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In this paper, we address the problem of determining the optimum antenna configuration for a multi-input multi-output (MIMO) system at any given signal-to-noise ratio (SNR). We used two-level differential evolution (DE) algorithm that finds both an appropriate expression among a set of candidate expressions within the list of the optimization software used, and the parameter values ( coefficients) belonging to the selected expression. The results of the proposed expression are compared with the results of high SNR approximation, asymptotic approach and optimum antenna number ratios. It is shown that the numerical outcomes produced by the new expression exhibit very good agreement with the optimum antenna number ratios, and this agreement is almost independent of the specific value of SNR. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a novel decomposition method based on user-preference and developed a variation of the decomposition based multi-objective optimization algorithm (MOEA/D) targeting only solutions in a small region of the Pareto-front defined by the preference information supplied by the decision maker (DM). This is particularly advantageous for solving multi-objective optimization problems (MOPs) with more than 3 objectives, i.e., many-objective optimization problems (MaOPs). As the number of objectives increases, the ability of an EMO algorithm to approximate the entire Pareto front (PF) is rapidly diminishing. In this paper, we first propose a novel scalarizing function making use of a series of new reference points derived from a reference point specified by the DM in the preference model. Based on this scalarizing function, we then develop a user-preference-based EMO algorithm, namely R-MOEA/D. One key merit of R-MOEA/D is that it does not rely on an estimation of the ideal point, which may impact significantly the performances of state-of-the-art decomposition based EMO algorithms. Our experimental results on multi-objective and many-objective benchmark problems have shown that R-MOEA/D provides a more direct and efficient search towards the preferred PF region, resulting in competitive performances. In an interactive setting when the DM changes the reference point during optimization, R-MOEA/D has a faster response speed and performance than the compared algorithms, showing its robustness and adaptability to changes of the preference model. Furthermore, the effectiveness of R-MOEA/D is verified on a real-world problem of reservoir flood control operations. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the inequality constrained vector problem with continuously Fréchet differentiable objective functions and constraints. We obtain second-order necessary optimality conditions of Karush-Kuhn-Tucker type for weak efficiency. A new second-order constraint qualification of Zangwill type is introduced. It is applied in the optimality conditions. Some connections with other constraint qualifications are established. [ABSTRACT FROM AUTHOR]

This paper introduces novel numerical solution strategies for generalized semi-infinite optimization problems (GSIP), a class of mathematical optimization problems which occur naturally in the context of design centering problems, robust optimization problems, and many fields of engineering science. GSIPs can be regarded as bilevel optimization problems, where a parametric lower-level maximization problem has to be solved in order to check feasibility of the upper level minimization problem. The current paper discusses several strategies to reformulate this class of problems into equivalent finite minimization problems by exploiting the concept of Wolfe duality for convex lower level problems. Here, the main contribution is the discussion of the non-degeneracy of the corresponding formulations under various assumptions. Finally, these non-degenerate reformulations of the original GSIP allow us to apply standard nonlinear optimization algorithms. [ABSTRACT FROM AUTHOR]

This paper points out that meta-heuristics should have not only robustness and adaptability to problems with different structure but also adjustability of parameters included in their algorithms. Particle swarm optimization (PSO), whose concept began as a simulation of a simplified social milieu, is known as one of the most powerful optimization methods for solving nonconvex continuous optimization problems. Then, in order to improve adjustability, a new parameter is introduced into PSO on the basis of the proximate optimality principle (POP). In this paper, we propose adaptive PSO and the effectiveness and the feasibility of the proposed approach are demonstrated on simulations using some typical nonconvex optimization problems. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 151(3): 41–49, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20077 [ABSTRACT FROM AUTHOR]

The purpose of this paper is to take stock of what is known and to suggest some conceptual foundations for future progress in the areas of postoptimality analysis and parametric optimization techniques for integer programming. [ABSTRACT FROM AUTHOR]

