Huge Solution Space Research Articles

The Lion's Algorithm: A New Nature-Inspired Search Algorithm

Natural Computing is an efficient computing field that intends to develop search, optimization and machine learning algorithms by the inspiration of nature's behavior in problem solving circumstances. In the same way, numerous biologically or naturally inspired search and optimization algorithms have been proposed in the literature. This paper proposes a novel solution search algorithm called lion's algorithm. The natural inspiration behind the proposed algorithm is lion's social behavior that aids to keep the mammal be strong in the world. The interpretation of such social behavior to algorithmic perspective helps in searching out highly optimal solutions from a huge solution space. The algorithm solves both single variable and multi-variable cost function problems through the generation of binary structured and integer structured lion, respectively. The algorithm is implemented and tested using De-Jong's Type I function and the results are compared against the evolutionary programming. The test results show the algorithm performance under varying sizes of solution spaces.

Embedding sensitivity theory in ordinal optimization for decentralized optimal power flow control

In this paper, the decentralized optimal power flow with continuous and discrete control variables problem is firstly formulated as a NP-hard optimization problem - Block Additive constrained with Continuous and Discrete variables (BACD) problem. Secondly, an algorithm of embedding sensitivity theory (ST) in ordinal optimization (OO), abbreviated as STOO, is proposed for solving this NP-hard optimization problem. The STOO algorithm consists of three stages and three models of performance evaluation. The proposed method not only copes with the computational complexity due to huge solution space but also obtains a good enough solution with high probability guaranteed by the OO theory. Finally, this work demonstrates the computational efficiency of the STOO algorithm via various tests on the IEEE 118-bus and 244-bus systems partitioned into four subsystems using a 4-PC network and compares the results with those obtained using other heuristic methods, Genetic Algorithm, Tabu Search, Ant Colony Optimization and Simulated Annealing. Test results show the validity, robustness and excellent computational efficiency of the STOO algorithm for obtaining a good enough solution.

Most Relevant Explanation: computational complexity and approximation methods

Most Relevant Explanation (MRE) is the problem of finding a partial instantiation of a set of target variables that maximizes the generalized Bayes factor as the explanation for given evidence in a Bayesian network. MRE has a huge solution space and is extremely difficult to solve in large Bayesian networks. In this paper, we first prove that MRE is at least NP-hard. We then define a subproblem of MRE called MRE k that finds the most relevant k-ary explanation and prove that the decision problem of MRE k is $NP^{\it PP}$ -complete. Since MRE needs to find the best solution by MRE k over all k, and we can also show that MRE is in $NP^{\it PP}$ , we conjecture that a decision problem of MRE is $NP^{\it PP}$ -complete as well. Furthermore, we show that MRE remains in $NP^{\it PP}$ even if we restrict the number of target variables to be within a log factor of the number of all unobserved variables. These complexity results prompt us to develop a suite of approximation algorithms for solving MRE, One algorithm finds an MRE solution by integrating reversible-jump MCMC and simulated annealing in simulating a non-homogeneous Markov chain that eventually concentrates its mass on the mode of a distribution of the GBF scores of all solutions. The other algorithms are all instances of local search methods, including forward search, backward search, and tabu search. We tested these algorithms on a set of benchmark diagnostic Bayesian networks. Our empirical results show that these methods could find optimal MRE solutions for most of the test cases in our experiments efficiently.

Ordinal Optimization Approach for Throughput Maximization Problems in MOFDM Uplink System

This work presents a two-stage ordinal optimization theory-based approach for solving the throughput maximization problems with power constraints of sub-carrier assignment and power allocation in multi-user orthogonal frequency division multiplexing uplink systems. In the first stage, a crude but efficient model is employed to evaluate the performance of a sub-carrier assignment pattern and the genetic algorithm is used to search through the huge solution space. In the second stage, an exact model is employed to evaluate s best sub-carrier assignment patterns obtained in stage 1 and form the select subset. Finally, the best one of the select subset is the good enough solution that we seek. Via numerous tests, this work demonstrates the efficiency of the proposed algorithm and compares it with those of other heuristic methods.

