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In this paper, we address the issue of solving problems with multiple components, multiple objectives, and target values for each objective. There are limitations in managing these multi-component, multi-goal problems such as the need for domain expertise to combine or prioritize the goals. In this paper, we propose a domain-independent method, Adaptive Leveling-Weighting-Clustering (ALWC), to manage the exploration of design scenarios of multi-goal, engineering-design problems. Using ALWC, designers explore combinations and priorities of the goals based on their interrelationships. Through iteration, design scenarios are obtained with higher goal achievements and an improved understanding of the relationship among subsystems. This is achieved without increasing computational complexity. This knowledge is helpful for multi-component design. The ALWC method is demonstrated using a thermal-system design problem. [ABSTRACT FROM AUTHOR]

The qualities of new data used in the sequential learning phase of the online sequential extreme learning machine algorithm (OS-ELM) have a significant impact on the performance of OS-ELM. This paper proposes a novel data filter mechanism for OS-ELM from the perspective of fuzziness and a fuzziness-based online sequential extreme learning machine algorithm (FOS-ELM). In FOS-ELM, when new data arrive, a fuzzy classifier first picks out the meaningful data according to the fuzziness of each sample. Specifically, the new samples with high-output fuzziness are selected and then used in sequential learning. The experimental results on eight binary classification problems and three multiclass classification problems have shown that FOS-ELM updated by the new samples with high-output fuzziness has better generalization performance than OS-ELM. Since the unimportant data are discarded before sequential learning, FOS-ELM can save more memory and have higher computational efficiency. In addition, FOS-ELM can handle data one-by-one or chunk-by-chunk with fixed or varying sizes. The relationship between the fuzziness of new samples and the model performance is also studied in this paper, which is expected to provide some useful guidelines for improving the generalization ability of online sequential learning algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we propose to use Artificial Bee Colony (ABC) optimization to solve the joint mode selection, channel assignment, and power allocation (JMSCPA) problem to maximize system throughput and spectral efficiency. JMSCPA is a problem where the allocation of channel and power depends on the mode selection. Such problems require two step solution and are called bi-level optimization problems. As bi-level optimization increases the complexity and computational time, we propose a modified version of single-level ABC algorithm aided with the adaptive transmission mode selection algorithm to allocate the cellular, reuse, and dedicated modes to the DUs along with channel and power allocation based on the network traffic load scenarios. A single variable, represented by the users (CUs and DUs) is used to allocate mode selection, and channel allocation to solve the JMSCPA problem, leading to a simpler solution with faster convergence, and significant reduction in the computational complexity which scales linearly with the number of users. Further, the proposed solution avoids premature stagnation of conventional ABC into local minima by incorporating a modification in its update procedure. The efficacy of the ABC-aided approach, as compared to the results reported in the literature, is validated by extensive numerical investigations under different simulation scenarios. [ABSTRACT FROM AUTHOR]

With low hardware cost and power consumption, direction-of-arrival (DOA) estimation exploiting one-bit quantized array data has become an attractive topic. In this paper, the gridless compressed sensing (CS) with multiple measurement vectors for one-bit DOA estimation is investigated. First, the one-bit quantized signal model is established. Then an atomic norm minimization scheme is proposed based on the output of one-bit quantizer, in which the objective function is reformulated as a semidefinite programming problem combined with a one-sided l 1 -norm constraint, representing the sign inconsistency between the quantized and unquantized measurements. To efficiently solve such a problem and reduce its computational complexity, an accelerated proximal gradient-based algorithm is developed. The proposed approach outperforms the one-bit MUSIC in a small number of measurements, and avoids the grid-mismatch issue of several existing one-bit CS methods. Numerical experiments are conducted to validate the superiorities of the proposed one-bit DOA estimation approach in accuracy and running time. [ABSTRACT FROM AUTHOR]