This paper considers the problem of finding minimal length tree networks on the unit sphere Φ of a given point set (V) where distance is measured along great circular arcs. The related problems of finding a Steiner Minimal Tree SMT (V) and of finding a Minimum Spanning Tree MST(V) are treated through a simplicial decomposition technique based on computing the Delaunay Triangulation DT (V) and the Voronoi Diagram VD(V) of the given point set. O (N log N) algorithms for computing DT(V), VD(V), and WST(V) as well as an O(N log N) heuristic for finding a sub-optimal SMT(V) solution are presented, together with experimental results for randomly distributed points on Φ. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to give a survey of methods, partly derived by the author in joint work with other researchers, concerning the problem of constructing e-optimal strategies for partially observable MDPs. The methods basically consist in transforming the problem into one of approximation: Starting from the original problem a sequence of approximating problems is constructed such that: (i) For each approximating problem an optimal strategy can actually be computed, (ii) Given ϵ » 0, there exists an approximating problem such that the optimal strategy for the latter is ϵ-optimal for the original problem. [ABSTRACT FROM AUTHOR]

The paper suggests a new-to the best of the author's knowledge-characterization of decisions, which are optimal in the multi-objective optimization problem with respect to a definite proper preference cone, a Euclidean cone with a prescribed angular radius. The main idea is to use the angle distances between the unit vector and points of utility space. A necessary and sufficient condition for the optimality in the form of an equation is derived. The first-order necessary optimality conditions are also obtained. [ABSTRACT FROM AUTHOR]

In this paper, an efficient computation method is developed for solving a general class of minmax optimal control problems, where the minimum deviation from the violation of the continuous state inequality constraints is maximized. The constraint transcription method is used to construct a smooth approximate function for each of the continuous state inequality constraints. We then obtain an approximate optimal control problem with the integral of the summation of these smooth approximate functions as its cost function. A necessary condition and a sufficient condition are derived showing the relationship between the original problem and the smooth approximate problem. We then construct a violation function from the solution of the smooth approximate optimal control problem and the original continuous state inequality constraints in such a way that the optimal control of the minmax problem is equivalent to the largest root of the violation function, and hence can be solved by the bisection search method. The control parametrization and a time scaling transform are applied to these optimal control problems. We then consider two practical problems: the obstacle avoidance optimal control problem and the abort landing of an aircraft in a windshear downburst. [ABSTRACT FROM AUTHOR]

During the last years nature inspired intelligent techniques have become attractive for analyzing large data sets and solving complex optimization problems. In this paper, one of the most interesting of them, the Ant Colony Optimization (ACO), is used for the construction of a hybrid algorithmic scheme which effectively handles the Pap Smear Cell classification problem. This algorithmic approach is properly combined with a number of nearest neighbor based approaches for performing the requested classification task, through the solution of the so-called optimal feature subset selection problem. The proposed complete algorithmic scheme is tested in two sets of data. The first one consists of 917 images of pap smear cells and the second set consists of 500 images, classified carefully by expert cyto-technicians and doctors. Each cell is described by 20 numerical features, and the cells fall into seven (7) classes, four (4) representing normal cells and three (3) abnormal cases. Nevertheless, from the medical diagnosis viewpoint, a minimum requirement corresponds to the general two-class problem of correct separation between normal from abnormal cells. [ABSTRACT FROM AUTHOR]

In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures, recently introduced by Föllmer and Schied (2002). The dynamic optimization problem of finding a self-financing strategy that minimizes the convex risk of the shortfall can be split into a static optimization problem and a representation problem. It follows that the optimal strategy consists in superhedging the modified claim [image omitted] , where H is the payoff of the claim and [image omitted] is a solution of the static optimization problem, an optimal randomized test. In this paper, necessary and sufficient optimality conditions are deduced for the static problem using convex duality methods. The solution of the static optimization problem turns out to be a randomized test with a typical 0-1-structure. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a definition of generalized convexlike functions (preconvexlike functions). Then, under the weakened convexity, we study vector optimization problems in Hausdorff topological linear spaces. We establish some generalized Motzkin theorems of the alternative. By use of these theorems of the alternative, we obtain some Lagrangian multiplier theorems. A saddle-point theorem and a scalarization theorem are also derived. [ABSTRACT FROM AUTHOR]

