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Clustering is a common task in data mining for constructing well-separated groups (clusters) from a large set of data points. The balanced minimum sum-of-squares clustering problem is a variant of the classic minimum sum-of-squares clustering (MSSC) problem and arises from broad real-life applications where the cardinalities of any two clusters differ by at most one. This study presents the first memetic algorithm for solving the balanced MSSC problem. The proposed algorithm combines a backbone-based crossover operator for generating offspring solutions and a responsive threshold search that alternates between a threshold-based exploration procedure and a descent-based improvement procedure for improving new offspring solutions. Numerical results on 16 real-life datasets show that the proposed algorithm competes very favorably with several state-of-the-art methods from the literature. Key components of the proposed algorithm are investigated to understand their effects on the performance of the algorithm.

We consider relative or subjective optimization problems where the goal function and feasible set are dependent on the current state of the system under consideration. In general, they are formulated as quasi-equilibrium problems, hence finding their solutions may be rather difficult. We describe a rather general class of relative optimization problems in metric spaces, which in addition depend on the starting state. We also utilize quasi-equilibrium type formulations of these problems and show that they admit rather simple descent solution methods. This approach gives suitable trajectories tending to a relatively optimal state. We describe several examples of applications of these problems. Preliminary results of computational experiments confirmed efficiency of the proposed method.

This article presents a new and fast indirect method for solving fuel-optimal descent trajectories in the gravitational field of an irregularly-shaped asteroid. The costates associated with a two-impulse descent trajectory are used as approximate costates for the costate initialization of a finite-thrust fuel-optimal trajectory planning problem. The approximate solutions of the initial velocity and mass costates are given in analytical forms. A simple shooting equation is derived to solve the approximate position costates. The two-impulsive descent trajectory is solved by an irregular gravitational Lambert solver. Based on the Lambert solver and approximate costates, an algorithm is proposed for trajectory optimization with varying time of flight. The effectiveness and efficiency of the proposed method are tested through the simulation of landing on the asteroid 433 Eros. Additionally, a computationally efficient approximate model is employed to replace the polyhedral model, which greatly improves the computational speed and enhance the ability to address uncertainties.

In this study, we focus mainly on the problem of finding the minimum-length path through a set of circular regions by a fixed-wing unmanned aerial vehicle. Such a problem is referred to as the Dubins traveling salesman problem with neighborhoods (DTSPN). Algorithms developed in the literature for solving DTSPN either are computationally demanding or generate low-quality solutions. To achieve a better trade-off between solution quality and computational cost, an efficient gradient-free descent method is designed. The core idea of the descent method is to decompose DTSPN into a series of subproblems, each of which consists of finding the minimum-length path of a Dubins vehicle from a configuration to another configuration via an intermediate circular region. By analyzing the geometric properties of the subproblems, we use a bisection method to solve the subproblems. As a result, the descent method can efficiently address DTSPN by successively solving a series of subproblems. Finally, several numerical experiments are carried out to demonstrate the descent method in comparison with several existing algorithms.

In this paper, we suggest a descent modification of the conjugate gradient method which converges globally provided that the exact minimization condition is satisfied. Preliminary numerical experiments on some benchmark problems show that the method is efficient and promising.

We propose a global optimization algorithm hybridizing a version of Bayesian global search with local minimization. The implementation of Bayesian algorithm is based on the simplician partition of the feasible region. Our implementation is free from the typical computational complexity of the standard implementations of Bayesian algorithms. The local minimization counterpart improves the efficiency of search in the indicated potential basins of global minimum. The performance of the proposed algorithm is illustrated by the results of a numerical experiment.