Network Function Virtualization (NFV) is a vital player of modern networks providing different types of services such as traffic optimization, content filtering, and load balancing. More precisely, NFV is a provisioning technology aims at reducing the large Capital Expenditure (CapEx) of network providers by moving services from dedicated hardware to commodity servers using Virtualized Network Functions (VNF). A sequence of VNFs/services following a logical goal is referred to as a Service Function Chain (SFC). The movement toward SFC introduces new challenges to those network services which require high reliability. To address this challenge, redundancy schemes are introduced. Existing redundancy schemes using dedicated protection enhance the reliability of services, however, they do not consider the cost of redundant VNFs. In this paper, we propose a novel reliability enhancement method using a shared protection scheme to reduce the cost of redundant VNFs. To this end, we mathematically formulate the problem as a Mixed Integer Linear Programming (MILP). The objective is to determine optimal reliability that could be achieved with minimum cost. Although the corresponding optimization problem can be solved using existing MILP solvers, the computational complexity is not rational for realistic scenarios. Thereafter, we propose a Reliability-aware and minimum-Cost based Genetic (RCG) algorithm to solve this problem with low computational complexity. In order to evaluate the proposed solution, we have compared it with four different solutions. Simulation results show that RCG achieves near-optimal performance at a much lower complexity compared with the optimal solution. [ABSTRACT FROM AUTHOR]

Recently, numerous meta-heuristic-based approaches are deliberated to reduce the computational complexities of several existing approaches that include tricky derivations, very large memory space requirement, initial value sensitivity, etc. However, several optimization algorithms namely firefly algorithm, sine–cosine algorithm, and particle swarm optimization algorithm have few drawbacks such as computational complexity and convergence speed. So to overcome such shortcomings, this paper aims in developing a novel chaotic sine–cosine firefly (CSCF) algorithm with numerous variants to solve optimization problems. Here, the chaotic form of two algorithms namely the sine–cosine algorithm and the firefly algorithms is integrated to improve the convergence speed and efficiency thus minimizing several complexity issues. Moreover, the proposed CSCF approach is operated under various chaotic phases and the optimal chaotic variants containing the best chaotic mapping are selected. Then numerous chaotic benchmark functions are utilized to examine the system performance of the CSCF algorithm. Finally, the simulation results for the problems based on engineering design are demonstrated to prove the efficiency, robustness and effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we propose a primal-dual interior-point method for semidefinite optimization problems. The algorithm is based on a new class of search directions and the Ai-Zhang's wide neighborhood for monotone linear complementarity problems. The theoretical complexity of the new algorithm is calculated. It is investigated that the proposed algorithm has polynomial iteration complexity $$O(\sqrt{n}L)$$ and coincides with the best known iteration bound for semidefinite optimization problems. [ABSTRACT FROM AUTHOR]

Jin et al. (in J. Optim. Theory Appl. 155:1073-1083, ) proposed homogeneous self-dual algorithms for stochastic semidefinite programs with finite event space. In this paper, we utilize their work to derive homogeneous self-dual algorithms for stochastic second-order cone programs with finite event space. We also show how the structure in the stochastic second-order cone programming problems may be exploited so that the algorithms developed for these problems have less complexity than the algorithms developed for stochastic semidefinite programs mentioned above. [ABSTRACT FROM AUTHOR]

Characterization of optimization problems with respect to their solvability is one of the focal points of many research projects in the field of global optimization. Our study contributes to these efforts with the usage of the computational and mathematical tools of network science. Given an optimization problem, a network formed by all the minima found by an optimization method can be constructed. In this paper we use the Basin Hopping method on well-known benchmarking problems and investigate the resulting networks using several measures. [ABSTRACT FROM AUTHOR]

In this paper, the berth allocation problem with stochastic vessel handling times is formulated as a bi-objective problem. To solve the resulting problem, an evolutionary algorithm-based heuristic and a simulation-based Pareto front pruning algorithm is proposed. Computational examples show that the proposed approach provides solutions superior to the ones where the expected value of the vessel handling times is used. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the optimization of process planning in which various flexibilities are considered. The objective is to minimize total weighted sum of manufacturing costs. Various flexibilities, including process flexibility, sequence flexibility, machine flexibility, tool flexibility, and tool access direction (TAD) flexibility, generally exist in process planning and consideration of these flexibilities is essential for improving production efficiency and system flexibility. However, process planning is strongly NP-hard due to the existence of various flexibilities as well as complex machining precedence constraints. To tackle this problem, an imperialist competitive algorithm (ICA) is employed to find promising solutions with reasonable computational cost. ICA is a novel socio-politically motivated metaheuristic algorithm inspired by imperialist competition. It starts with an initial population and proceeds through assimilation, position exchange, imperialistic competition, and elimination. Computational experiments on three sets of process planning problem taken from literature are carried out, and comparisons with some existing algorithms developed for process planning are presented. The results show that the algorithm performs significantly better than existing algorithms like genetic algorithm (GA), simulated annealing (SA), tabu search (TS), and particle swarm optimization (PSO). [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel algorithm for solving the classical P-median problem. The essential aim is to identify the optimal extended Lagrangian multipliers corresponding to the optimal solution of the underlying problem. For this, we first explore the structure of the data matrix in P-median problem to recast it as another equivalent global optimization problem over the space of the extended Lagrangian multipliers. Then we present a stochastic search algorithm to find the extended Lagrangian multipliers corresponding to the optimal solution of the original P-median problem. Numerical experiments illustrate that the proposed algorithm can effectively find a global optimal or very good suboptimal solution to the underlying P-median problem, especially for the computationally challenging subclass of P-median problems with a large gap between the optimal solution of the original problem and that of its Lagrangian relaxation. [ABSTRACT FROM AUTHOR]

