 2016-05-01

Abstract: Abstract
We examine Malfatti’s problem which dates back to 200 years ago from the view point of global optimization. The problem has been formulated as the convex maximization problem over a nonconvex set. Global optimality condition by Strekalovsky (Sov Math Dokl 292(5):1062–1066, 1987) has been applied to this problem. For solving numerically Malfatti’s problem, we propose the algorithm in Enkhbat (J Glob Optim 8:379–391, 1996) which converges globally. Some computational results are provided. PubDate: 2016-05-01

Abstract: Abstract
This paper studies the practical exponential set stabilization problem for switched nonlinear systems via a
\(\tau \)
-persistent approach. In these kinds of switched systems, every autonomous subsystem has one unique equilibrium point and these subsystems’ equilibria are different each other. Based on previous stability results of switched systems and a set of Gronwall–Bellman inequalities, we prove that the switched nonlinear system will reach the neighborhood of the corresponding subsystem equilibrium at every switching time. In addition, we constructively design a suitable
\(\tau \)
-persistent switching law to practically exponentially set stabilize the switched system. Finally, a numerical example is presented to illustrate the obtained results. PubDate: 2016-05-01

Abstract: Abstract
Given a p-dimensional nonnegative, integral vector
\(\varvec{\alpha },\)
this paper characterizes the convex hull of the set S of nonnegative, integral vectors
\(\varvec{x}\)
that is lexicographically less than or equal to
\(\varvec{\alpha }.\)
To obtain a finite number of elements in S, the vectors
\(\varvec{x}\)
are restricted to be component-wise upper-bounded by an integral vector
\(\varvec{u}.\)
We show that a linear number of facets is sufficient to describe the convex hull. For the special case in which every entry of
\(\varvec{u}\)
takes the same value
\((n-1)\)
for some integer
\(n \ge 2,\)
the convex hull of the set of n-ary vectors results. Our facets generalize the known family of cover inequalities for the
\(n=2\)
binary case. They allow for advances relative to both the modeling of integer variables using base-n expansions, and the solving of knapsack problems having weakly super-decreasing coefficients. Insight is gained by alternately constructing the convex hull representation in a higher-variable space using disjunctive programming arguments. PubDate: 2016-04-25

Abstract: Abstract
The derivative-free global optimization algorithms developed in Part I of this study, for linearly constrained problems, are extended to nonconvex n-dimensional problems with convex constraints. The initial
\(n+1\)
feasible datapoints are chosen in such a way that the volume of the simplex generated by these datapoints is maximized; as the algorithm proceeds, additional feasible datapoints are added in such a way that the convex hull of the available datapoints efficiently increases towards the boundaries of the feasible domain. Similar to the algorithms developed in Part I of this study, at each step of the algorithm, a search function is defined based on an interpolating function which passes through all available datapoints and a synthetic uncertainty function which characterizes the distance to the nearest datapoints. This uncertainty function, in turn, is built on the framework of a Delaunay triangulation, which is itself based on all available datapoints together with the (infeasible) vertices of an exterior simplex which completely contains the feasible domain. The search function is minimized within those simplices of this Delaunay triangulation that do not include the vertices of the exterior simplex. If the outcome of this minimization is contained within the circumsphere of a simplex which includes a vertex of the exterior simplex, this new point is projected out to the boundary of the feasible domain. For problems in which the feasible domain includes edges (due to the intersection of multiple twice-differentiable constraints), a modified search function is considered in the vicinity of these edges to assure convergence. PubDate: 2016-04-19

Abstract: Abstract
The huge computational overhead is the main challenge in the application of community based optimization methods, such as multi-objective particle swarm optimization and multi-objective genetic algorithm, to deal with the multi-objective optimization involving costly simulations. This paper proposes a Kriging metamodel assisted multi-objective particle swarm optimization method to solve this kind of expensively black-box multi-objective optimization problems. On the basis of crowding distance based multi-objective particle swarm optimization algorithm, the new proposed method constructs Kriging metamodel for each expensive objective function adaptively, and then the non-dominated solutions of the metamodels are utilized to guide the update of particle population. To reduce the computational cost, the generalized expected improvements of each particle predicted by metamodels are presented to determine which particles need to perform actual function evaluations. The suggested method is tested on 12 benchmark functions and compared with the original crowding distance based multi-objective particle swarm optimization algorithm and non-dominated sorting genetic algorithm-II algorithm. The test results show that the application of Kriging metamodel improves the search ability and reduces the number of evaluations. Additionally, the new proposed method is applied to the optimal design of a cycloid gear pump and achieves desirable results. PubDate: 2016-04-19

Abstract: Abstract
Answering a question of Haugland, we show that the pooling problem with one pool and a bounded number of inputs can be solved in polynomial time by solving a polynomial number of linear programs of polynomial size. We also give an overview of known complexity results and remaining open problems to further characterize the border between (strongly) NP-hard and polynomially solvable cases of the pooling problem. PubDate: 2016-04-18