The notion and the theory of constructing planetary powered descent guidance laws based on fractional polynomials are introduced. Along the way a new perspective to the classical Apollo powered descent guidance designs is gained. As a foundation of this work, a theory is first developed on how to derive an explicit powered descent guidance law by selecting the feedback gains in a unique way in an implicit tracking guidance law. Then by employing a particular profile of the reference thrust acceleration in the tracking law with a special set of gains, a large family of powered descent guidance laws is obtained that offer the flexibility in trajectory shaping and thrust characteristics by two adjustable parameters. An equivalence theory is established to show that each in this family of guidance laws is actually the explicit guidance law from a fractional-polynomial thrust acceleration profile. This insight provides a perfect explanation to the predictable behavior and good targeting performance of these guidance laws. The well-known Apollo lunar descent guidance and E-guidance laws are revealed to be two members of this much broader class of fractional-polynomial powered descent guidance laws.

This paper proposes a discrete-time, distributed algorithm for multi-agent networks to achieve the minimum l1-norm solution to a group of linear equations known to possess a family of solutions. We assume each agent in the network knows only one equation and can communicate with only its neighbors. The algorithm is developed based on a combination of the projection-consensus idea and the sub-gradient descent method. Given the underlying network graph to be directed and strongly connected, we prove that the algorithm enables all agents to achieve a common minimum l1-norm solution. The major difficulty to be dealt with is the non-smooth nature of the norm and the lack of strict convexity of the associated relevant performance index.

Momentum method has been used extensively in optimizers for deep learning. Recent studies show that distributed training through K-step averaging has many nice properties. We propose a momentum method for such model averaging approaches. At each individual learner level traditional stochastic gradient is applied. At the meta-level (global learner level), one momentum term is applied and we call it block momentum. We analyze the convergence and scaling properties of such momentum methods. Our experimental results show that block momentum not only accelerates training, but also achieves better results.

Three-term conjugate gradient methods have attracted much attention for large-scale unconstrained problems in recent years, since they have attractive practical factors such as simple computation, low memory requirement, better descent property and strong global convergence property. In this paper, a hybrid three-term conjugate gradient algorithm is proposed and it owns a sufficient descent property, independent of any line search technique. Under some mild conditions, the proposed method is globally convergent for uniformly convex objective functions. Meanwhile, by using the modified secant equation, the proposed method is also global convergence without convexity assumption on the objective function. Numerical results also indicate that the proposed algorithm is more efficient and reliable than the other methods for the testing problems.

In this paper, we present a new modified inertial forward–backward algorithm for finding a common solution of the quasi-variational inclusion problem and the variational inequality problem in a q-uniformly smooth Banach space. The proposed algorithm is based on descent, splitting and inertial ideas. Under suitable assumptions, we prove that the sequence generated by the iterative algorithm converges strongly to the unique solution of the abovementioned problems. Numerical examples are also given to demonstrate our results.

In this paper, the distributed optimization problem over multi-cluster networks is considered. Different from the existing works, this paper studies the optimization algorithm under uncoordinated step sizes. More specifically, by combining a random sleep strategy and the round-robin communication among clusters, a new hierarchical algorithm is developed to solve the considered problem. In the proposed algorithm, the random sleep strategy enables each agent to independently choose either performing the projected subgradient descent, or keeping the previous estimate by a Bernoulli decision, based on which the step size of each agent is selected as an uncoordinated form that only relates to the independent Bernoulli decision variable. Technically, by introducing a key definition on the algorithm history, it is proven that the estimates of the proposed algorithm can converge to the optimal solution even with the uncoordinated step sizes. In addition, we also study the convergence performance of the proposed algorithm with simpler constant step sizes. In this case, it is proven that the random sleep strategy can efficiently improve the convergence accuracy of the algorithm. Finally, the theoretical findings are verified via simulation examples.

Descent & landing (D&L) on small planetary bodies are scientifically rewarding exploration missions but they are technically challenging due to the complex and poorly-known environment around those bodies. The standard guidance synthesis approach considers nominal conditions and applies optimal control theory to obtain guidance law gains, followed by intensive verification and validation. In this article, it is shown that the standard approach may yield gains that are not optimal once dispersions (and/or other optimality metrics) are taken into account and a tuning approach is then proposed based on a priori methodological system assessment. The proposed approach employs systematic high-fidelity simulations to generate trade-off maps. These maps can be generated by on ground operators based on the best estimated conditions and uploaded to the spacecraft as it approaches the target. The proposed systematic guidance tuning and resulting maps also provide a valuable understanding of the system dynamics towards the application of other industry-oriented tools such as structured Η∞ optimisation. It is shown that the proposed tuning enables propellant consumption reductions of around 40% compared to state-of-practice gain selections.