An important aspect in the solution process of constraint satisfaction problems is to identify exclusion boxes which are boxes that do not contain feasible points. This paper presents a certificate of infeasibility for finding such boxes by solving a linearly constrained nonsmooth optimization problem. Furthermore, the constructed certificate can be used to enlarge an exclusion box by solving a nonlinearly constrained nonsmooth optimization problem. [ABSTRACT FROM AUTHOR]

In this paper, a compressed membership problem for finite automata, both deterministic (DFAs) and non-deterministic (NFAs), with compressed transition labels is studied. The compression is represented by straight-line programs (SLPs), i.e. context-free grammars generating exactly one string. A novel technique of dealing with SLPs is employed: the SLPs are recompressed, so that substrings of the input word are encoded in SLPs labelling the transitions of the NFA (DFA) in the same way, as in the SLP representing the input text. To this end, the SLPs are locally decompressed and then recompressed in a uniform way. Furthermore, in order to reflect the recompression in the NFA, we need to modify it only a little, in particular its size stays polynomial in the input size. Using this technique it is shown that the compressed membership for NFA with compressed labels is in NP, thus confirming the conjecture of Plandowski and Rytter (Jewels Are Forever, pp. 262-272, Springer, Berlin, ) and extending the partial result of Lohrey and Mathissen (in CSR, LNCS, vol. 6651, pp. 275-288, Springer, Berlin, ); as this problem is known to be NP-hard (in Plandowski and Rytter, Jewels Are Forever, pp. 262-272, Springer, Berlin, ), we settle its exact computational complexity. Moreover, the same technique applied to the compressed membership for DFA with compressed labels yields that this problem is in P, and this problem is known to be P-hard (in Markey and Schnoebelen, Inf. Process. Lett. 90(1):3-6, ; Beaudry et al., SIAM J. Comput. 26(1):138-152, ). [ABSTRACT FROM AUTHOR]

The m-machine no-wait flowshop scheduling problem, with the objective of minimizing total completion time subject to the constraint that makespan has to be less than or equal to a certain value, is addressed in this paper. First, an algorithm is proposed to find an upper bound on the makespan in case the upper bound is not given or unknown. Given the upper bound on makespan, a proposed algorithm ( PAL) with five versions L (1, 5, 10, 15, and 20) and a genetic algorithm ( GA) are utilized for solving the problem. Furthermore, a dominance relation is established for the case of four machines. The five versions of PAL and GA are evaluated on randomly generated problems with different number of jobs and number of machines. Computational experiments show that the errors of PA10, PA15, and PA20 are much smaller than that of GA while the CPU times of PA10, PA15, and PA20 are significantly smaller than that of GA. Therefore, the algorithms PA10, PA15, and PA20 are superior to the GA algorithm. [ABSTRACT FROM AUTHOR]

As a strongly NP-hard problem, the hybrid flow-shop problem with multiprocessor tasks (HFSPMT) has gained increasing attention due to its academic significance and application value. In this paper, an effective algorithm based on the shuffled frog leaping algorithm (SFLA) is proposed for solving the HFSPMT. First, three decoding methods are used together to decode a solution to a better schedule. Especially, the forward scheduling decoding method is employed, aiming at narrowing the idle time between consecutive operations in the processor as well as increasing the flexibility in selecting processors to schedule the following operations. Second, a bilevel crossover is designed to make each individual share the good “meme” within each memeplex and exchange the good “meme” between different memeplexes. Third, multiple local search operators are used in an effective way by employing the meta-Lamarckian learning strategy to enhance the local exploitation ability. Meanwhile, the use of crossover and local search together in the SFLA can enrich the memetic search behavior and balance the exploration and exploitation abilities. In addition, the effect of parameter setting of the algorithm is investigated based on the Taguchi method of design of experiment, and suitable values are suggested for the parameters. Extensive testing results based on two types of well-known benchmarks are provided. And the effectiveness of the proposed algorithm is demonstrated by the comparisons with some existing algorithms. [ABSTRACT FROM AUTHOR]

