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The proximal point algorithm (PPA) is a powerful tool for solving monotone inclusion problems. Recently, Tao and Yuan [On the optimal linear convergence rate of a generalized proximal point algorithm, J. Sci. Comput. 74 (2018), 826-850] proposed a generalized PPA (GPPA) for finding a zero point of a maximal monotone operator, and obtained the linear convergence rate of the generalized PPA. In this paper, we consider accelerating the GPPA with the aid of the inertial extrapolation. We propose a generalized proximal point algorithm with alternating inertial steps solving monotone inclusion problem, and obtain weak convergence results under some mild conditions. When the inverse of the involved monotone operator is Lipschitz continuous at the origin, we prove that the iterative sequence generated by our generalized proximal point algorithm is linearly convergent. The Fej'er monotonicity of even subsequences of the iterative sequence is also recovered. Finally, we give some priori and posteriori error estimates of our generated sequences. [ABSTRACT FROM AUTHOR]

In this paper, we consider the varying stepsize gradient projection algorithm (GPA) for solving the split equality problem (SEP) in Hilbert spaces, and study its linear convergence. In particular, we introduce a notion of bounded linear regularity property for the SEP, and use it to establish the linear convergence property for the varying stepsize GPA. We provide some mild sufficient conditions to ensure the bounded linear regularity property, and then conclude the linear convergence rate of the varying stepsize GPA. To the best of our knowledge, this is the first work to study the linear convergence for the SEP. [ABSTRACT FROM AUTHOR]

Currently, in various fields and disciplines problem optimization are used commonly. In this concern, we have to define solutions which are two known concepts optimal or near optimal optimization problems in regards to some objects. Usually, it is surely difficult to sort problems out in only one step, but some processes can be followed by us which people usually call it problem solving. Frequently, the solution process is split into various steps which are accomplishing one after the other. Therefore, in this paper we consider some algorithms that help us to sort out problems, for exemplify, finding the shortest path, minimum spanning tree, maximum network flows and maximum matching. More importantly, the algorithm comparison will be presented. Additionally, the limitation of each algorithm. The last but not the least, the future research in this area will be approached. [ABSTRACT FROM AUTHOR]

This paper proposes a new and more efficient solution to the problem of determining optimal form-closure constraints of polygonal objects using four contacts. New grasp parameters are determined based only on the directions of the applied forces, which are then used to determine the optimal grasp. Given a set of contact edges, using an analytical procedure a solution that is either the optimal one or is very close to it is obtained (only in this second case an iterative procedure is needed to find a root of a nonlinear equation). This procedure is used for an efficient determination of the optimal grasp on the whole object. The algorithms have been implemented and numerical examples are shown. Note to Practitioners--This paper presents an algorithm that improves previous approaches in terms of efficiency in the determination of the optimal object constraint maximizing the minimum wrench that the object can support in any direction. The problem can always be solved using numerical optimization techniques but when time is relevant an efficient algorithm becomes of interest. Practical applications include optimal determination of fixtures and object grasps. [ABSTRACT FROM AUTHOR]

For interpolating between elements of SO(n), it is attractive to work in n, passing from one space to the other via the exponential map. However, the logarithm is a multi-valued map and the choice of a particular image affects the quality of the interpolation. In this paper, we propose a fast and accurate algorithm to compute the image that seems the most appropriate for interpolation: given Q ∈ SO(n) and A ∈ n, our algorithm returns the logarithm of Q which is the closest to A, under minimal conditions on Q. We carefully study the mathematical properties of our problem to establish the algorithm, discuss its implementation and demonstrate its efficiency. [ABSTRACT FROM AUTHOR]

Abstract. This paper deals with an extremal problem concerning hypergraph colorings. Let k be an integer. The problem is to find the value m( n) equal to the minimum number of edges in an n-uniform hypergraph not admitting two-colorings of the vertex set such that every edge of the hypergraph contains at least k vertices of each color. In this paper, we obtain upper bounds of m( n) for small k and n, the exact value of m(8), and a lower bound for m(7). [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a new coloring problem of a graph called the dominated coloring. A dominated coloring of a graph $$G$$ is a proper vertex coloring of $$G$$ such that each color class is dominated by at least one vertex of $$G$$ . The minimum number of colors among all dominated colorings is called the dominated chromatic number, denoted by $$\chi _{dom}(G)$$ . In this paper, we establish the close relationship between the dominated chromatic number $$\chi _{dom}(G)$$ and the total domination number $$\gamma _t(G)$$ ; and the equivalence for triangle-free graphs. We study the complexity of the problem by proving its NP-completeness for arbitrary graphs having $$\chi _{dom}(G) \ge 4$$ and by giving a polynomial time algorithm for recognizing graphs having $$\chi _{dom}(G) \le 3$$ . We also give some bounds for planar and star-free graphs and exact values for split graphs. [ABSTRACT FROM AUTHOR]