This paper presents an optimal control problem to analyze the efficacy of counter-terrorism tactics. We present an algorithm that efficiently combines the Minimum Principle of Pontryagin, the shooting method and the cyclic descent of coordinates. We also present a result that allows us to know a priori the steady state solutions. Using this technique we are able to choose parameters that reach a specific solution, of which there are two. Numerical examples are presented to illustrate the possibilities of the method. Finally, we study the sufficient conditions for optimality and suggest an improvement on the functional which also guarantees local optimality.

In the paper we propose an accelerated directional search method with non-euclidian prox-structure. We consider convex unconstraint optimization problem in $\mathbb{R}^n$. For simplicity we start from the zero point. We expect in advance that 1-norm of the solution is close enough to its 2-norm. In this case the standard accelerated Nesterov's directional search method can be improved. In the paper we show how to make Nesterov's method $n$-times faster (up to a $\log n$-factor) in this case. The basic idea is to use linear coupling, proposed by Allen-Zhu & Orecchia in 2014, and to make Grad-step in 2-norm, but Mirr-step in 1-norm. We show that for constrained optimization problems this approach stable upon an obstacle., in Russian, 13 pages, 3 figures

Memoryless quasi-Newton methods are studied for solving large-scale unconstrained optimization problems. Recently, memoryless quasi-Newton methods based on several kinds of updating formulas were proposed. Since the methods closely related to the conjugate gradient method, the methods are promising. In this paper, we propose a memoryless quasi-Newton method based on the Broyden family with the spectral-scaling secant condition. We focus on the convex and preconvex classes of the Broyden family, and we show that the proposed method satisfies the sufficient descent condition and converges globally. Finally, some numerical experiments are given.

Sparse channel estimation for massive multiple-input multiple-output systems has drawn much attention in recent years. The required pilots are substantially reduced when the sparse channel state vectors can be reconstructed from a few numbers of measurements. A popular approach for sparse reconstruction is to solve the least-squares problem with a convex regularization. However, the convex regularizer is either too loose to force sparsity or lead to biased estimation. In this paper, the sparse channel reconstruction is solved by minimizing the least-squares objective with a nonconvex regularizer, which can exactly express the sparsity constraint and avoid introducing serious bias in the solution. A novel algorithm is proposed for solving the resulting nonconvex optimization via the difference of convex functions programming and the gradient projection descent. Simulation results show that the proposed algorithm is fast and accurate, and it outperforms the existing sparse recovery algorithms in terms of reconstruction errors., Comment: 2020 IEEE Global Communications Conference

The conjugate gradient is a useful tool in solving large- and small-scale unconstrained optimization problems. In addition, the conjugate gradient method can be applied in many fields, such as engineering, medical research, and computer science. In this paper, a convex combination of two different search directions is proposed. The new combination satisfies the sufficient descent condition and the convergence analysis. Moreover, a new conjugate gradient formula is proposed. The new formula satisfies the convergence properties with the descent property related to Hestenes–Stiefel conjugate gradient formula. The numerical results show that the new search direction outperforms both two search directions, making it convex between them. The numerical result includes the number of iterations, function evaluations, and central processing unit time. Finally, we present some examples about image restoration as an application of the proposed conjugate gradient method.

Logistic regression is a classic classification method in machine learning. Classical logistic regression uses a general gradient descent method to solve the best parameters of the loss function, but it is easy to fall into the dilemma of local extremes. The fractional step descent method cannot converge to the exact extreme point, and there is always a deviation, so we use a variable fractional step descent method to simulate a new type of iteration to ensure the global convergence of the optimization algorithm. In this paper, the new variable fractional gradient descent method is used to solve the optimal parameters of the loss function, which overcomes the limitation of the gradient function on the step size of the loss function. In this paper, logistic regression and variable fractional step descent methods are used to deal with the problem of data dimensionality reduction to verify the effectiveness of the algorithm after optimization.