Intelligent GIS for solving high‐dimensional site selection problems using ant colony optimization techniques

This paper presents a new method to solve site selection problems using ant colony optimization (ACO) techniques. Optimal spatial search for siting public facilities is a common task for urban planning. The objective is to find N optimal sites (targets) for sitting a facility so that the total benefits are maximized or the total costs are minimized. It is straightforward to use the brute‐force method for identifying the optimal solution by enumerating all possible combinations. However, the brute‐force method has difficulty in solving complex spatial search problems because of a huge solution space. Ant colony optimization can provide a useful tool for site selection. In this study, the integration of ACO with geographic information systems is proposed to include various types of spatial variables in the optimization. A number of modifications have also been introduced so that ACO can fit spatial allocation problems. The novelty of this research includes the adoption of the strategies of neighborhood pheromone diffusion, tabu table adjusting, and multi‐scale optimization. This method has been applied to the allocation of a hypothetical facility in Guangzhou City, China. The experiment indicates that the proposed model has better performance than the single search and the genetic algorithm for solving common site search problems.

A Computationally Efficient Method for Large Dimension Subcarrier Assignment and Bit Allocation Problem of Multiuser OFDM System

In this paper, we propose a computationally efficient method to solve the large dimension Adaptive Subcarrier Assignment and Bit Allocation (ASABA) problem of multiuser orthogonal frequency division multiplexing system. Our algorithm consists of three Ordinal Optimization (OO) stages to find a good enough solution to the considered problem. First of all, we reformulate the considered problem to separate it into subcarrier assignment and bit allocation problem such that the objective function of a feasible subcarrier assignment pattern is the corresponding optimal bit allocation for minimizing the total consumed power. Then in the first stage, we develop an approximate objective function to evaluate the performance of a subcarrier assignment pattern and use a genetic algorithm to search through the huge solution space and select s best subcarrier assignment patterns based on the approximate objective values. In the second stage, we employ an off-line trained artificial neural network to estimate the objective values of the s subcarrier assignment patterns obtained in stage 1 and select the l best patterns. In the third stage, we use the exact objective function to evaluate the l subcarrier assignment patterns obtained in stage 2, and the best one associated with the corresponding optimal bit allocation is the good enough solution that we seek. We apply our algorithm to numerous cases of large-dimension ASABA problems and compare the results with those obtained by four existing algorithms. The test results show that our algorithm is the best in both aspects of solution quality and computational efficiency.

Tabu Search Strategies for the Public Transportation Network Optimizations with Variable Transit Demand

Abstract: Systematic tabu search (TS)‐based heuristic methods are put forward in this article and applied for the design of public transportation networks with variable demand. A multi‐objective nonlinear mixed integer model is formulated. Solution methodologies are proposed, which consist of three main components: an initial candidate route set generation procedure (ICRSGP) that generates all feasible routes incorporating practical bus transit industry guidelines; a network analysis procedure (NAP) that decides transit demand matrix, assigns transit trips, determines service frequencies, and computes performance measures; and a Tabu search method (TSM) that combines these two parts, guides the candidate solution generation process, and selects an optimal set of routes from the huge solution space. Comprehensive tests are conducted and sensitivity analyses are performed. Characteristics analyses are undertaken and solution qualities from different algorithms are compared. Numerical results clearly indicate that the preferred TSM outperforms the genetic algorithm used as a benchmark for the optimal bus transit route network design problem without zone demand aggregation.

Instruction-Matrix-Based Genetic Programming

In genetic programming (GP), evolving tree nodes separately would reduce the huge solution space. However, tree nodes are highly interdependent with respect to their fitness. In this paper, we propose a new GP framework, namely, instruction-matrix (IM)-based GP (IMGP), to handle their interactions. IMGP maintains an IM to evolve tree nodes and subtrees separately. IMGP extracts program trees from an IM and updates the IM with the information of the extracted program trees. As the IM actually keeps most of the information of the schemata of GP and evolves the schemata directly, IMGP is effective and efficient. Our experimental results on benchmark problems have verified that IMGP is not only better than those of canonical GP in terms of the qualities of the solutions and the number of program evaluations, but they are also better than some of the related GP algorithms. IMGP can also be used to evolve programs for classification problems. The classifiers obtained have higher classification accuracies than four other GP classification algorithms on four benchmark classification problems. The testing errors are also comparable to or better than those obtained with well-known classifiers. Furthermore, an extended version, called condition matrix for rule learning, has been used successfully to handle multiclass classification problems.