The paper presents a new approach to solving a class of combinatorial economic allocation problems. One member of this class is known as the quadratic assignment problem. Besides presenting an algorithm to solve this problem, we will discuss in general terms the techniques for treating combinatorial problems. A novel feature of the paper is the development of the statistical properties of the criterion function. These statistical properties are used in conjunction with a general enumerative procedure to form the main parts of the algorithm. Using the idea of confidence level enumeration, an extension of the algorithm is proposed which should allow for the effective treatment of large scale combinatorial problems. Finally we present some computational results in order to illustrate the effectiveness of the general approach. [ABSTRACT FROM AUTHOR]

This paper first proposes a trust region algorithm to obtain a stationary point of unconstrained multiobjective optimisation problem. Under suitable assumptions, the global convergence of the new algorithm is established. We then extend the trust region method to solve the non-smooth multiobjective optimisation problem. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce a natural variation of the problem of computing all bichro-matic intersections between two sets of segments. Given two sets R and B of n points in the plane defining two sets of segments, say red and blue, we present an O(n²) time and space algorithm for solving the problem of reporting the set of segments of each color intersected by segments of the other color. We also prove that this problem is 3-Sum hard and provide some illustrative examples of several point configuration. [ABSTRACT FROM AUTHOR]

Under the condition that the values of mapping F are evaluated approximately, we propose a proximal analytic center cutting plane algorithm for solving variational inequalities. It can be considered as an approximation of the earlier cutting plane method, and the conditions we impose on the corresponding mappings are more relaxed. The convergence analysis for the proposed algorithm is also given at the end of this paper. [ABSTRACT FROM AUTHOR]

The job-shop scheduling problems with fuzzy processing time and fuzzy due date are investigated in this paper. The ranking concept among fuzzy numbers based on possibility and necessity measures which are developed in fuzzy sets theory is introduced. And on the basis of two consistent measures in this concept, several novel objective functions are proposed. The purpose of our research is to obtain the optimal schedules based on these objective functions. A modified DE algorithm will be designed to solve these objective functions. Several jop-shop scheduling problems with fuzzy processing time and fuzzy due date are experimented to show the efficiency and comparability of our approach. Through the experimental results, the potential application of the possibility and necessity theory in the real world is shown. [ABSTRACT FROM AUTHOR]

The paper considers nonconvex quadratic semidefinite problems. This class arises, for instance, as subproblems in the sequential semidefinite programming algorithm for solving general smooth nonlinear semidefinite problems. We extend locally the concept of self-concordance to problems that satisfy a weak version of the second order sufficient optimality conditions. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to improve the bound of complexity of the well-known algorithms on polynomial ideals having complexities polynomial in dn, where d is the maximal degree of input polynomials and n is the number of variables. Instead of this bound, we present the more accurate bound max{S, Dn} where S is the size of the input polynomials in dense representation, and D is the arithmetic mean value of the degrees of input polynomials. [ABSTRACT FROM AUTHOR]

We consider a problem of partitioning a partially ordered set into chains by first-fit algorithm. In general this algorithm uses arbitrarily many chains on a class of bounded width posets. In this paper we prove that First-Fit uses at most 3tw2 chains to partition any poset of width w which does not induce two incomparable chains of height t. In this way we get a wide class of posets with polynomial bound for the on-line chain partitioning problem. We also discuss some consequences of our result for coloring graphs by First-Fit. [ABSTRACT FROM AUTHOR]

Copyright of RAIRO -- Operations Research is the property of EDP Sciences and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The author responds to the paper "The Loading Problem," by Eilon and Christofides. He focuses on suggesting a solution to the problem. The recommended solution involves a heuristic algorithm that allegedly requires fewer computations than the one proposed by Eilon and Christofides. It is suggested that the simpler algorithm offered by the author reaches mathematical optimization as often as the aforementioned algorithm. It is further proposed that the algorithm presented by Eilon and Christofides cannot be used to solve multi-dimensional programming problems. The author goes on to discuss a numerical analysis that can be used for the allocation of industrial resources. Related mathematical models are discussed in detail. A table comparing the results of the two algorithms is also presented.