A direct multiple shooting (MS) method is implemented to solve optimal control problems (OCP) in the Mayer form. The use of an MS method gives rise to the so-called ‘continuity conditions’ that must be satisfied together with general algebraic equality and inequality constraints. The resulting finite nonlinear optimization problem is solved by a first-order descent method based on the filter methodology. In the equivalent tri-objective problem, the descent method aims to minimize the objective function, the violation of the ‘continuity conditions’ and the violation of the algebraic constraints simultaneously. The numerical experiments carried out with different types of benchmark OCP are encouraging., We acknowledge the financial support of CIDEM, R&D unit funded by the FCT - Portuguese Foundation for the Development of Science and Technology, Ministry of Science, Technology and Higher Education, under the Project UID/EMS/0615/2019, and FCT within the Projects Scope: UID/CEC/00319/2019 and UID/MAT/00013/2013.

We present a novel probabilistic Zeroth-Order optimization method, which can handle higher dimensions, and can also be used for fast online optimization, for instance for multichannel source separation. We compared it to the Gradientless Descent (GLD) algorithm on a multichannel source separation task, and found that our method results in faster and better separation (for the 2-channels case). For the multichannel case, only our method resulted in useful separation. We also applied it to separating sources from 3-dimensional microphone arrays, with comparable results.

International audience; In this paper, we consider the integrated Berth Allocation and Crane Assignment problem, with availability constraints and high tides restrictions, in bulk port context. We were inspired by a real case study of a port owned by our industrial partner. The objective is to minimize the total penalty of tardiness. First, we implemented a greedy heuristic to compute an initial solution. Then, we proposed a sequential Variable Neighborhood Descent (seq-VND) for the problem. In addition, we compared the efficiency of different scenarios for the seq-VND against results given by a mathematical model for the problem.

The discrete logarithm problem (DLP) is a cornerstone in the public-key cryptography with various applications. Recently there is a new computational record for the DLP in a 795-bit prime field using the number field sieve for discrete logarithms (NFS-DL). The main technique used in the computation is choosing good parameters for each step of NFS-DL which reduces the time estimated by the asymptotic complexity significantly. In this article, we propose a new algorithm to find relations for high degree prime ideals and remove the previous restriction that only degree one prime ideals are allowed to appear in the descent step. This will increase the success probability of the descent step and reduce the actual running time. As the descent step could be done separately in some sense, improving the descent step is beneficial to find optimal parameters such as the smoothness bound which may result in better performance of the NFS-DL algorithm. We also give an experiment to demonstrate the effectiveness of our algorithm.

In this work, we applied the Supervised Descent Method (SDM) to 3D model-based inversion with limited microwave data. The target shapes are described by parameters based on prior information. The values of these parameters are reconstructed iteratively using SDM in which the descent directions are learned from data set constructed based on prior information. The model-based inversion has less non-uniqueness compared with typical pixel-based inversion. Furthermore, sufficient prior information allows SDM to predict the parameter values with a good accuracy, even with data of limited view. This algorithm is validated using synthetic data. The results show that we can correctly recover target shape parameters with only mono-static reflection data.

For the case of public transport, we consider the problem of demand estimation. Given an origin-destination matrix representing the public transport demand, the distribution of flow among different lines can be obtained assuming that it corresponds to a certain equilibrium characterized by an optimization problem. In particular we will focus on the assignment model proposed by Cepeda et al. (2006). However the knowledge of origin-destination matrix is expensive and sometimes unaffordable in practice. Traditionally, it is estimated using statistical or econometrical considerations. In this work, we explore the estimation through the numerical solution of a bilevel optimization problem. One disadvantage of this formulation is the difficulty of obtaining descent directions, hence, for the resolution of the optimization problem we use a derivative-free method. This method was applied for small networks getting good results.

