Paths Beyond Local Search: A Tight Bound for Randomized Fixed-Point Computation

In 1986, Saks and Wigderson conjectured that the largest separation between deterministic and zero-error randomized query complexity for a total boolean function is given by the function f on n=2k bits defined by a complete binary tree of NAND gates of depth k, which achieves R0(f) = O(D(f)0.7537…). We show this is false by giving an example of a total boolean function f on n bits whose deterministic query complexity is Ω(n/log(n)) while its zero-error randomized query complexity is O(√n). We further show that the quantum query complexity of the same function is O(n1/4), giving the first example of a total function with a super-quadratic gap between its quantum and deterministic query complexities. We also construct a total boolean function g on n variables that has zero-error randomized query complexity Ω(n/log(n)) and bounded-error randomized query complexity R(g) = O(√n). This is the first super-linear separation between these two complexity measures. The exact quantum query complexity of the same function is QE(g) = O(√n). These functions show that the relations D(f) = O(R1(f)2) and R0(f) = O(R(f)2) are optimal, up to poly-logarithmic factors. Further variations of these functions give additional separations between other query complexity measures: a cubic separation between Q and R0, a 3/2-power separation between QE and R, and a 4th power separation between approximate degree and bounded-error randomized query complexity. All of these examples are variants of a function recently introduced by Goos, Pitassi, and Watson which they used to separate the unambiguous 1-certificate complexity from deterministic query complexity and to resolve the famous Clique versus Independent Set problem in communication complexity.

MEMPSODE: A global optimization software based on hybridization of population-based algorithms and local searches

Purpose At this work, we propose a local approximation based search method to optimize any function. For this purpose, an approximation method is combined with an estimation filter, and a new local search mechanism is constituted. Design/methodology/approach RBF network is very efficient interpolation method especially if we have sufficient reference data. Here, reference data refers to the exact value of the objective function at some points. Using this capability of RBFs, we can approximately inspect the vicinity each point in search space. Meanwhile, in order to obtain a smooth, rapid and better trajectory toward the global optimum, the alpha-beta filter can be integrated to this mechanism. For better description and visualization, the operations are defined in 2-dimensional search space; but the outlined procedure can be extended to higher dimensions without loss of generality. Findings When compared with our previous studies using conventional heuristic methods, approximation based curvilinear local search mechanism provide better minimization performance for almost all benchmark functions. Moreover computational cost of this method too less than heuristics. The number of iteration down to at least 1/10 compared to conventional heuristic algorithm. Additionally, the solution accuracy is very improved for majority of the test cases. Originality/value This paper proposes a new search approach to solve optimization problems with less cost. For this purpose, a new local curvilinear search mechanism is built using RBF based approximation technique and alpha-beta estimation filter.

This article presents a new multidimensional descent method for solving global optimization problems with box-constraints. This is a hybrid method where local search method is used for a local descent and global search is used for further multidimensional search on the subsets of intersection of cones generated by the local search method and the feasible region. The discrete gradient method is used for local search and the cutting angle method is used for global search. Two- and three-dimensional cones are used for the global search. Such an approach allows one, as a rule, to escape local minimizers which are not global ones. The proposed method is local optimization method with strong global search properties. We present results of numerical experiments using both smooth and non-smooth global optimization test problems. These results demonstrate that the proposed algorithm allows one to find a global or a near global minimizer.

We study pseudo-deterministic query complexity - randomized query algorithms that are required to output the same answer with high probability on all inputs. We prove Ω(√n) lower bounds on the pseudo-deterministic complexity of a large family of search problems based on unsatisfiable random CNF instances, and also for the promise problem (FIND1) of finding a 1 in a vector populated with at least half one’s. This gives an exponential separation between randomized query complexity and pseudo-deterministic complexity, which is tight in the quantum setting. As applications we partially solve a related combinatorial coloring problem, and we separate random tree-like Resolution from its pseudo-deterministic version. In contrast to our lower bound, we show, surprisingly, that in the zero-error, average case setting, the three notions (deterministic, randomized, pseudo-deterministic) collapse.

When solving applied problems in various areas of human activity, the need appears to find the best set of parameters according to the given criterion. Usually such a problem is being formulated as a parametric optimization problem. The paper considers optimization problems represented by the black-box model. As such problems dimension grows, it becomes difficult to find a satisfactory solution for many traditional optimization approaches even with a significant increase in the number of objective function calculations. A new hybrid evolutionary method in coordinating the self-adjusting coevolution algorithms with the COSACC-LS1 local search is proposed to solve the problems of global material optimization of the extra-large dimension. COSACC-LS1 is based on the idea of the computing resources automatic allocation between a group of self-tuning differential evolution algorithms based on coevolution and local search algorithm. Effectiveness of the proposed algorithm was evaluated on 15 reference test problems from the LSGO CE 2013 set. Results of the COSACC-LS1-based algorithm were compared with a number of modern metaheuristic algorithms that were designed specifically for solving the very large-scale optimization problems and were the winners and prize-winners in the optimization competitions conducted within the framework of the IEEE CEC. With the help of numerical experiments, it is demonstrated that the proposed algorithm is better than most other popular algorithms according to the average accuracy criterion of the solution found

