Search Restarts Research Articles

Comment on "Inverse Square Lévy Walks are not Optimal Search Strategies for d≥2".

It is widely accepted that inverse square L\'evy walks are optimal search strategies because they maximize the encounter rate with sparse, randomly distributed, replenishable targets when the search restarts in the vicinity of the previously visited target, which becomes revisitable again with high probability, i.e., non-destructive foraging [Nature 401, 911 (1999)]. The precise conditions for the validity of this L\'evy flight foraging hypothesis (LFH) have been widely described in the literature [Phys. Life Rev. 14, 94 (2015)]. Nevertheless, three objecting claims to the LFH have been raised recently for $d \geq 2$: (i) the capture rate $\eta$ has linear dependence on the target density $\rho$ for all values of the L\'evy index $\alpha$; (ii) "the gain $\eta_{max}/\eta$ achieved by varying $\alpha $ is bounded even in the limit $\rho \to 0 $" so that "tuning $\alpha$ can only yield a marginal gain"; (iii) depending on the values of the radius of detection $a$, the restarting distance $l_c$ and the scale parameter $s$, the optimum is realized for a range of $\alpha$ [Phys. Rev. Lett. 124, 080601 (2020)]. Here we answer each of these three criticisms in detail and show that claims (i)-(iii) do not actually invalidate the LFH. Our results and analyses restore the original result of the LFH for non-destructive foraging.

Frontier Search and Plan Reconstruction in Oversubscription Planning

Oversubscription planning (OSP) is the problem of choosing an action sequence which reaches a state with a high utility, given a budget for total action cost. This formulation allows us to handle situations with under-constrained resources, which do not allow us to achieve all possible goal facts. In optimal OSP, the task is further constrained to finding a path which achieves a state with maximal utility. An incremental BFBB search algorithm with landmark-based approximations, proposed for OSP heuristic search to address tasks with non-negative and 0-binary utility functions. Incremental BFBB maintained with the best solution so far and a set of reference states, extended with all the non-redundant value-carrying states discovered during the search. Each iteration requires search re-start in order to exploit the new knowledge obtained along the search. Recent work proposed an approach of relative estimation of achievements with value-driven landmarks to address arbitrary utility functions, which incrementally improves the best existing solution so far eliminating the need to maintain a set of reference states. We now propose a progressive frontier search algorithm, which alleviates the need to re-start from scratch once new information is acquired by capturing the frontier achieved at the end of each iteration which is used as a dynamic reference point to continue the search, leading to improved efficiency of the search.

Time-Bounded Best-First Search for Reversible and Non-reversible Search Graphs

Time-Bounded A* is a real-time, single-agent, deterministic search algorithm that expands states of a graph in the same order as A* does, but that unlike A* interleaves search and action execution. Known to outperform state-of-the-art real-time search algorithms based on Korf's Learning Real-Time A* (LRTA*) in some benchmarks, it has not been studied in detail and is sometimes not considered as a ``true'' real-time search algorithm since it fails in non-reversible problems even it the goal is still reachable from the current state. In this paper we propose and study Time-Bounded Best-First Search (TB(BFS)) a straightforward generalization of the time-bounded approach to any best-first search algorithm. Furthermore, we propose Restarting Time-Bounded Weighted A* (TB_R(WA*)), an algorithm that deals more adequately with non-reversible search graphs, eliminating ``backtracking moves'' and incorporating search restarts and heuristic learning. In non-reversible problems we prove that TB(BFS) terminates and we deduce cost bounds for the solutions returned by Time-Bounded Weighted A* (TB(WA*)), an instance of TB(BFS). Furthermore, we prove TB_R(WA*), under reasonable conditions, terminates. We evaluate TB(WA) in both grid pathfinding and the 15-puzzle. In addition, we evaluate TB_R(WA*) on the racetrack problem. We compare our algorithms to LSS-LRTWA*, a variant of LRTA* that can exploit lookahead search and a weighted heuristic. A general observation is that the performance of both TB(WA*) and TB_R(WA*) improves as the weight parameter is increased. In addition, our time-bounded algorithms almost always outperform LSS-LRTWA* by a significant margin.

A novel approach to the optimum design of MTMDs under seismic excitations

Summary This paper presents an efficient single-stage scheme for the global optimization of multiple tuned mass dampers subjected to seismic excitations. To take into account the oscillators' vertical and horizontal distribution, the use of the ground structure concept is proposed. This procedure is very useful because it avoids the pre-definition of the tuned mass dampers number and their placement. Because the multiple tuned mass dampers optimization problem is nonconvex and multimodal, this paper presents a novel hybrid stochastic/deterministic algorithm. The Firefly algorithm is used in the stochastic part, that is, to locate the global solution region and to provide a starting point to the local optimizer. The Nelder–Mead algorithm is then used as a local optimizer. Global search restarts are applied after convergence of the local search, allowing convergence to the global solution. In addition, because the structural response is obtained in the frequency domain, the scheme becomes very robust and requires considerably less computational effort than time history analysis. For illustration purposes, a numerical example on a ten-story shear building is demonstrated. Copyright © 2016 John Wiley & Sons, Ltd.