In this paper the Fiacco-McCormick SUMT technique is embedded in a class of inside-out algorithms. Convergence is demonstrated for the nonlinear programming problem under fairly general conditions and the algorithms are interpreted in a geometric structure. [ABSTRACT FROM AUTHOR]

In this paper, we study the weak linear bilevel programming problems. For such problems, under some conditions, we first conclude that there exists a solution which is a vertex of the constraint region. Based on the classicalKth-Best algorithm, we then present a solution approach. Finally, an illustrative example shows that the proposed approach is feasible. [ABSTRACT FROM PUBLISHER]

In this paper, a three-term conjugate gradient algorithm is developed for solving large-scale unconstrained optimization problems. The search direction at each iteration of the algorithm is determined by rectifying the steepest descent direction with the difference between the current iterative points and that between the gradients. It is proved that such a direction satisfies the approximate secant condition as well as the conjugacy condition. The strategies of acceleration and restart are incorporated into designing the algorithm to improve its numerical performance. Global convergence of the proposed algorithm is established under two mild assumptions. By implementing the algorithm to solve 75 benchmark test problems available in the literature, the obtained results indicate that the algorithm developed in this paper outperforms the existent similar state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

A kernel J of a digraph D is an independent set of vertices of D such that for every vertex w ϵ V (D) \ J there exists an arc from w to a vertex in J: In this paper, among other results, a characterization of 2-regular circulant digraph having a kernel is obtained. This characterization is a partial solution to the following problem: Characterize circulant digraphs which have kernels; it appeared in the book Digraphs - theory, algorithms and applications, Second Edition, Springer-Verlag, 2009, by J. Bang-Jensen and G. Gutin. [ABSTRACT FROM AUTHOR]

Let G = (V, E) be a connected simple graph and let M be a nonempty subset of V. The M-distance pattern of a vertex u in G is the set of all distances from u to the vertices in M. If the distance patterns of all vertices in V are distinct, then the set Mis a distance pattern distinguishing set of G. A graph G with a distance pattern distinguishing set is called a distance pattern distinguishing graph. Minimum number of vertices in a distance pattern distinguishing set is called distance pattern distinguishing number of a graph. This paper initiates a study on the problem of finding distance pattern distinguishing number of a graph and gives bounds for distance pattern distinguishing number. Further, this paper provides an algorithm to determine whether a graph is a distance pattern distinguishing graph or not and hence to determine the distance pattern distinguishing number of that graph. [ABSTRACT FROM AUTHOR]

Highlights: [•] Aiming at the problem that how to classify T-splines this paper gives a mathematical analysis, and a sufficient condition of standard T-splines is also given. [•] Then this paper presents an algorithm of determining the T-spline classification, and we can get the inherently mathematical properties of T-splines by the algorithm. [ABSTRACT FROM AUTHOR]

In this paper we consider the following problem: given a finite set of straight-line segmentsSin ℝ2, find minimum in size setVof points on the segments, such that each segment ofScontains at least one point inV. We call this problem guarding a set of segments (GSS). GSS is a special case of the set cover problem where the given family of subsets can be taken as a set of intersections of the straight-line segments inS. Requiring that the given subsets can be interpreted geometrically this way is a major restriction on the input, yet it has been shown that the problem is still strongly NP-complete [V.E. Brimkov, A. Leach, M. Mastroianni, and J. Wu,Guarding a set of line segments in the plane, Theor. Comput. Sci. 412 (2011), pp. 1313–1324]. In light of this result, in Brimkovet al.[Experimental studies on approximation algorithms for guarding sets of line segments, inAdvances in Visual Computing, G. Bebis, R. Boyle, B. Parvin, D. Koracin, R. Chung, R. Hammoud, M. Hussain, T. Kar-Han, R. Crawfis, D. Thalmann, D. Kao, and L. Avila, eds., ISVC 2010, Part I, Lecture Notes in Computer Science, Vol. 6453, Springer, Berlin, 2010, pp. 592–601; V.E. Brimkov, A. Leach, M. Mastroianni, and J. Wu,Approximation algorithms for a geometric set cover problem, Discrete Appl. Math. 160 (2012), pp. 1039–1052] the GSS approximability was studied both theoretically and experimentally. Here we continue these investigations. In particular, we obtain conditions under which GSS admits good approximation. [ABSTRACT FROM AUTHOR]