A Business Process (BP for short) consists of a set of activities which, combined in a flow, achieve some business goal. A given BP may have a large, possibly infinite, number of possible execution flows (EX-flows for short), each having some probability to occur at run time. This paper studies query evaluation over such probabilistic BPs. We focus on two important classes of queries, namely boolean queries that compute the probability that a random EX-flow of a BP satisfies a given property, and projection queries focusing on portions of EX-flows that are of interest to the user. For the latter queries the answer consists of the top- k instances of these portions that are most likely to occur at run-time. We study the complexity of query evaluation for both kinds of queries, showing in particular that projection queries may be harder to evaluate than boolean queries. We present a picture of which combinations of BP classes and query features lead to PTIME algorithms and which to NP-hard or infeasible problems. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the applicability of a constraint satisfaction problem solving (CSP) model, recently developed for deadline scheduling, to more commonly studied problems of schedule optimization. Our hypothesis is twofold: (1) that CSP scheduling techniques provide a basis for developing high-performance approximate solution procedures in optimization contexts, and (2) that the representational assumptions underlying CSP models allow these procedures to naturally accommodate the idiosyncratic constraints that complicate most real-world applications. We focus specifically on the objective criterion of makespan minimization, which has received the most attention within the job shop scheduling literature. We define an extended solution procedure somewhat unconventionally by reformulating the makespan problem as one of solving a series of different but related deadline scheduling problems, and embedding a simple CSP procedure as the subproblem solver. We first present the results of an empirical evaluation of our procedure performed on a range of previously studied benchmark problems. Our procedure is found to provide strong cost/performance, producing solutions competitive with those obtained using recently reported shifting bottleneck search procedures at reduced computational expense. To demonstrate generality, we also consider application of our procedure to a more complicated, multi-product hoist scheduling problem. With only minor adjustments, our procedure is found to significantly outperform previously published procedures for solving this problem across a range of input assumptions. [ABSTRACT FROM AUTHOR]

Satisfiability problems are of importance for many practical problems. They are NP-complete problems. However, some instances of the SAT problem can be solved efficiently. This paper reports on a study concerning the behaviour of a variety of algorithmic approaches to this problem tested on a set of problems collected at FAW. The results obtained give a lot of insight into the algorithms and problems, yet also show some general technical and methodological problems associated with such comparisons. [ABSTRACT FROM AUTHOR]

We devise a new numerical method for solving the minimization problem over the Stiefel manifold, that is, the set of matrices of order n × p (here p ≤ n ) with orthonormal columns. Our approach consists in a nonmonotone feasible arc search along a sufficient descent direction to assure convergence to stationary points, regardless the initial point considered. The feasibility of the iterates is maintained through a variation of the Cayley transform and thus our scheme can be seen as a retraction-based algorithm for minimization with orthogonality constraints. We emphasize that our scheme solves a p × p linear system at each iteration and has computational complexity of O (n p 2) + O (p 3) , which is interesting when p ≪ n . We present a general algorithmic framework for minimization on Stiefel manifold, give its global convergence properties and report numerical experiments on interesting applications. [ABSTRACT FROM AUTHOR]

Decomposition hybrid algorithms with the recursive framework which recursively decompose the structural task into structural subtasks to reduce computational complexity are employed to learn Bayesian network (BN) structure. Merging rules are commonly adopted as the combination method in the combination step. The direction determination rule of merging rules has problems in using the idea of keeping v-structures unchanged before and after combination to determine directions of edges in the whole structure. It breaks down in one case due to appearances of wrong v-structures, and is hard to operate in practice. Therefore, we adopt a novel approach for direction determination and propose a two-stage combination method. In the first-stage combination method, we determine nodes, links of edges by merging rules and adopt the idea of permutation and combination to determine directions of contradictory edges. In the second-stage combination method, we restrict edges between nodes that do not satisfy the decomposition property and their parent nodes by determining the target domain according to the decomposition property. Simulation experiments on four networks show that the proposed algorithm can obtain BN structure with higher accuracy compared with other algorithms. Finally, the proposed algorithm is applied to the thickening process of gold hydrometallurgy to solve the practical problem. [ABSTRACT FROM AUTHOR]