In this paper, we study the relationship between bilevel optimization and multicriteria optimization. Given a bilevel optimization problem, we introduce an order relation such that the optimal solutions of the bilevel problem are the nondominated points with respect to the order relation. In the case where the lower-level problem of the bilevel optimization problem is convex and continuously differentiable in the lower-level variables, this order relation is equivalent to a second, more tractable order relation. Then, we show how to construct a (nonconvex) cone for which we can prove that the nondominated points with respect to the order relation induced by the cone are also nondominated points with respect to any of the two order relations mentioned before. We comment also on the practical and computational implications of our approach. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to extend, as much as possible, the modern theory of condition numbers for conic convex optimization: ... to the more general nonconic format: ... where P is any closed convex set, not necessarily a cone, which we call the ground-set. Although any convex problem can be transformed to conic form, such transformations are neither unique nor natural given the natural description of many problems, thereby diminishing the relevance of data-based condition number theory. Herein we extend the modern theory of condition numbers to the problem format (GPd). As a byproduct, we are able to state and prove natural extensions of many theorems from the conic-based theory of condition numbers to this broader problem format. [ABSTRACT FROM AUTHOR]

We introduce a new barrier-type function which is not, a barrier function in the usual sense: it has finite value at the boundary of the feasible region. Despite this, the iteration bound of a large-update interior-point method based on this function is shown to be O(square root of n (log n) log n/epsilon), which is as good as tile currently best known bound for large update methods. The recently introduced properly of exponential convexity for the kernel function underlying the barrier function, as well as the strong convexity of the kernel function, are crucial in the analysis. [ABSTRACT FROM AUTHOR]

The paper presents an analytical description of a state-dependent assignment policy, where different assignments of attributes to objects are employed under different states. Various considerations, other than optimizing an objective function, present themselves for such cases—for example, the existence of groups of assignees with certain levels of intragroup assignment uniformity, the stability of the policy over states, the presence of a revealed preference ordering of the assignments, and others. An approach towards a quantitative treatment of such features of a state-dependent assignment policy is discussed, and in particular a uniformity measure is defined and its properties are investigated. Potential uses of the model are suggested for urban emergency services, questionnaire analysis, task allocation, medical diagnosis, and dynamic computer program behavior. Three implementations for questionnaire analysis are reported. [ABSTRACT FROM AUTHOR]

In this paper, two different decision models for the planning of highway pavement improvements are presented. In the first model, we want to get a prescribed improvement in the state of the highway network with minimal agency cost. In the second model, a given amount of money is distributed between the highway sections in different states in such a way that the achieved improvements should be the best in some sense. The first model helps the administration in the estimation of the necessary cost for the annual highway improvements. The second model in addition gives an objective tool to the administration for the distribution of the total amount of money between the different regions of the country. We present the construction of the models in detail. Both of them use Markov transition probabilities according to the states of the highway sections and produce a special structure, large-scale, linear programming problem. Some numerical results are presented on the data from Hungarian highways. [ABSTRACT FROM AUTHOR]

This work presents an algorithm for multiobjective optimization that is structured as: (i) a descent direction is calculated, within the cone of descent and feasible directions, and (ii) a multiobjective line search is conducted over such direction, with a new multiobjective golden section segment partitioning scheme that directly finds line-constrained efficient points that dominate the current one. This multiobjective line search procedure exploits the structure of the line-constrained efficient set, presenting a faster compression rate of the search segment than single-objective golden section line search. The proposed multiobjective optimization algorithm converges to points that satisfy the Kuhn-Tucker first-order necessary conditions for efficiency (the Pareto-critical points). Numerical results on two antenna design problems support the conclusion that the proposed method can solve robustly difficult nonlinear multiobjective problems defined in terms of computationally expensive black-box objective functions. [ABSTRACT FROM AUTHOR]