The paper considers conditions under which rank factorizations of a two-parameter polynomial matrix can be affected with the use of unimodular matrices, as in the one-parameter case. Algorithms for computing such factorizations and a minimal basis of the null space of the corresponding matrix are presented. Also an algorithm for inverting unimodular two-parameter polynomial matrices is suggested. Bibliography: 4 titles. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the problem of observer design for a class of implicit nonlinear systems of index one. To solve this problem, an implicit observer which is given by an implicit system is usually used. The implementation of this kind of observer requires an optimization algorithm to solve at each time the algebraic constraints. Alternatively, an explicit observer which is described by an ordinary differential equation can be used. The advantage of this approach is that no optimization algorithm is required. Moreover the observer initialization may be done outside the constraints. In this paper it is shown that, under some conditions, the existence of an implicit observer implies the existence of an explicit one. Then, an explicit observer is given for implicit state affine systems whose dynamic involves an additional nonlinear term depending on the input, the output and the implicit variable. [Copyright &y& Elsevier]

In this paper we survey recent developments in the theory of groups acting on A-trees. We are trying to unify all significant methods and techniques, both classical and recently developed, in an attempt to present various faces of the theory and to show how these methods can be used to solve major problems about finitely presented A-free groups. Besides surveying results known up to date we draw many new corollaries concerning structural and algorithmic properties of such groups. [ABSTRACT FROM AUTHOR]

In this paper, we consider an extension of ordinary linear programming (LP) that adds weighted logarithmic barrier terms for some variables. The resulting problem generalizes both LP and the problem of finding the weighted analytic centre of a polytope. We show that the problem has a dual of the same form and give complexity results for several different interior-point algorithms. We obtain an improved complexity result for certain cases by utilizing a combination of the volumetric and logarithmic barriers. As an application, we consider the complexity of solving the Eisenberg–Gale formulation of a Fisher equilibrium problem with linear utility functions. [ABSTRACT FROM PUBLISHER]

The impact of this paper is twofold. First, we study convergence rates of the iteratively regularized Gauss-Newton (IRGN) algorithm with a linear penalty term under a generalized source assumption and show how the regularizing properties of new iterations depend on the solution smoothness. Secondly, we introduce an adaptive IRGN procedure, which is investigated under a relaxed smoothness condition. The introduction and analysis of a more general penalty term are of great importance since, apart from bringing stability to the numerical scheme designed for solving a large class of applied inverse problems, it allows us to incorporate various types of a priori information available on the model. Both a priori and a posteriori stopping rules are investigated. For the a priori stopping rule, optimal convergence rates are derived. A numerical example illustrating convergence rates is considered [ABSTRACT FROM AUTHOR]

Büchi's square problem asks if there exists a positive integer M such that all x1, ..., xM ∈ ℤ satisfying the equations $x_{r-2}^2-2x_{r-1}^2+x_{r}^2 = 2$ for all 3 ≤ r ≤ M must also satisfy $x_r^2 = (x+r)^2$ for some integer x and for all 1 ≤ r ≤ M. Hensley's problem asks if there exists a positive integer M such that, for any integers ν and a, if (ν + r)2 - a is a square for all 1 ≤ r ≤ M, then a = 0. It is not difficult to see that a positive answer to Hensley's problem implies a positive answer to Büchi's square problem. One can ask a more general version of Hensley's problem by replacing the square power by an nth power for any integer n ≥ 2 which is called Hensley's problem for nth powers. In this paper, we will study Hensley's problem for nth powers over function fields of any characteristic. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. DeMol (2004) . This generalization is useful for solving many practical problems in which more than one constraint are involved. In this regard, we will conclude the findings of many papers (most of which are on image processing) from this generalization. It is hoped that the approach proposed in this paper will be a suitable reference for some applied works where multi-frames, multi-wavelets, or multi-constraints are present in linear inverse problems. [Copyright &y& Elsevier]

