Random Initial Solutions Research Articles

On the performance of Scatter Search for post-enrolment course timetabling problems

This study presents an investigation of enhancing the capability of the Scatter Search (SS) metaheuristic in guiding the search effectively toward elite solutions. Generally, SS generates a population of random initial solutions and systematically selects a set of diverse and elite solutions as a reference set for guiding the search. The work focuses on three strategies that may have an impact on the performance of SS. These are: explicit solutions combination, dynamic memory update, and systematic search re-initialization. First, the original SS is applied. Second, we propose two versions of the SS (V1 and V2) with different strategies. In contrast to the original SS, SSV1 and SSV2 use the quality and diversity of solutions to create and update the memory, to perform solutions combinations, and to update the search. The differences between SSV1 and SSV2 is that SSV1 employs the hill climbing routine twice whilst SSV2 employs hill climbing and iterated local search method. In addition, SSV1 combines all pairs (of quality and diverse solutions) from the RefSet whilst SSV2 combines only one pair. Both SSV1 and SSV2 update the RefSet dynamically rather than static (as in the original SS), where, whenever a better quality or more diverse solution is found, the worst solution in RefSet is replaced by the new solution. SSV1 and SSV2 employ diversification generation method twice to re-initialize the search. The performance of the SS is tested on three benchmark post-enrolment course timetabling problems. The results had shown that SSV2 performs better than the original SS and SSV1 (in terms of solution's quality and computational time). It clearly demonstrates the effectiveness of using dynamic memory update, systematic search re-initialization, and combining only one pair of elite solutions. Apart from that, SSV1 and SSV2 can produce good quality solutions (comparable with other approaches), and outperforms some approaches reported in the literature (on some instances with regards to the tested datasets). Moreover, the study shows that by combining (simple crossover) only one pair of elite solutions in each RefSet update, and updating the memory dynamically, the computational time is reduced.

A discrete dynamic convexized method for the max-cut problem

The max-cut problem is a classical NP-hard problem in graph theory. In this paper, we adopt a local search method, called MCFM, which is a simple modification of the Fiduccia-Mattheyses heuristic method in Fiduccia and Mattheyses (Proc. ACM/IEEE DAC, pp. 175–181, 1982) for the circuit partitioning problem in very large scale integration of circuits and systems. The method uses much less computational cost than general local search methods. Then, an auxiliary function is presented which has the same global maximizers as the max-cut problem. We show that maximization of the function using MCFM can escape successfully from previously converged discrete local maximizers by taking increasing values of a parameter. An algorithm is proposed for the max-cut problem, by maximizing the auxiliary function using MCFM from random initial solutions. Computational experiments were conducted on three sets of standard test instances from the literature. Experimental results show that the proposed algorithm is effective for the three sets of standard test instances.

Grid-connected photovoltaic-systems design using evolutionary strategies

This paper addresses the problem of electrical losses that occur in the electrical conductors in photovoltaic (PV) plants with trackers. Thus, we propose a method which makes an optimal sizing and distribution of the elements that compose the PV to make the electrical losses by Joule effect as low as possible. To solve this problem, evolutionary algorithms implemented in matlab, have been used. Specifically the steady-state genetic algorithm (GA), the generational GA and the cross generational elitist selection, heterogeneous recombination and cataclism mutation (CHC) algorithm, which from random initial solutions, possibly far from optimal, will evolve into solutions that are increasingly closer to the desired optimum. Results have been very satisfactory, since all proposed examples have reduced by more than 40%, and CHC algorithm by more than 50%, electrical losses originated by not optimally designing the PV plant.

Hybrid genetic algorithm for minimizing non productive machining time during 2.5 D milling

Minimization of non-productive time of tool during machining for 2.5 D milling significantly reduces the machining cost. The tool gets retracted and repositioned several times in multi pocket jobs during rough machining which consumes 15 to 30% of total machining time depending on the complexity of job. The automatic CNC program commonly generates contour parallel tool path. Optimization of tool path length during on-productive time can be modeled on Traveling Salesman Problem (TSP) which belongs to family of non-deterministic polynomial (NP) hard problem. In the present work, a Hybrid Genetic Algorithm (HGA) has been proposed to optimize the non-productive tool path in which the initial seed solution is generated by special heuristic and combined with random initial solution generated by simple genetic algorithm (SGA). A defined performance index known as Relative percentage deviation (RPD) has been used for analyzing the results by varying the size of the jobs. From the analysis, it is found that HGA shows superiority over SGA for same computation time limit as the stopping criteria.