It is well-known that for general convex optimization problems, block-coordinate descent can get stuck in poor local optima. Despite that, versions of this method known as convergent message passing are very successful to approximately solve the dual LP relaxation of the MAP inference problem in graphical models. In attempt to identify the reason why these methods often achieve good local minima, we argue that if in block-coordinate descent the set of minimizers over a variable block has multiple elements, one should choose an element from the relative interior of this set. We show that this rule is not worse than any other rule for choosing block-minimizers. Based on this observation, we develop a theoretical framework for block-coordinate descent applied to general convex problems. We illustrate this theory on convergent message-passing methods.

The robust result of analytical fuzzy reliability analysis (FRA) represents the main effort at evaluating the fuzzy reliability index. In this study, a bioloop-based hybrid method is propos...

In this paper, we study a hybrid forward&ndash, backward algorithm for sparse reconstruction. Our algorithm involves descent, splitting and inertial ideas. Under suitable conditions on the algorithm parameters, we establish a strong convergence solution theorem in the framework of Hilbert spaces. Numerical experiments are also provided to illustrate the applications in the field of signal processing.

The physical support of the Internet infrastructure is fiber-optics network (FON). Since the global Internet traffic doubles each year, FONs are suffering the capacity crunch problem, and several proposals offer content-oriented solutions, combined with a smart spectral utilization.It is well known that the physical implementation of FONs is robust under single failures on its links, or 2-connected. Unfortunately, simultaneous failures occur, and the service is disrupted for some hours per year in average.In this paper we propose a smart network augmentation which solves the previous problems simultaneously. The resulting network is a locally most-reliable 3-connected augmentation. Our methodology to build 3-connected networks is supported by the theory of uniformly most-reliable networks, elementary properties of cubic networks and a careful selection of local searches in a Variable Neighborhood Descent (VND) metaheuristic.

In this article, a deterministic annealing neural network algorithm is proposed to solve the minimum concave cost transportation problem. Specifically, the algorithm is derived from two neural network models and Lagrange–barrier functions. The Lagrange function is used to handle linear equality constraints, and the barrier function is used to force the solution to move to the global or near-global optimal solution. In both neural network models, two descent directions are constructed, and an iterative procedure for the optimization of the neural network is proposed. As a result, two corresponding Lyapunov functions are naturally obtained from these two descent directions. Furthermore, the proposed neural network models are proved to be completely stable and converge to the stable equilibrium state, therefore, the proposed algorithm converges. At last, the computer simulations on several test problems are made, and the results indicate that the proposed algorithm always generates global or near-global optimal solutions.

[EN] Solving optimization problems using heuristic algorithms requires the selection of its parameters. Traditionally, these parameters are selected by a trial and error process that cannot guarantee the quality of the results obtained because not all the potential combinations of parameters are checked. To fill this gap, this paper proposes the application of Taguchi's orthogonal arrays to calibrate the parameters of a heuristic optimization algorithm (the descent local search algorithm). This process is based on the study of the combinations of discrete values of the heuristic tool parameters and it enables optimization of the heuristic tool performance with a reduced computational effort. To check its efficiency, this methodology is applied to a technical challenge never studied before: the optimization of the tensioning process of cable-stayed bridges. The statistical improvement of the heuristic tool performance is studied by the optimization of the tensioning process of a real cable-stayed bridge. Results show that the proposed calibration technique provided robust values of the objective function (with lower minimum and mean values, and lower standard deviation) with reduced computational cost., The authors are indebted to the Spanish Ministry of Economy and Competitiveness for the funding provided through the research projects BIA2013-47290-R and BIA2017-86811-C2-1-R founded with FEDER funds and directed by Professor Jose Turmo and through the research project BIA2017-86811-C2-2-R directed by Jose Antonio Lozano-Galant.

Block-coordinate descent (BCD) is a popular method in large-scale optimization. Unfortunately, its fixed points are not global optima even for convex problems. A succinct characterization of convex problems optimally solvable by BCD is unknown. Focusing on linear programs, we show that BCD fixed points are identical to fixed points of another method, which uses constraint propagation to detect infeasibility of a system of linear inequalities in a primal-dual loop (a special case of this method is the Virtual Arc Consistency algorithm by Cooper et al.). This implies that BCD fixed points are global optima iff a certain propagation rule decides feasibility of a certain class of systems of linear inequalities.