Abstract: In this paper, we study the numerical behavior of the semismooth and smoothing Newton methods for solving Pareto eigenvalue problem of the formwhere (A, B) is a pair of possibly asymmetric matrices of order n. Such an eigenvalue problem arises in mechanics and in other areas of applied mathematics. By using the (smoothing) Fischer-Burmeister NCP function and the normalization condition e T x =1, the Pareto eigenvalue problem can be converted into a equivalent semismooth (or smoothing) system of equations, where e =(1,…,1) T . Then a semismooth (or smoothing) Newton algorithm is designed to solve such a semismooth (or smoothing) system of equations. Some numerical results are reported in the paper, which indicates that the proposed algorithms are very effective. [Copyright &y& Elsevier]

Recently, Xiao et al. proposed a nonsmooth equations-based method to solve the l₁-norm minimization problem (2011). The advantage of this method is its simplicity and lower storage. In this paper, based on new nonsmooth equations reformulation, we investigate new nonsmooth equations-based algorithms for solving l₁-norm minimization problems. Under mild conditions, we show that the proposed algorithms are globally convergent. The preliminary numerical results demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the properties of permutation binomials over finite fields and the possibility to use permutation binomials as encryption functions. We present an algorithm for enumeration of permutation binomials. Using this algorithm, all permutation binomials for finite fields up to order 15000 were generated. Using this data, we investigate the groups generated by the permutation binomials and discover that over some finite fields $$ {{\mathbb F}_q} $$, every bijective function on [1.. q − 1] can be represented as a composition of binomials. We study the problem of generating permutation binomials over large prime fields. We also prove that a generalization of RSA using permutation binomials is not secure. Bibliography: 9 titles. [ABSTRACT FROM AUTHOR]

Abstract: “Clarithmetic” is a generic name for formal number theories similar to Peano arithmetic, but based on computability logic instead of the more traditional classical or intuitionistic logics. Formulas of clarithmetical theories represent interactive computational problems, and their “truth” is understood as existence of an algorithmic solution. Imposing various complexity constraints on such solutions yields various versions of clarithmetic. The present paper introduces a system of clarithmetic for polynomial time computability, which is shown to be sound and complete. Sound in the sense that every theorem T of the system represents an interactive number-theoretic computational problem with a polynomial time solution and, furthermore, such a solution can be efficiently extracted from a proof of T. And complete in the sense that every interactive number-theoretic problem with a polynomial time solution is represented by some theorem T of the system. The paper is written in a semitutorial style and targets readers with no prior familiarity with computability logic. [Copyright &y& Elsevier]

The solution of multidimensional Lipschitz optimization problem requires a lot of computing time and memory resources. Parallel OpenMP and MPI versions of branch and bound algorithm with simplicial partitions and Lipschitz bounds were created, investigated and compared in this paper. The efficiency of the developed parallel algorithms is investigated by solving multidimensional test problems for global optimization. [ABSTRACT FROM AUTHOR]

Detection of copositivity plays an important role in combinatorial and quadratic optimization. Recently, an algorithm for copositivity detection by simplicial partition has been proposed. In this paper, we develop an improved depth-first simplicial partition algorithm which reduces memory requirements significantly and therefore enables copositivity checks of much larger matrices - of size up to a few thousands instead of a few hundreds. The algorithm has been investigated experimentally on a number of MaxClique problems as well as on generated random problems. We present numerical results showing that the algorithm is much faster than a recently published linear algebraic algorithm for copositivity detection based on traditional ideas - checking properties of principal sub-matrices. We also show that the algorithm works very well for solving MaxClique problems through copositivity checks. [ABSTRACT FROM AUTHOR]

In this paper we consider global optimization algorithms based on multiple local searches for the Molecular Distance Geometry Problem (MDGP). Three distinct approaches (Multistart, Monotonic Basin Hopping, Population Basin Hopping) are presented and for each of them a computational analysis is performed. The results are also compared with those of two other approaches in the literature, the DGSOL approach (Moré, Wu in J. Glob. Optim. 15:219–234, ) and a SDP based approach (Biswas et al. in An SDP based approach for anchor-free 3D graph realization, Technical Report, Operations Research, Stanford University, ). [ABSTRACT FROM AUTHOR]

Discrete approximations to chance constrained and mixed-integer two-stage stochastic programs require moderately sized scenario sets. The relevant distances of (multivariate) probability distributions for deriving quantitative stability results for such stochastic programs are ℬ-discrepancies, where the class ℬ of Borel sets depends on their structural properties. Hence, the optimal scenario reduction problem for such models is stated with respect to ℬ-discrepancies. In this paper, upper and lower bounds, and some explicit solutions for optimal scenario reduction problems are derived. In addition, we develop heuristic algorithms for determining nearly optimally reduced probability measures, discuss the case of the cell discrepancy (or Kolmogorov metric) in some detail and provide some numerical experience. [ABSTRACT FROM AUTHOR]