Hybrid optimization with improved tabu search

Finding a global optimum of an unknown system has attracted a great deal of interest in many engineering problems. In this settings, meta-heuristics are very common as efficient approaches for solving complex real-world problems in global continuous optimization problems (GCOPs) as they can approximate solutions without considering mathematical constraints such as differentiability. In this study, we propose a method based on tabu search (TS) and Nelder–Mead (NM) search strategy in application to GCOPs. To increase the robustness of the proposed method, we add a new phase, referred to as partitioning phase, before diversification which is realized by the TS. The TS is improved and then followed by the NM search strategy. The partitioning phase aims at distributing initial random solutions in the search space. By doing this, we increase the robustness of the method. The TS has an interesting ability of covering a wide solution space by promoting the search far away from the current solution and consecutively decreasing the possibility of trapping in local minima. The neighbour search-strategy of the TS is improved to accelerate the speed of finding the near optimum solution. Instead of just generating random neighbours around the current solution, we generate some neighbours in the direction of the previous move as well as some neighbours in the previous best crown. When certain criteria are reached for the diversification of the search space, the NM search strategy is carried out with the focus on the intensification of the solution found in the diversification phase. We assess the performance of the algorithm for a range of standard test functions available in the literature and compare the obtained results with those available in the literature. There are two main advantages of the proposed method; first, it can apply to any GCOP without considering any constraints and secondly, it shows better performance (in terms of function evaluation, success rate, and average error) for the functions with less than four input variables and relatively small or medium input domains. In other cases, the method still has acceptable perfomance and produces the results that are comparable with the results produced by other methods.

An Implementation of an Initial Scale in Solving Binary Knapsack Problem Using a Genetic Algorithm

In this paper, we used a new operation in a Genetic Algorithm for solving the binary Knapsack problem depending on it 's LP Relaxation solution after eliminating the fractional part of the non-binary values. The benefit is to make a filter to the initial random population from the farness of the optimal solution and unsuitable chromosomes. This good property will be fixed automatically in all generations in the Genetic Algorithm until reaching the optimal binary solution. 1. Introduction to Genetic Algorithm: A Genetic Algorithm (GA) was first introducted by John Holland for the formal investigation of the mechanisims of natural adaptation but the algorithm has been since modified to solve computational search problems, GA has been used to solve the NP-hard combinatorial problems effectively such as Knapsack Problem.(2) GA is a heuristic search algorithm for the solution of optimization problems in which starting from a random initial guess solution, better descendants are tried in an attempt to find one that is the best under some criteria and conditions.(5) GA is a computer algorithm that searches for good solutions to a problem from among a large number of possible solutions. It begins with a set of candidate solutions (chromosomes) called population. A new population is created from solutions of an old population in hope of getting a better population. Solutions which are chosen to the new solutions

Random walk biclustering for microarray data

A biclustering algorithm, based on a greedy technique and enriched with a local search strategy to escape poor local minima, is proposed. The algorithm starts with an initial random solution and searches for a locally optimal solution by successive transformations that improve a gain function. The gain function combines the mean squared residue, the row variance, and the size of the bicluster. Different strategies to escape local minima are introduced and compared. Experimental results on several microarray data sets show that the method is able to find significant biclusters, also from a biological point of view.

123 静定トラス列挙アルゴリズムを利用した柔構造物の最適設計

An efficient approach for generating pin-jointed compliant mechanisms is presented. A compliant mechanism uses the elastic deformation of structural parts to realize the mechanism for shape transformation of the entire structure, which is contrary to the conventional link mechanism. Ohsaki and Nishiwaki (Struct. Multidisc. Optim., Vol.30, pp.327-334, 2005) presented a method for generating flexible multistable bar-joint mechanisms using nonlinear programming approach. However, due to highly nonlinear property of the problem, the nonlinear programming problem should be solved many times with random initial solutions to obtain several types of mechanisms. Since the compliant pin-jointed mechanism is usually statically determinate, the optimization problem can be solved easily if the design space is limited to statically determinate structures. Avis et al. (Proc. of COCOON 2006, LNCS 4112, pp.205-215, 2006) presented an algorithm for enumerating all the non-crossing generically minimally rigid bar-joint frameworks, which are regarded as statically determinate trusses in structural engineering. In this paper, bistable mechanisms utilizing snapthrough behavior are obtained more efficiently with the algorithm. In the numerical example, many types of bistable compliant mechanisms are generated.

Fixed channel assignment using new dynamic programming approach in cellular radio networks

In this paper, we propose a new approach to the fixed channel assignment problem by modifying the dynamic programming technique. This new strategy extends the already known dynamic programming so that the channel assignment solutions can be obtained. There is no need to have an initial random solution for convergence. One of the questions in the fixed channel assignment is the minimum bandwidth, which is usually unknown; the new strategy can obtain this lower bound. Parallel processing can be implemented over the proposed algorithm. The existing fixed channel assignment methods do not have all these in one place. The performance of modified dynamic programming (MDP) is evaluated by computer simulation, applied to seven well-known benchmark problems on channel assignment. The channel assignment strategies results shows that required bandwidths of modified dynamic programming are closely match or sometimes better than the algorithms that we have investigated.