The renewed interest in Steepest Descent (SD) methods following the work of Barzilai and Borwein [IMA Journal of Numerical Analysis, 8 (1988)] has driven us to consider a globalization strategy based on SD, which is applicable to any line-search method. In particular, we combine Newton-type directions with scaled SD steps to have suitable descent directions. Scaling the SD directions with a suitable step length makes a significant difference with respect to similar globalization approaches, in terms of both theoretical features and computational behavior. We apply our strategy to Newton's method and the BFGS method, with computational results that appear interesting compared with the results of well-established globalization strategies devised ad hoc for those methods., Comment: 22 pages, 11 Figures

This paper considers a refinement problem for the flight altitude, speed, and flight-path angle of an aircraft during aerodynamic deceleration in the atmosphere of Mars using inaccurate discrete g-load measurements. For solving this problem, several suboptimal discrete nonlinear filters of higher accuracy than the extended Kalman filter based on the Taylor linearization procedure with static (Gaussian) linearization of the nonlinearities are applied and compared with each other. The equations of these filters are derived, the Gaussian moments of their structural functions are calculated, and the resulting accuracy of these filters is analyzed in statistical terms.

This paper develops a distributed discrete-time algorithm to seek Nash equilibrium for games under Markovian switching topologies. In the game problem considered in this paper, all players are assumed to use gradient-like descent method to update their own actions based on the estimation of all the other players’ actions with the intention to minimize their cost functions. All players exchange their estimation information with their neighbors at each discrete time instant through some undirected graphs that are Markovian switching. Suppose that the transition probability matrix is specified and the union of all switching topologies is connected, it is shown that the players’ actions can converge to the unique Nash equilibrium in the mean square sense for any initial condition. The convergence result is established by utilizing Lyapunov stability theory for discrete-time stochastic systems.

Focusing on the trajectory curvature, this paper presents an innovative and analytical guidance law for the construction of geometrically convex trajectories. Moving along such trajectories, the lander can increase the probability of a safe landing in hazardous terrains. Initially, the curvature theorems of the powered descent trajectories are developed. In these theorems, the inner relationship between trajectory curvature and lander states is revealed, and the state constraints for a geometrically convex trajectory are derived. Next, the trajectory curvature guidance is developed in an analytical formulation by satisfying the state constraints for a convex trajectory, and the selection of the key guidance parameters is investigated. Finally, the performance of the trajectory curvature guidance is analyzed in detail, illustrating its superior hazard avoidance and the camera’s field of view.

An innovative computational guidance framework is proposed for planetary powered descent using collaborative optimization approach. First, the dynamical model and constraints for planetary powered descent are presented. Then, using collaborative optimization strategy, the computational guidance framework for powered descent is formulated as a multi-discipline optimization problem including trajectory optimization, optimal guidance, and system-level optimization. Finally, the computational guidance approach employs three algorithms for respectively solving the three optimization modules to implement numerical simulations. The optimality and robustness of the computational guidance approach are verified with all constraints satisfied even in the presence of initial state uncertainty.

Some methods for finding the maximum feasible subsystems of systems of linear inequalities are considered. The problem of finding the most accurate algorithm in a parametric family of linear classification algorithms is one of the most important problems in machine learning. In order to solve this discrete optimization problem, an exact (combinatorial) algorithm, its approximations (relaxation and greedy combinatorial descent algorithms), and the approximation algorithm are given. The latter consists in replacing the original discrete optimization problem with a nonlinear programming problem by changing from linear inequalities to their sigmoid functions. The initial results of their comparison are presented.