Application of an Ordinal Optimization Algorithm to the Wafer Testing Process

In this correspondence, we have formulated a stochastic optimization problem to find the optimal threshold values to reduce the overkills of dies under a tolerable retest level in wafer testing process. The problem is a hard optimization problem with a huge solution space. We propose an ordinal optimization theory-based two-level algorithm to solve for a vector of good enough threshold values and compare with those obtained by others using a set of 521 real test wafers. The test results confirm the feature of controlling the retest level in our formulation, and the pairs of overkills and retests resulted from our approach are almost Pareto optimal. In addition, our approach spends only 6.05 min in total in a Pentium IV personal computer to obtain the good enough threshold values

Optimisation of Infrastructure Location

This paper presents a model aimed at finding an efficient allocation of infrastructure investments in a region. The problem’s complexity is due not only to its combinatorial nature, but also due to the intrinsic multidimensional spatio-temporal relationships of its variables. Furthermore, there is no explicit solution for such NP-complete combinatorial optimisation problem; thus a heuristic optimisation technique such as Simulated Annealing is used to search for ‘‘good’’ solutions in a finite but huge solution space. In this paper, the approach applied in the ‘‘Xuzhou Integrated Settlement and Transportation Planning Project’’, carried out in the People’s Republic of China as a joint venture between the Jiangsu Development Planning Commission (JDPC) and the Institute of Regional Development Planning of the University of Stuttgart (IREUS), is to be presented. This study considered projects in 18 realms of infrastructure, in 115 locations of an administrative unit with about 9 million inhabitants. The results of the study suggest a significant gain in allocation efficiency due to the applied method of optimisation.

Using a Simulated Annealing Algorithm to Solve the Transit Route Network Design Problem

This paper uses a simulated annealing algorithm to solve the optimal bus transit route network design problem (BTRNDP) at the distribution node level. A multiobjective nonlinear mixed integer model is formulated for the BTRNDP. The proposed solution framework consists of three main components: An initial candidate route set generation procedure that generates all feasible routes incorporating practical bus transit industry guidelines; and a network analysis procedure that assigns transit trips, determines service frequencies, and computes performance measures; and a simulated annealing procedure that combines these two parts, guides the candidate solution generation process and selects an optimal set of routes from the huge solution space. Three experimental networks are successfully tested as a pilot study. A genetic algorithm is also used as a benchmark to measure the quality of the simulated annealing algorithm. The presented numerical results clearly indicate that the simulated annealing outperforms the genetic algorithm in most cases using the example networks. Sensitivity analyses are performed and related characteristics and tradeoffs underlying the BTRNDP are also discussed.

Optimal Transit Route Network Design Problem with Variable Transit Demand: Genetic Algorithm Approach

This paper uses a genetic algorithm to systematically examine the underlying characteristics of the optimal bus transit route network design problem (BTRNDP) with variable transit demand. A multiobjective nonlinear mixed integer model is formulated for the BTRNDP. The proposed solution framework consists of three main components: an initial candidate route set generation procedure (ICRSGP) that generates all feasible routes incorporating practical bus transit industry guidelines; and a network analysis procedure (NAP) that decides transit demand matrix, assigns transit trips, determines service frequencies, and computes performance measures; and a genetic algorithm procedure (GAP) that combines these two parts, guides the candidate solution generation process, and selects an optimal set of routes from the huge solution space. A C++ program code is developed to implement the proposed solution methodology for the BTRNDP with variable transit demand. An example network is successfully tested as a pilot study. Sensitivity analyses are performed. Comprehensive characteristics underlying the BTRNDP, including the effect of route set size, the effect of demand aggregation, and the redesign of the existing transit network issue, are also presented.