Supervised Neural Network (NN) learning is a process in which input patterns and known targets are presented to a NN while it learns to recognize (classify, map, fit, etc.) them as desired. The learning is mathematically defined as an optimisation problem, i.e., an error function representing the differences between the desired and actual output, is being minimized (Bishop, 1995; Haykin, 1999). Because the most popular supervised learning techniques are gradient based (Backpropagation BP), they suffer from the so-called Local Minima Problem (Bishop, 1995). This has motivated the employment of Global Optimisation (GO) methods for the supervised NN learning. Stochastic and heuristic GO approaches including Evolutionary Algorithms (EA) demonstrated promising performance over the last decades (Smagt, 1994; Sexton et al., 1998; Jordanov & Georgieva, 2007; etc.). EA appeared more powerful than BP and its modifications (Sexton et al., 1998; Alba & Chicone 2004), but hybrid methods that combine the advantages of one or more GO techniques and local searches were proven to be even better (Yao, 1999; Rocha et al., 2003; Alba & Chicano, 2004; Ludemir et al., 2006). Hybrid methods were promoted over local searches and simple population based techniques in Alba & Chicone (2004). The authors compared five methods: two BP implementations (gradient descent and Levenberg-Marquardt), Genetic Algorithms (GA), and two hybrid methods, combining GA with different local methods. The methods were used for NN learning applied to problems arising in medicine. Ludemir et al. (2006) optimized simultaneously NN weights and topology with a hybrid method combining Simulated Annealing (SA), Tabu Search (TS) and BP. A set of new solutions was generated on each iteration by TS rules, but the best solution was only accepted according to the probability distribution as in conventional SA. Meanwhile, the topology of the NN was also optimized and the best solution was kept. Finally, BP was used to train the best NN topology found in the previous stages. The new methodology compared favorably with SA and TS on four classification and one prediction problems. Plaginakos et al. (2001) performed several experiments to evaluate various training methods – six Differential Evolution (DE) implementations (with different mutation operators), BP, BPD (BP with deflection), SA, hybridization of BP and SA (BPSA), and GA. They reported O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg

Local search techniques have been applied in variant global optimization methods. The effect of local search to the function landscape can make multimodal problems easier to solve. For evolutionary algorithms, the usage of the step size control concept normally will result in failure by the individual to escape from the local optima during the final stage. We propose an algorithm combining landscape approximation and local search (LALS) which is designed to tackle those difficult multimodal problems. We demonstrate that LALS can solve problems with very rough landscapes and also that LALS has very good global reliability.

To the present day, the control of prosthetic mechanisms and the classification of surface Electro-Myography (sEMG) signals is heavily influenced by multiple factors, such as the overall quality of the signal acquired, the number and the position of electrodes, and unwanted noise or crosstalk between them. For this reason, the technological state-of-the-art is moving from the analysis of low-order features (e.g. Median Absolute Value and spectral features) that could suffer the aforementioned issues, to more complex techniques, such as Independent Component Analysis (ICA) separation Non-Negative Matrix Factorization (NMF) decomposition of signal channels. The latter hypothesizes a high-order modular control of muscles at the Central Nervous System (CNS) level built upon coordinated motor patterns (called muscle synergies), and it removes the limitations on Degrees-of-Freedom (DoF) per electrode given by standard sEMG controllers. Unfortunately, the utilisation of such techniques in prosthetics is limited by their computational complexity, which limits them to research laboratories and bulky processing systems, calling for novel algorithms and hardware implementations that achieve same the level of accuracy and speed necessary for movement control, while minimizing the power consumption and the device size. This paper presents a FPGA-based, real-time NMF processor that extracts muscle synergies from a 8-electrode sEMG recording. The execution of the NMF algorithm is entirely performed using a fixed-point architecture, in order to increase computation speed and minimize the amount of DSPs used. The NMF fixed-point decomposition is then fed to two software different classifiers, a Support Vector Machine (SVM) and a Neural Network, in order to quantify the degradation of the accuracy given by fixed-point calculations and to understand which mechanism is more robust. Preliminary results show that there are no remarkable differences between the classification results obtained using floating-point or fixed-point operations.