Although different satisfiability decision procedures can be combined by algorithms such as those of Nelson–Oppen or Shostak, current tools typically can only support a finite number of theories to use in such combinations. To make SMT solving more widely applicable one needs theory-generic satisfiability algorithms allowing a potentially infinite number of decidable theories to be user-definable, instead of needing to be built in by tool implementers. This work studies how folding variant narrowing, a generic unification algorithm that offers good extensibility in unification theory, can be extended to a generic variant-based satisfiability algorithm for the initial algebras of user-specified input theories when such theories satisfy Comon and Delaune's finite variant property (FVP) and some extra conditions. Several, increasingly larger infinite classes of theories whose initial algebras enjoy decidable variant-based satisfiability are identified and illustrated with examples. A method based on descent maps to bring other theories into these classes and to improve the generic algorithm's efficiency is also proposed.

We revisit the static coverage control problem for placement of vehicles with simple motion on the real line, under the assumption that the cost is a polynomial function of the locations of the vehicles. The main contribution of this paper is to demonstrate the use of tools from numerical algebraic geometry, in particular, a numerical polynomial homotopy continuation method that guarantees to find all solutions of polynomial equations, in order to characterize the \emph{global minima} for the coverage control problem. The results are then compared against a classic distributed approach involving the use of Lloyd descent, which is known to converge only to a local minimum under certain technical conditions., 6 pages, 2 figures

Optic disc (OD) segmentation is an important step in analyzing the color fundus image. Most existing approaches are based on the shape prior and visual appearance of the OD boundary. However, the current ways of integrating the shape and appearance are simple. We argue that the performance of OD segmentation can be improved by better shape-appearance modeling. In this paper, we propose to learn a sequence of supervised descent directions between the coordinates of OD boundary and their surrounding visual appearances for OD segmentation. In addition, we introduce the histograms of gradient orientations to represent the OD appearance. Experimental results on six datasets clearly show that the proposed method improves the OD segmentation and outperforms the state-of-the-art.

One important problem in radiation therapy for cancer treatment is the selection of the set of beam angles radiation will be delivered from. A primary goal in this problem is to find a beam angle configuration (BAC) that leads to a clinically acceptable treatment plan. Further, this process must be done within clinically acceptable times. Since the problem of selecting beam angles in radiation therapy is known to be extremely hard to solve as well as time-consuming, both exact algorithms and population-based heuristics might not be suitable to solve this problem. In this paper, we compare two matheuristic methods based on local search algorithms, to approximately solve the beam angle optimisation problem (BAO). Although the steepest descent algorithm is able to find locally optimal BACs for the BAO problem, it takes too long before convergence, which is not acceptable in clinical practice. Thus, we propose to use a next descent algorithm that converges quickly to good quality solutions although no (local) optimality guarantee is given. We apply our two matheuristic methods on a prostate case which considers two organs at risk, namely, the rectum and the bladder. Results show that the matheuristic algorithm based on the next descent local search is able to quickly find solutions as good as the ones found by the steepest descent algorithm.

In this paper, we propose a distributed algorithm, called Directed-Distributed Subgradient Descent (D-DSD), to solve multi-agent optimization problems over directed graphs. Existing algorithms mostly deal with similar problems under the assumption of undirected networks, i.e., requiring the weight matrices to be doubly-stochastic. The row-stochasticity of the weight matrix guarantees that all agents reach consensus, while the column-stochasticity ensures that each agent’s local (sub)gradient contributes equally to the global objective. In a directed graph, however, it may not be possible to construct a doubly-stochastic weight matrix in a distributed manner. We overcome this difficulty by augmenting an additional variable for each agent to record the change in the state evolution. In each iteration, the algorithm simultaneously constructs a row-stochastic matrix and a column-stochastic matrix instead of only a doubly-stochastic matrix. The convergence of the new weight matrix, depending on the row-stochastic and column-stochastic matrices, ensures agents to reach both consensus and optimality. The analysis shows that the proposed algorithm converges at a rate of O ( ln k k ) , where k is the number of iterations.