Capacity optimisation in MC‐CDMA systems

AbstractA novel efficient algorithm is proposed for the optimisation of capacity assignment in a MC‐CDMA system with an additional frequency division multiplexing component. Based on an estimate of the frequency‐selective channel, the algorithm optimises the assignment of the sub‐bands to the users with respect to the overall system capacity. Moreover, in the optimisation process the algorithm can efficiently cope with a given prioritisation among classes of user‐services, i.e. user‐groups, identified on the basis of a certain demand, such as throughput, tolerable delay and/or error rate etc. From an initial random solution, the algorithm proceeds progressively towards the optimisation of the target function, yielding, in general, a local optimum. By trying a few different initial solutions a very good approximation of the global optimum can be obtained. Futhermore, the algorithm complexity grows only as the square of the number of carriers. Simulation results show that its application provides a very significant gain in the downlink performance of the overall system or of the prioritised user‐groups.

An improved tabu search heuristic for solving facility layout design problems

The design of the facility layout of a manufacturing system, usually formulated and solved as a quadratic assignment problem (QAP), is of tremendous importance for its effective utilization. In this paper we discuss a new implementation of the tabu search metaheuristic to solve the QAP. Our tabu search implementation includes recency-based and long term memory structure, dynamic tabu list size strategies, and intensification and diversification strategies. The tabu search algorithm converges with a reasonable speed from any random initial solution to very good layouts. Our extensive computational experiments, including statistical analysis and library analysis, strongly support the superiority of our tabu search implementation (we refer to it as (CK)) over existing algorithms in the literature.

On the Significance of the Initial Solution in Travelling Salesman Heuristics

The quality requirements set by edge exchange heuristics on their initial solutions are evaluated in connection with the travelling salesman problem. The performance of the heuristics is measured using the expected value of the best solution achievable in a certain computing time. The computational results show that the use of initial solutions generated by applying a construction heuristic, instead of random initial solutions, typically improves the performance of edge exchange heuristics. The improvement, however, is dependent on the edge exchange heuristic to be used, the properties of the problem, and the computing time available.

On the Significance of the Initial Solution in Travelling Salesman Heuristics

The quality requirements set by edge exchange heuristics on their initial solutions are evaluated in connection with the travelling salesman problem. The performance of the heuristics is measured using the expected value of the best solution achievable in a certain computing time. The computational results show that the use of initial solutions generated by applying a construction heuristic, instead of random initial solutions, typically improves the performance of edge exchange heuristics. The improvement, however, is dependent on the edge exchange heuristic to be used, the properties of the problem, and the computing time available.

SIMULATED ANNEALING AND TABU SEARCH ALGORITHMS FOR MULTIWAY GRAPH PARTITION

For a given graph G with vertex and edge weights, we partition the vertices into subsets to minimize the total weights for edges crossing the subsets (weighted cut size) under the constraint that the vertex weights are evenly distributed among the subsets. We propose two new effective graph partition algorithms based on simulated annealing and tabu search, and compare their performance with that of the LPK algorithm reported in Ref. 12. Extensive experimental study shows that both of our new algorithms produce significantly better solutions than the LPK algorithm (maximal and minimal improvements on average weighted cut size are roughly 51.8% and 10.5% respectively) with longer running time, and this advantage in solution quality would not change even if we run the LPK algorithm repeatedly with random initial solutions in the same time frame as required by our algorithms.

Effective neural algorithms for the traveling salesman problem

Recently, several researchers have tried to solve the Traveling Salesman Problem (TSP) using the Hopfield model. Unfortunately, the results obtained so far are not good enough compared with the results obtained by conventional heuristic algorithms. This article presents two new neural algorithms. The first one uses Hopfield's neural network, and is a neural implementation of the Karp and Steele algorithm. Based on a generalized neural network, the second neural algorithm improves the first one by adaptively changing the neural network and thus the optimization function.On 40 TSP instances with random distance matrices, the Neural Algorithm 2 is better than Neural Algorithm 1 with confidence level α = 0.05, and much better than the 2-OPT (30 runs) and the Lin and Kernighan algorithm (30 runs).For random planar instances, Neural Algorithm 2 provides excellent initial solutions for iterative improvement algorithms, such as 2-OPT or Lin and Kernighan algorithm. For example, on 40 instances (each having 100 cities), the results of Neural Algorithm 2 improved by 2-OPT are better by at least 1.1% (with confidence level α = 0.0069) than the results produced by 2-OPT with 25 random initial solutions. If the results are postprocessed by the Lin and Kernighan algorithm, the Neural Algorithm 2 also outperforms the Lin and Kernighan algorithm with 20 random initial solutions (for each problem instance). Furthermore, the Neural Algorithm 2 scales up better than Lin and Kernighan algorithm (30 runs).

A Note on Garfinkel, Neebe and Rao's LP Decomposition for the p-Median Problem

The convergence problems of Garfinkel, Neebe and Rao's linear programming decomposition algorithm for the relaxed p-median problem are analyzed and traced back to the very degenerate nature of the LP formulation. Extensive computational experience with this algorithm is described. One surprising outcome of the tests conducted with the decomposition algorithm was that convergence was obtained more consistently when a random (and usually worse) initial solution was used instead of a “good” initial solution provided by heuristic methods.