Two basic disadvantages of the symmetric rank one (SR1) update are that the SR1 update may not preserve positive definiteness when starting with a positive definite approximation and the SR1 update can be undefined. A simple remedy to these problems is to restart the update with the initial approximation, mostly the identity matrix, whenever these difficulties arise. However, numerical experience shows that restart with the identity matrix is not a good choice. Instead of using the identity matrix we used a positive multiple of the identity matrix. The used positive scaling factor is the optimal solution of the measure defined by the problem—maximize the determinant of the update subject to a bound of one on the largest eigenvalue. This measure is motivated by considering the volume of the symmetric difference of the two ellipsoids, which arise from the current and updated quadratic models in quasi-Newton methods. A replacement in the form of a positive multiple of the identity matrix is provided for the SR1 update when it is not positive definite or undefined. Our experiments indicate that with such simple initial scaling the possibility of an undefined update or the loss of positive definiteness for the SR1 method is avoided on all iterations. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we use the third order shear deformation theory of Reddy [Reddy JN. Mechanics of laminated composite plates and shells. CRC Press; 2004] with a meshless numerical method to analyze the static deformation of composite plates and shells. Numerical results are compared with Navier solutions in various examples. The meshless collocation method based on radial basis functions requires a user-defined shape parameter than can compromise the quality of the solution when poorly chosen. To improve the choice of this shape parameter, we apply an optimization technique based on the leave-one-out cross validation analysis to obtain the shape parameter in a given interval. The results obtained were significantly better than those produced with a user-defined shape parameter. [Copyright &y& Elsevier]

Abstract: Optimization design is the most important key technique of Air-breathing Hypersonic Cruise Vehicle (HCV). To improve the design level and get better integrated performances of HCV, this paper researches the integrated optimization design method of waverider hypersonic cruise vehicle. In the optimization design, Multi-Objective Genetic Algorithms (MOGA) is selected as the optimization algorithm, and the shape parameters of aircraft are as design variables. Some performances, such as aerodynamics, aeroheating, radar cross section (RCS), airframe/scramjet integration, and volume of airframe, trimmed characteristic, static stability and maneuverability at cruise phase are selected as the objectives. When the optimization process finishes, the Pareto front side is got, in which many Pareto solutions whose integrated performances are more excellent than basic configuration are found. According to the design idea, we choose a Pareto solution from the Pareto front side as the recommended shape configuration for further research. To validate the aerodynamics of recommended configuration, wind tunnel test is done. And the comparison results show that the optimization design is successful. [Copyright &y& Elsevier]

Abstract: Recently, genetic algorithms (GA) and particle swarm optimization (PSO) technique have attracted considerable attention among various modern heuristic optimization techniques. The GA has been popular in academia and the industry mainly because of its intuitiveness, ease of implementation, and the ability to effectively solve highly non-linear, mixed integer optimization problems that are typical of complex engineering systems. PSO technique is a relatively recent heuristic search method whose mechanics are inspired by the swarming or collaborative behavior of biological populations. Since the two approaches are supposed to find a solution to a given objective function but employ different strategies and computational effort, it is appropriate to compare their performance. This paper presents the application and performance comparison of PSO and GA optimization techniques, for flexible ac transmission system (FACTS)-based controller design. The design objective is to enhance the power system stability. The design problem of the FACTS-based controller is formulated as an optimization problem and both PSO and GA optimization techniques are employed to search for optimal controller parameters. The performance of both optimization techniques in terms of computational effort, computational time and convergence rate is compared. Further, the optimized controllers are tested on a weakly connected power system subjected to different disturbances over a wide range of loading conditions and parameter variations and their performance is compared with the conventional power system stabilizer (CPSS). The eigenvalue analysis and non-linear simulation results are presented and compared to show the effectiveness of both the techniques in designing a FACTS-based controller, to enhance power system stability. [Copyright &y& Elsevier]

Abstract: In this paper, two conjugate dual problems based on weak efficiency to a constrained vector optimization problem are introduced. Some inclusion relations between the dual objective mappings and the properties of the Lagrangian maps and their saddle points for primal problem are discussed. Gap functions for a vector equilibrium problem are established by using the weak and strong duality. [Copyright &y& Elsevier]

Abstract: An improved particle swarm optimization (IPSO) is proposed in this paper. In the new algorithm, a population of points sampled randomly from the feasible space. Then the population is partitioned into several sub-swarms, each of which is made to evolve based on particle swarm optimization (PSO) algorithm. At periodic stages in the evolution, the entire population is shuffled, and then points are reassigned to sub-swarms to ensure information sharing. This method greatly elevates the ability of exploration and exploitation. Simulations for three benchmark test functions show that IPSO possesses better ability to find the global optimum than that of the standard PSO algorithm. Compared with PSO, IPSO is also applied to identify the hydrologic model. The results show that IPSO remarkably improves the calculation accuracy and is an effective global optimization to calibrate hydrologic model. [Copyright &y& Elsevier]