Speeding Up a Genetic Algorithm for EPR-Based Spin Label Characterization of Biosystem Complexity

Complexity of biological systems is one of the toughest problems for any experimental technique. Complex biochemical composition and a variety of biophysical interactions governing the evolution of a state of a biological system imply that the experimental response of the system would be superimposed of many different responses. To obtain a reliable characterization of such a system based on spin-label Electron Paramagnetic Resonance (EPR) spectroscopy, multiple Hybrid Evolutionary Optimization (HEO) combined with spectral simulation can be applied. Implemented as the GHOST algorithm this approach is capable of handling the huge solution space and provides an insight into the "quasicontinuous" distribution of parameters that describe the biophysical properties of an experimental system. However, the analysis procedure requires several hundreds of runs of the evolutionary optimization routine making this algorithm extremely computationally demanding. As only the best parameter sets from each run are assumed to contribute into the final solution, this algorithm appears far from being optimized. The goal of this study is to modify the optimization routine in a way that 20-40 runs would be enough to obtain qualitatively the same characterization. However, to keep the solution diversity throughout the HEO run, fitness sharing and newly developed shaking mechanisms are applied and tested on various test EPR spectra. In addition, other evolutionary optimization parameters such as population size and probability of genetic operators were also varied to tune the algorithm. According to the testing examples a speed-up factor of 5-7 was achieved.

AN EFFICIENT META-HEURISTIC ALGORITHM FOR ROUTING PRODUCT COLLECTING VEHICLES OF DEHYDRATION PLANTS. II. ALGORITHM PERFORMANCE AND CASE STUDIES

Routing of vehicle fleet for collecting newly cropped raw materials for multi-product dehydration plants is a component of plant production schedule of utmost significance. A meta-heuristic algorithm for efficiently solving the collecting vehicle routing problem was developed and analyzed in detail in Tarantilis and Kiranoudis (2000). Meta-heuristic algorithms are broadly characterized by a stochastic nature in producing tender solution configurations in linear search terms, which sweep the huge solution space in a guided and rational way. Algorithm performance is examined through an analysis of the impact of model parameters on solution procedure during the execution of typical routing problems. The most important model parameter examined was found to be the value of the initial threshold as well as the way that the value of this actual parameter is appropriately adjusted during the optimization process. The main characteristic of the algorithm is the way that threshold is not only lowered but also raised, or backtracked, depending on the success of the inner loop iterations to provide for an acceptable new solution that would replace an older one. An important feature of the algorithm is the fact that appearance of better configurations within a process run is distributed according to the Poisson probability distribution. The suggested algorithm is tested against typical literature benchmarks as well against real-world problem encountered in the production planning procedures of dehydration plants in Greece.

Performance-oriented technology mapping for LUT-based FPGA's

An efficient and effective optimization technique is developed for technology mapping of lookup table (LUT) based field programmable gate arrays. In our algorithm, minimal depth of a Boolean network is found and then the given cost function is minimized by nodes of the given Boolean network without increasing the depth. The sweeping allows an efficient search over a huge solution space since it utilizes the topological structure of the network. Optimization for reconvergent paths and duplication of logic can be automatically considered during the sweeping procedure. Experimental results show that our approach is very promising. Typically our method, called SWEEP, produced the same depth for the 17 benchmark circuits tried as those of FlowMap which guarantees the optimum depth. Furthermore, SWEEP outperforms FlowMap by 17% in the total number of LUT's required to implement the benchmark circuits. >

Depth-first-search and dynamic programming algorithms for efficient CMOS cell generation

An algorithmic framework is presented for mapping CMOS circuit diagrams into area-efficient, high-performance layouts in the style of one-dimensional transistor arrays. Using efficient search techniques and accurate evaluation methods, the huge solution space that is typical to such problems is transversed extremely fast, yielding designs of hand-layout quality. In addition to generating circuits that meet prespecified layout constraints in the context of a fixed target image, on-the-fly optimizations are performed to meet secondary optimization criteria. A practical dynamic programming routing algorithm is utilized to accommodate the special conditions that arise in this context. This algorithm has been implemented and is currently used at IBM for cell-library generation. >