The soft-clustered vehicle-routing problem (SoftCluVRP) is a variant of the classical capacitated vehicle-routing problem. Customers are partitioned into clusters and all customers of the same cluster must be served by the same vehicle. In this paper, we present a large multiple neighborhood search for the SoftCluVRP. We design and analyze multiple cluster destroy and repair operators as well as two post-optimization components, which are both based on variable neighborhood descent. The first allows inter-route exchanges of complete clusters, while the second searches for intra-route improvements by combining classical neighborhoods (2-opt, Or-opt, double-bridge) and the Balas-Simonetti neighborhood. Computational experiments show that our algorithm clearly outperforms the only existing heuristic approach from the literature. By solving benchmark instances, we provide 130 new best solutions for 220 medium-sized instances with up to 483 customers and prove 12 of them to be optimal. Furthermore, we describe a straightforward adaption of our algorithm to the clustered vehicle-routing problem, a variant of the SoftCluVRP.

A multi-period, multi-echelon, multi-product, and multi-modal sustainable supply chain network design problem is considered. The problem is formulated as a multi-objective Mixed-Integer Linear Programming (MILP) model that explicitly considers the environmental footprint and social responsibilities. We introduce the Multi-Neighborhood Descent Traversal Algorithm (MNDTA), which can solve this problem efficiently. The MNDTA begins with a structured initial solution of the model and improves the incumbent solution by sequentially traversing several specifically designed neighborhoods over generations. A lower-bound-based evaluation method is introduced to reduce the computational complexity involved in solving the integer programming problem. Experimental results demonstrate that the proposed MNDTA can provide high-quality solutions that are close to the optimal solutions with a negligibly small (relative) gap and can solve large instances much more quickly than CPLEX can. In addition, the MNDTA outperforms existing solution algorithms. A numerical comparison of the results of the proposed model with those of a model that only considers financial aspects demonstrates that explicitly using our model when designing a supply chain network can substantially reduce the environmental impact and increase social responsibility at a negligible cost increase.

In this paper, we present a new nonmonotone memory gradient algorithm for unconstrained optimization problems. An attractive property of the proposed method is that the search direction always provides sufficient descent step at each iteration. This property is independent of the line search used. Under mild assumptions, the global and local convergence results of the proposed algorithm are established respectively. Numerical results are also reported to show that the proposed method is suitable to solve large-scale optimization problems and is more stable than other similar methods in practical computation.

In this study, we introduce a new global optimization method, named Esthetic Delving Method, based on the auxiliary function approach. First, we design the method theoretically and then present its implementable version. Finally, we apply the algorithm to the test problems in order to demonstrate its efficiency.

We propose an unsupervised method for saliency detection with multiple functions by a universal descent model. The basic descent model is concise, which is a minimization equation conducted by a relationship matrix and background prior. The relationship matrix is calculated by the contrast of features which contains much information between superpixels. So saliency maps with high performance can be obtained even if only one feature is included. Besides, various terms can be appended to the basic descent model to achieve multiple functions. For example, considering an neighbor matrix into the basic model can further smooth saliency maps. The refinement term can also refine existing results by introducing prior saliency maps, demonstrating the universal applications of our model. Extensive experiments on different datasets indicate that the basic model outperforms state-of-the-art methods. The universal descent models with smoothness and refinement terms are able to promote the performance of state-of-the-art methods by a large margin.

This paper describes an optimization technique of neural networks radial basis function multi-model identification of nonlinear system. Indeed, this paper treats the multi-model approach based on parametric identification. The used architecture of the neural multi-model is radial basis function. We have used the descent gradient and the genetic algorithm technique and we have compared the found results. The effectiveness of the proposed approach is shown through a numerical simulation of a nonlinear system and we have confirmed that the genetic algorithm give a very good results.

We propose a policy search method for synthesizing optimal feedback control laws for reference tracking directly from data. During the learning phase, the control law is optimized by using stochastic gradient descent iterations and (optionally) applied to the plant while collecting data. Differently from model-based methods, in which a full model of the open-loop plant is first identified from data, here a simple linear model is recursively identified with forgetting factor for the only reason of computing approximately the gradients required for the descent. We report examples showing that the method recovers the optimal feedback law in case the underlying plant is linear, and outperforms the best control law that is achieved by first identifying an open-loop linear model in case the underlying plant is nonlinear.