Abstract: In this paper, we study the positive almost periodic solutions for a class of almost periodic Lotka-Volterra type system with delays and feedback controls. Applying Schauder’s fixed point theorem, a criterion on the existence of the positive almost periodic solution of the system is obtained. Our new criterion, which improves and generalizes some well known results, can be easily checked. [Copyright &y& Elsevier]

Abstract: Packing and decomposition of combinatorial objects such as graphs, digraphs, and hypergraphs by smaller objects are central problems in combinatorics and combinatorial optimization. Their study combines probabilistic, combinatorial, and algebraic methods. In addition to being among the most fascinating purely combinatorial problems, they are often motivated by algorithmic applications. There is a considerable number of intriguing fundamental problems and results in this area, and the goal of this paper is to survey the state-of-the-art. [Copyright &y& Elsevier]

Abstract: The optimal design of digital systems can be complicated by non-linearities that arise from discrete optimization processes, and conventional methods often attain suboptimal results. Quantum computing may be an interesting technology to overcome that issue, but so far its effectiveness has been addressed from a most abstract perspective. This paper tackles the digital-design problem from a practical viewpoint, and derives universal criteria for assessing whether, and how much, quantum technologies can improve over conventional methods: the advantage is expressed in terms of computing time required to attain optimal design. The general framework is applied to two modern problems, i.e., training support vector machines and building vector quantizers. The experimental comparison between conventional and quantum methods addresses the actual performances of the designed systems in the case of vector quantization. Empirical evidence matches theoretical expectations and supports the design method’s consistency. [Copyright &y& Elsevier]

Abstract: In this paper we present a novel method for the numerical solution of dynamic optimization problems. After obtaining a first solution at a coarse resolution of the control profiles with a direct sequential approach, the structure of the control profiles is analyzed for possible switching times and arcs. Subsequently, the problem is reformulated automatically and solved as a multi-stage problem, with each stage corresponding to a potential arc. Order and resolution of the control parameterization are adapted to the type of the particular arc. By means of some case studies we show that accurate solutions with only few degrees of freedom can be obtained. [Copyright &y& Elsevier]

Abstract: This paper considers the mixed sensitivity optimization problem for a class of infinite-dimensional stable plants. This problem is reducible to a two- or one-block control problem with structured weighting functions. We first show that these weighting functions violate the genericity assumptions of existing Hamiltonian-based solutions such as the well-known Zhou–Khargonekar formula. Then, we derive a new closed form formula for the computation of the optimal performance level, when the underlying plant structure is specified by a pseudorational transfer function. [Copyright &y& Elsevier]

A local search framework for the (undirected) Rural Postman Problem (RPP) is presented in this paper. The framework allows local search approaches that have been applied successfully to the well-known Travelling Salesman Problem also to be applied to the RPP. New heuristics for the RPP, based on this framework, are introduced and these are capable of solving significantly larger instances of the RPP than have been reported in the literature. Test results are presented for a number of benchmark RPP instances in a bid to compare efficiency and solution quality against known methods. [ABSTRACT FROM AUTHOR]

A new multi-step curve search method for unconstrained minimization problems is proposed. The convergence of the algorithm is proved under some mild conditions. The linear convergence rate is also investigated when the objective function is uniformly convex. This method uses previous multi-step iterative information and curve search rule to generate new iterative points. Using more previous iterative information and curve search rule can make the new method converge more stably than traditional descent methods and be suitable to solve large scale problems. [ABSTRACT FROM AUTHOR]

The paper studies the problem of determining the measurements of a given number of sizes of apparel so as to maximize expected sales or minimize an index of discomfort. It develops general necessary conditions for optimization in one control body dimension and calculates optimal sizes for the special case where the population distribution is normal. [ABSTRACT FROM AUTHOR]

This paper presents a new algorithm for solving the assignment problem. The algorithm is based on a scheme of relaxing the given problem into a series of simple network flow (transportation) problems for each of which an optimal solution can be easily obtained The algorithm is thus seen to be able to take advantage of the nice properties in both the primal and the dual approaches for the assignment problem. The computational bound for the algorithm is shown to be O(n[sup 3]) and the average computation time is better than most of the specialized assignment algorithms. [ABSTRACT FROM AUTHOR]