We show that unless P = NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of degree four (or higher even degree) is globally convex. This solves a problem that has been open since 1992 when N. Z. Shor asked for the complexity of deciding convexity for quartic polynomials. We also prove that deciding strict convexity, strong convexity, quasiconvexity, and pseudoconvexity of polynomials of even degree four or higher is strongly NP-hard. By contrast, we show that quasiconvexity and pseudoconvexity of odd degree polynomials can be decided in polynomial time. [ABSTRACT FROM AUTHOR]

This study deals with the task assignment problem in a heterogeneous unmanned aerial vehicle system under the multiple constraints of limited resources, effective task execution scope, obstacle avoidance and task priority. Considering the nonlinearity, multimoding and high complexity of the task assignment problem, many existing optimization methods may fall into local optimum and even fail to provide satisfactory solutions. To address the issues, the discrete adaptive search whale optimization algorithm is proposed. First, we present the obstacle-avoiding distance estimation method to provide precise task scenario information and reduce the computational complexity. Then, the crossover-based updating method is presented to enable the algorithm to solve discrete problems such as task assignment. In addition, the search intensity adaptive mechanism is presented to optimize and balance the exploration and exploitation intensities in the solution space reasonably, thereby achieving high-quality task assignment results quickly. Further, joint leadership mechanism and local search mechanism are proposed to enhance the exploration ability of the algorithm. Simulation results demonstrate the effectiveness and superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Matrix regression model can directly take matrix data as input data, and its loss function is defined by left and right regression matrices. The spectral clustering-based matrix regression model can perform feature selection for unsupervised images. However, the graph weight matrix used in the existing spectral clustering models is predefined, which is often inaccurate, especially for noisy images. Moreover, they do not consider the preservation of local structure of image samples in transformation space. To this end, we propose a nonnegative spectral clustering and adaptive graph-based matrix regression model for unsupervised image feature selection. This model can make the prediction label matrix as smooth as possible on the whole graph, and the graph weight matrix can be adaptively learned instead of being predefined as fixed matrix. Thus, the accurate local structure of the sample data is preserved in transformation space and the discriminative information of these pseudo class labels can be revealed. Finally, we devise an efficient optimization algorithm to solve the proposed problem and analyze the computational complexity and convergence of the algorithm. Some experimental results on several datasets also show the effectiveness and superiority of our proposed method. [ABSTRACT FROM AUTHOR]

We develop local search algorithms for routing problems with time windows. The presented algorithms are based on the k-interchange concept. The presence of time windows introduces feasibility constraints, the checking of which normally requires O(N) time. Our method reduces this checking effort to O(1) time. We also consider the problem of finding initial solutions. A complexity result is given and an insertion heuristic is described. [ABSTRACT FROM AUTHOR]

Strategically applied geo-environmental clean-up methods require a better groundwater flow and transport model. Hydraulic conductivity of the subsurface is one of great sources of uncertainty of this model. In order to search hydraulic conductivities, the simultaneous search-based pilot point method (SSBM) was developed to reduce computational procedure of pilot point method and increase characterization accuracy using a global optimization tool (genetic algorithm). SSBM searches pilot point locations and hydraulic conductivities at selected pilot points simultaneously. In the four different scenarios, the comparison between random pilot point locations and SSBM showed that SSBM produced less than two orders magnitude differences in terms of average of minimum fitness for thirty trials (e.g. 4.05E−02 for scenario 2). With respect to average minimum fitness and average hydraulic conductivity difference, SSBM was comparable to D-optimality based pilot point method (DBM). SSBM produced lower average minimum fitness values and similar average hydraulic conductivity difference but it had more variance. Through these results, SSBM showed the potential to replace the DBM through reduced computational procedures in sensitivity calculation with consideration of variance minimization. [ABSTRACT FROM AUTHOR]

We study algorithmic problems in multi-stage open shop processing systems that are centered around reachability and deadlock detection questions. We characterize safe and unsafe system states. We show that it is easy to recognize system states that can be reached from the initial state (where the system is empty), but that in general it is hard to decide whether one given system state is reachable from another given system state. We show that the problem of identifying reachable deadlock states is hard in general open shop systems, but is easy in the special case where no job needs processing on more than two machines (by linear programming and matching theory), and in the special case where all machines have capacity one (by graph-theoretic arguments). [ABSTRACT FROM AUTHOR]