Abstract: Abstract
The multiple depot ring-star problem (MDRSP) is an important combinatorial optimization problem that arises in optical fiber network design and in applications that collect data using stationary sensing devices and autonomous vehicles. Given the locations of a set of customers and a set of depots, the goal is to (i) find a set of simple cycles such that each cycle (ring) passes through a subset of customers and exactly one depot, (ii) assign each non-visited customer to a visited customer or a depot, and (iii) minimize the sum of the routing costs, i.e., the cost of the cycles and the assignment costs. We present a mixed integer linear programming formulation for the MDRSP and propose valid inequalities to strengthen the linear programming relaxation. Furthermore, we present a polyhedral analysis and derive facet-inducing results for the MDRSP. All these results are then used to develop a branch-and-cut algorithm to obtain optimal solutions to the MDRSP. The performance of the branch-and-cut algorithm is evaluated through extensive computational experiments on several classes of test instances. PubDate: 2016-04-12

Abstract: Abstract
The Maximum Minsum Dispersion Problem (Max-Minsum DP) is a strongly NP-Hard problem that belongs to the family of equitable dispersion problems. When dealing with dispersion, the operations research literature has focused on optimizing efficiency-based objectives while neglecting, for the most part, measures of equity. The most common efficiency-based functions are the sum of the inter-element distances or the minimum inter-element distance. Equitable dispersion problems, on the other hand, attempt to address the balance between efficiency and equity when selecting a subset of elements from a larger set. The objective of the Max-Minsum DP is to maximize the minimum aggregate dispersion among the chosen elements. We develop tabu search and GRASP solution procedures for this problem and compare them against the best in the literature. We also apply LocalSolver, a commercially available black-box optimizer, to compare our results. Our computational experiments show that we are able to establish new benchmarks in the solution of the Max-Minsum DP. PubDate: 2016-04-09

Abstract: Abstract
Due to the growing interest in approximation for multiobjective optimization problems (MOPs), a theoretical framework for defining and classifying sets representing or approximating solution sets for MOPs is developed. The concept of tolerance function is proposed as a tool for modeling representation quality. This notion leads to the extension of the traditional dominance relation to
\(t\hbox {-}\)
dominance. Two types of sets representing the solution sets are defined: covers and approximations. Their properties are examined in a broader context of multiple solution sets, multiple cones, and multiple quality measures. Applications to complex MOPs are included. PubDate: 2016-04-06

Abstract: Abstract
This article addresses the problem of derivative-free (single- or multi-objective) optimization subject to multiple inequality constraints. Both the objective and constraint functions are assumed to be smooth, non-linear and expensive to evaluate. As a consequence, the number of evaluations that can be used to carry out the optimization is very limited, as in complex industrial design optimization problems. The method we propose to overcome this difficulty has its roots in both the Bayesian and the multi-objective optimization literatures. More specifically, an extended domination rule is used to handle objectives and constraints in a unified way, and a corresponding expected hyper-volume improvement sampling criterion is proposed. This new criterion is naturally adapted to the search of a feasible point when none is available, and reduces to existing Bayesian sampling criteria—the classical Expected Improvement (EI) criterion and some of its constrained/multi-objective extensions—as soon as at least one feasible point is available. The calculation and optimization of the criterion are performed using Sequential Monte Carlo techniques. In particular, an algorithm similar to the subset simulation method, which is well known in the field of structural reliability, is used to estimate the criterion. The method, which we call BMOO (for Bayesian Multi-Objective Optimization), is compared to state-of-the-art algorithms for single- and multi-objective constrained optimization. PubDate: 2016-04-04

Abstract: Abstract
We study the proximal method with the regularized logarithmic barrier, originally stated by Attouch and Teboulle for positively constrained optimization problems, in the more general context of nonlinear complementarity problems with monotone operators. We consider two sequences generated by the method. We prove that one of them, called the ergodic sequence, is globally convergent to the solution set of the problem, assuming just monotonicity of the operator and existence of solutions; for convergence of the other one, called the proximal sequence, we demand some stronger property, like paramonotonicity of the operator or the so called “cut property” of the problem. PubDate: 2016-04-01

Abstract: Abstract
In real-time trajectory planning for unmanned vehicles, on-board sensors, radars and other instruments are used to collect information on possible obstacles to be avoided and pathways to be followed. Since, in practice, observations of the sensors have measurement errors, the stochasticity of the data has to be incorporated into the models. In this paper, we consider using a genetic algorithm for the constrained optimization problem of finding the trajectory with minimum length between two locations, avoiding the obstacles on the way. To incorporate the variability of the sensor readings, we propose a modified genetic algorithm, addressing the stochasticity of the feasible regions. In this way, the probability that a possible solution in the search space, say x, is feasible can be derived from the random observations of obstacles and pathways, creating a real-time data learning algorithm. By building a confidence region from the observed data such that its border intersects with the solution point x, the level of the confidence region defines the probability that x is feasible. We propose using a smooth penalty function based on the Gaussian distribution, facilitating the borders of the feasible regions to be reached by the algorithm. PubDate: 2016-04-01

Abstract: Abstract
Optimal control problems with a nonconvex quadratic functional of Lagrange are considered. On the base of global optimality conditions we develop a global search algorithm, one of the principal module of which is represented by special local search method. The results of computational testing presented. PubDate: 2016-03-11