We discuss the complexity of a class of highly structured global optimization problems, namely the maximization of separable functions, with each one-dimensional component convex and nondecreasing, over polytopes defined by a 0-1 constraint matrix with at most two variables involved in each constraint. In particular, we prove some inapproximability and approximability results. [ABSTRACT FROM AUTHOR]

We consider single-carrier and single-user transmissions over a frequency-selective channel. We address the problem of joint estimation of the channel and the carrier frequency offset using a known training sequence (TS). Since in general the TS that is optimum for CFO estimation is not optimum for channel estimation, here we design the TS to minimize the mean-square error on the soft estimates of the data symbols obtained using a Wiener equalizer after CFO compensation. Our design results apply to the general scenarios of correlated and/or Ricean channel taps. Simulations measuring the bit error rate show an interesting gain when using the proposed training schemes in lieu of standard schemes. [ABSTRACT FROM AUTHOR]

The classes of reward-risk optimization problems that arise from different choices of reward and risk measures are considered. In certain examples the generic problem reduces to linear or quadratic programming problems. An algorithm based on a sequence of convex feasibility problems is given for the general quasi-concave ratio problem. Reward-risk ratios that are appropriate in particular for non-normal assets return distributions and are not quasi-concave are also considered. [ABSTRACT FROM AUTHOR]

The article presents information on tabu search (TS), a mathematical optimization method. It mentions that a starting premise of TS is that intelligent inhibition plays a critical role in making effective use of memory. It is worth stressing that discoveries about effective uses of memory within the search methods may provide clues about strategies that humans are adept at employing.

We consider a continuous optimization model of a one-dimensional connected transportation network under the assumption that the cost of transportation with the use of network is negligible in comparison with the cost of transportation without it. We investigate the connections between this problem and its important special case, the minimization of the average distance functional. For the average distance minimization problem we formulate a number of conditions for the partial geometric regularity of a solution in ℝn with an arbitrary dimension n ⩾ 2. The corresponding results are applied to solutions to the general optimization problem. Bibliography: 26 titles. Illustrations: 1 Figure. [ABSTRACT FROM AUTHOR]

The multidimensional assignment problem (MAPs) is a higher dimensional version of the standard linear assignment problem. Test problems of known solution are useful in exercising solution methods. A method of generating an axial MAP of controllable size with a known unique solution is presented. Certain characteristics of the generated MAPs that determine realism and difficulty are investigated. [ABSTRACT FROM AUTHOR]

Traveling Salesman, Steiner Tree, and many other famous geometric optimization problems are NP-hard. Since we do not expect to design efficient algorithms that solve these problems optimally, researchers have tried to design approximation algorithms, which can compute a provably near-optimal solution in polynomial time.We survey such algorithms, in particular a new technique developed over the past few years that allows us to design approximation schemes for many of these problems. For any fixed constant c> 0, the algorithm can compute a solution whose cost is at most (1 + c) times the optimum. (The running time is polynomial for every fixed c> 0, and in many cases is even nearly linear.) We describe how these schemes are designed, and survey the status of a large number of problems. [ABSTRACT FROM AUTHOR]

We study the on-line problem of assigning tasks to identical machines whose regular working time — assumed to be unitary — can be extended. If the tasks assigned to a machine do not exceed the regular working time, then the working time of the machine is considered to be 1; otherwise, it is the completion time of the last task assigned to the machine. Each incoming task has to be assigned immediately to a machine and the assignment cannot be changed later. The objective is to minimize the sum of the working times of the machines. Since the regular working time of the machines can be seen as a given capacity, the problem can also be described through the bin packing terminology: the machines are viewed as bins and the tasks as items. A lower bound of 7/6 on the worst-case relative error of any on-line algorithm is shown. Then it is shown that a list scheduling heuristic which assigns the incoming task to the machine with smallest current load has worst-case error equal to 5/4. The bound is improved to 1.228 by a new algorithm which tends to load the partially loaded machines, as long as this does not cause an increase of the working time by more than a fixed and appropriately chosen quantity x » 0. [ABSTRACT FROM AUTHOR]