We present a new generic sequential importance sampling algorithm, called stochastic enumeration (SE) for counting #P-complete problems, such as the number of satisfiability assignments and the number of perfect matchings (permanent). We show that SE presents a natural generalization of the classic one-step-look-ahead algorithm in the sense that it: Runs in parallel multiple trajectories instead of a single one; Employs a polynomial time decision making oracle, which can be viewed as an n-step-look-ahead algorithm, where n is the size of the problem. Our simulation studies indicate good performance of SE as compared with the well-known splitting and SampleSearch methods. [ABSTRACT FROM AUTHOR]

The aim of this study is to investigate the solution algorithm for solving the problem of determining reliable shortest paths in road networks with stochastic travel times. The availability of reliable shortest paths enables travelers, in the face of travel time uncertainty, to plan their trips with a pre-specified on-time arrival probability. In this study, the reliable shortest path between origin and destination nodes is determined using a multiple-criteria shortest path approach when link travel times follow normal distributions. The dominance conditions involved in such problems are established, thereby reducing the number of generated non-dominated paths during the search processes. Two solution algorithms, multi-criteria label-setting and A* algorithms, are proposed and their complexities analyzed. Computational results using large scale networks are presented. Numerical examples using data from a real-world advanced traveller information system is also given to illustrate the applicability of the solution algorithms in practice. [ABSTRACT FROM AUTHOR]

We consider the problem of minimizing the makespan in open shop scheduling. The decision problem whether a given sequence in open shop scheduling is irreducible has already been considered, however, has not been solved yet. A sequence is an acyclic orientation of the Hamming graph K× K. Irreducible sequences in open shop are the local optimal elements. We present two variants of algorithms based on the specific properties of the H-comparability graph. The first is polynomial whereas the second is exponential. The irreducibility is co- NP. The stated properties argue whether it belongs to P. The complexity status of the considered decision problem is updated. [ABSTRACT FROM AUTHOR]

We develop a tractable, consistent bootstrap algorithm for inference about Farrell-Debreu efficiency scores estimated by non-parametric data envelopment analysis (DEA) methods. The algorithm allows for very general situations where the distribution of the inefficiencies in the input-output space may be heterogeneous. Computational efficiency and tractability are achieved by avoiding the complex double-smoothing procedure in the algorithm proposed by Kneip et al. (Econometric Theory 24:1663-1697, 2008). In particular, we avoid technical difficulties in the earlier algorithm associated with smoothed estimates of a density with unknown, nonlinear, multivariate bounded support requiring complicated reflection methods. The new procedure described here is relatively simple and easy to implement: for particular values of a pair of smoothing parameters, the computational complexity is the same as the (inconsistent) naive bootstrap. The resulting computational speed allows the bootstrap to be iterated in order to optimize the smoothing parameters. From a practical viewpoint, only standard packages for computing DEA efficiency estimates, i.e., solving linear problems, are required for implementation. The performance of the method in finite samples is illustrated through some simulated examples. [ABSTRACT FROM AUTHOR]

We study some problems solvable in deterministic polynomial time given oracle access to the (promise version of) Arthur-Merlin class. Our main results are the following: In addition to providing new upper bounds for the classes $${{{\rm S}_2^p}}$$ and $${{\rm BPP}^{{\rm NP}}_{||}}$$ , these results are interesting from a derandomization perspective. In conjunction with the hitting set generator construction of Miltersen and Vinodchandran ( Computational Complexity 14(3), ), we get that $${{{\rm S}_2^p} = {{\rm P}^{\rm NP}}}$$ and $${{\rm BPP}^{{\rm NP}}_{||} = {\rm P}^{{\rm NP}}_{||}}$$ , under the hardness hypothesis associated with derandomizing the class AM. This gives an alternative proof of the same result obtained by Shaltiel and Umans ( Computational Complexity 15(4), ). We also show that if NP has polynomial size circuits, then the polynomial time hierarchy (PH) collapses as PH = P. Under the same hypothesis, we also derive a FP algorithm for learning circuits for SAT; this improves the ZPP algorithm for the same problem by Bshouty et al. ( JCSS 52(3), ). Finally, we design a FP algorithm for the problem of finding near-optimal strategies for succinctly presented zero-sum games. For the same problem, Fortnow et al. ( Computational Complexity 17(3), ) described a ZPP algorithm. One advantage of our FP algorithm is that it can be derandomized using the construction of Miltersen and Vinodchandran yielding a FP algorithm, under a hardness hypothesis used for derandomizing AM. [ABSTRACT FROM AUTHOR]