Shuffled Frog Leaping Algorithm (SFLA) is a meta-heuristic for solving discrete optimization problems. Here it is applied to determine optimal discrete pipe sizes for new pipe networks and for network expansions. SFLA is a population based, cooperative search metaphor inspired by natural memetics. The algorithm uses memetic evolution in the form of infection of ideas from one individual to another in a local search. The local search is similar in concept to particle swarm optimization. A shuffling strategy allows for the exchange of information between local searches to move toward a global optimum. This paper summarizes the development of SFLANET, a computer model that links SFLA and the hydraulic simulation software EPANET and its library functions. Application of SFLANET to literature network design problems is then described. Although the algorithm is in its initial stages of development, promising results were obtained.

Memetic algorithms are effective algorithms to obtain reliable and accurate solutions for complex continuous optimization problems. Nowadays, high dimensional optimization problems are an interesting field of research. The high dimensionality introduces new problems for the optimization process, requiring more scalable algorithms that, at the same time, could explore better the higher domain space around each solution. In this work, we proposed a memetic algorithm, MA-SW-Chains, for large scale global optimization. This algorithm assigns to each individual a local search intensity that depends on its features, by chaining different local search applications. MA-SW-Chains is an adaptation to large scale optimization of a previous algorithm, MA-CMA-Chains, to improve its performance on high-dimensional problems. Finally, we present the results obtained by our proposal using the benchmark problems defined in the Special Session of Large Scale Global Optimization on the IEEE Congress on Evolutionary Computation in 2010.

We study the power of four query models in the context of property testing in general graphs (i.e., with arbitrary edge densities), where our main case study is the problem of testing k-colorability. Two query types, which have been studied extensively in the past, are pair queries and neighbor queries. The former corresponds to asking whether there is an edge between any particular pair of vertices, and the latter to asking for the i’th neighbor of a particular vertex. We show that while for pair queries, testing k-colorability requires a number of queries that is a monotone decreasing function in the average degree d, the query complexity in the case of neighbor queries remains roughly the same for every density and for large values of k. We also consider a combined model that allows both types of queries, and we propose a new, stronger, query model, related to the field of Group Testing. We give one-sided error upper and lower bounds for all the models, where the bounds are nearly tight for three of the models. In some of the cases our lower bounds extend to two-sided error algorithms.The problem of testing k-colorability was previously studied in the contexts of dense and sparse graphs, and in our proofs we unify approaches from those cases, and also provide some new tools and techniques that may be of independent interest.Keywordspair queriesneighbor queriesgroup queriesk-colorability

Having many attractive advantages, genetic algorithms (GAs) have been applied to many design optimization problems. However, the practical application of GAs to realistic tall building design is still rather limited, since GAs require a large number of structural reanalyses and perform poorly in local searching. While the Optimality Criteria (OC) method can be applied effectively to the element sizing optimization of tall buildings, there is no guarantee that the OC method can always lead to the global optimum. In this paper, the so-called hybrid OC-GA method is presented to fully exploit the merits of both OC and GA for topology and element sizing optimization of braced tall steel frameworks. While the GA is particularly useful in the global exploration for optimal topologies, the OC technique serves as an efficient local optimizer for resizing elements of selected topologies. The effect of population size and the importance of the local OC search operator have been investigated. The applicability and efficiency of the hybrid OC-GA method were tested with two braced steel building examples. Results indicate that the incorporation of the OC operator into the GA has remarkably improved the efficiency and robustness of the evolutionary algorithm and thus make the hybrid method particularly useful for topology optimization of practical tall building structures involving a large number of structural elements and the use of numerous structural forms.

Local search is commonly used in a population-based evolutionary algorithm to fine tune the quality of the solutions in the population. However, because local search is a costly process, previous work often suggests applying local search only to the current best solution instead of all of the solutions in the population. Imperialist Competitive Algorithm (ICA) is a population-based evolutionary algorithm that bases on the meta-heuristics of the human's socio-political evolution. It divides its population into several sub-populations and allows these sub-populations to evolve independently and, at the same time, compete against each other. These subpopulations in ICA motivate the idea of applying local search on the best solution of each sub-population, as a compromise method between applying local search to all of the solutions and applying local search only to the best solution in the population. Our experimental results show that ICA with local search on the best solution of each sub-population yields competitive performance, when compared to ICA with local search only on the best solution of the population.

We propose a crossover-based adaptive local search (LS) operation for enhancing the performance of standard differential evolution (DE) algorithm. Incorporating LS heuristics is often very useful in designing an effective evolutionary algorithm for global optimization. However, determining a single LS length that can serve for a wide range of problems is a critical issue. We present a LS technique to solve this problem by adaptively adjusting the length of the search, using a hill-climbing heuristic. The emphasis of this paper is to demonstrate how this LS scheme can improve the performance of DE. Experimenting with a wide range of benchmark functions, we show that the proposed new version of DE, with the adaptive LS, performs better, or at least comparably, to classic DE algorithm. Performance comparisons with other LS heuristics and with some other well-known evolutionary algorithms from literature are also presented.