The paper provides some theoretical results on the analysis of the expected time needed by a class of Ant Colony Optimization algorithms to solve combinatorial optimization problems. A part of the study refers to some general results on the expected runtime of the considered class of algorithms. These results are then specialized to the case of pseudo-Boolean functions. In particular, three well known functions and a combination of two of them are considered: the OneMax, the Needle-in-a-Haystack, the LeadingOnes, and the OneMax-Needle-in-a-Haystack. The results obtained for these functions are also compared to those from the well-investigated (1+1)-Evolutionary Algorithm. The results shed light on a suitable parameter choice for the considered class of algorithms. Furthermore, it turns out that for two of the four studied problems, the expected runtime for the considered class, expressed in terms of the problem size, is of the same order as that for (1+1)-Evolutionary Algorithm. For the other two problems, the results are significantly in favour of the considered class of Ant Colony Optimization algorithms. [ABSTRACT FROM AUTHOR]

The general single-period optimal portfolio selection problem with a risk-free asset can be solved by a two-stage approach In the first stage, one solves a certain fractional program, and in the second, a simple stochastic program with one single variable. This paper proposes a parametric approach for the solution of the fractional program wa its equivalent linear complementarity formulation. In the latter part of the paper, we specialize the proposed method to a specific model of the portfolio problem with upper bounds and outline how the method can take advantage of the special structure arising from the model Finally, we report some computational results and a brief comparison between our method and Lemke's algorithm. [ABSTRACT FROM AUTHOR]

The Linear Programming Problem is by far the most widely used optimization model. Its impact on economic and government modeling is immense. The Simplex Method for solving the Linear Programming (LP) Problem, due to George Dantzig, has been an extremely efficient computational tool for almost four decades. The method has been the subject of intense investigations for many years, but some major aspects of its behavior are not fully understood yet. The purpose of this paper is to survey the body of knowledge on the efficiency of the Simplex Method, from both practical and theoretical points of view. Adopting the number of iterations (pivot steps) as the yardstick for efficiency, we survey four aspects of the issue: 1. Reports on practical experience of the method's performance on real-life LP problems. 2. Results on controlled (Monte-Carlo) experiments solving LP problems which were randomly generated according to some predetermined distributions. 3. Complexity results, including theoretical analyses on both upper and lower bounds for the performance of the Simplex as well as non-Simplex algorithms for LP. 4. Results of recent theoretical studies using probabilistic analysis to derive bounds on the average behavior of the Simplex Method. We discuss the consequences and limitations of the various studies. Special emphasis is given to open questions. [ABSTRACT FROM AUTHOR]

Multiobjective mathematical programming has been one of the fastest growing areas of OR/MS during the last 15 years. This paper presents: 1. some reasons for the rapidly growing increase in interest in multiobjective mathematical programming. 2. a discussion of the advantages and disadvantages of the three general approaches (articulation of the decision maker's preference structure over the multiple objectives prior to, during, or after the optimization) towards multiobjective mathematical programming, 3. a nontechnical overview of many of the specific solution techniques for multiobjective mathematical programming, and 4. a discussion of important areas for further research. The overview concentrates on those techniques which require an articulation of the decision maker's preference structure either during or after the optimization, since these are the areas where most of the recent research has been conducted. It differs from previous overviews in that, in addition to the timing of the elicited preference information, the techniques are also classified according to the types of decision variables contained in the model (i.e., only continuous decision variables, or at least some discrete decision variables). In addition, the types of preference information (e.g., a ranking of outcomes) required of the various techniques are also discussed. [ABSTRACT FROM AUTHOR]

This paper addresses the dynamic lot sizing problem of a Wagner-Whitin type in which the transportation mode as well as the order size of a deteriorating product are considered simultaneously. The problem is presented in a forward formulation. An algorithm is developed which utilizes properties of the optimal solution and planning horizon procedure. An actual case involving palm oil industry is solved and the algorithm is shown to be efficient in computation. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for the solution of the knapsack problem. The method involves searching the nodes of a tree along a single branch at a time. The algorithm eliminates the computational drawbacks inherent in the usual branch and bound schemes. [ABSTRACT FROM AUTHOR]