An efficient local search with noising strategy for Google Machine Reassignment problem

We present a local search method combined with noising strategy to efficiently solve the Google Machine Reassignment problem (GMRP), proposed at the ROADEF/EURO Challenge 2012 competition. The GMRP is a challenging and novel optimization problem, aimed at maximizing the usage of a set of machines by reallocating processes among those machines in a cost-efficient manner, while respecting a set of technological constraints. The search explores three different neighborhoods. Intensification and diversification of the search is achieved through the noising strategy, sorting the processes and search restarts. The noising is done by simple and suitable change of the objective function. The method is tested on 30 instances proposed by Google and used challenge evaluation. Most of the numerical results obtained here are proven to be optimal, near optimal, or the best known. The presented method was ranked first at ROADEF/EURO Challenge 2012 competition.

Stochastic Constriction Cockroach Swarm Optimization for Multidimensional Space Function Problems

The effect of stochastic constriction on cockroach swarm optimization (CSO) algorithm performance was examined in this paper. A stochastic constriction cockroach swarm optimization (SCCSO) algorithm is proposed. A stochastic constriction factor is introduced into CSO algorithm for swarm stability enhancement; control cockroach movement from one position to another while searching for solution to avoid explosion; enhanced local and global searching capabilities. SCCSO performance was tested through simulation studies and its performance on multidimensional functions is compared with that of original CSO, modified cockroach swarm optimization (MCSO), and one of the well-known global optimization techniques in the literature known as line search restart techniques (LSRS). Standard benchmarks that have been widely used for global optimization problems are considered for evaluating the proposed algorithm. The selected benchmarks were solved up to 3000 dimensions by the proposed algorithm.

A line search approach for high dimensional function optimization

This paper proposes a modified line search method which makes use of partial derivatives and re-starts the search process after a given number of iterations by modifying the boundaries based on the best solution obtained at the previous iteration (or set of iterations). Using several high dimensional benchmark functions, we illustrate that the proposed Line Search Re-Start (LSRS) approach is very suitable for high dimensional global optimization problems. Performance of the proposed algorithm is compared with two popular global optimization approaches, namely, genetic algorithm and particle swarm optimization method. Empirical results for up to 10,000 dimensions clearly illustrate that the proposed approach performs very well for the tested high dimensional functions.

A novel global optimization technique for high dimensional functions

Several types of line search methods are documented in the literature and are well known for unconstraint optimization problems. This paper proposes a modified line search method, which makes use of partial derivatives and restarts the search process after a given number of iterations by modifying the boundaries based on the best solution obtained at the previous iteration (or set of iterations). Using several high-dimensional benchmark functions, we illustrate that the proposed line search restart (LSRS) approach is very suitable for high-dimensional global optimization problems. Performance of the proposed algorithm is compared with two popular global optimization approaches, namely, genetic algorithm and particle swarm optimization method. Empirical results for up to 2000 dimensions clearly illustrate that the proposed approach performs very well for the tested high-dimensional functions. © 2009 Wiley Periodicals, Inc.

An approach to efficient planning with numerical fluents and multi-criteria plan quality

Dealing with numerical information is practically important in many real-world planning domains where the executability of an action can depend on certain numerical conditions, and the action effects can consume or renew some critical continuous resources, which in pddl can be represented by numerical fluents. When a planning problem involves numerical fluents, the quality of the solutions can be expressed by an objective function that can take different plan quality criteria into account. We propose an incremental approach to automated planning with numerical fluents and multi-criteria objective functions for pddl numerical planning problems. The techniques in this paper significantly extend the framework of planning with action graphs and local search implemented in the lpg planner. We define the numerical action graph (NA-graph) representation for numerical plans and we propose some new local search techniques using this representation, including a heuristic search neighborhood for NA-graphs, a heuristic evaluation function based on relaxed numerical plans, and an incremental method for plan quality optimization based on particular search restarts. Moreover, we analyze our approach through an extensive experimental study aimed at evaluating the importance of some specific techniques for the performance of the approach, and at analyzing its effectiveness in terms of fast computation of a valid plan and quality of the best plan that can be generated within a given CPU-time limit. Overall, the results show that our planner performs quite well compared to other state-of-the-art planners handling numerical fluents.

On Using Cutting Planes in Pseudo-Boolean Optimization

Cutting planes are a well-known, widely used, and very eectiv e technique for Integer Linear Programming (ILP). However, cutting plane techniques are seldom used in PseudoBoolean Optimization (PBO) algorithms. This paper addresses the utilization of Gomory mixed-integer and clique cuts, in Satisabilit y-based algorithms for PBO, and shows how these cuts can be used for computing lower bounds and for learning new constraints. A side result of learning new constraints is that the utilization of cutting planes enables nonchronological backtracking. Besides cutting planes, the paper also shows that the utilization of search restarts in PBO can be eectiv e in practice, allowing the computation of tighter lower bounds each time the search restarts. The more aggressive lower bounds result from the constraints learned due to the utilization of cutting planes. Experimental results show that the integration of cutting planes and search restarts in a SAT-based algorithm for PBO yields a competitive new solution for PBO.

Optimization-Based Synthesis of Grashof Geared Five-Bar Mechanisms

A quasi-Newton optimization routine and Grashof criteria for geared five-bar mechanisms are used to develop a Grashof five-bar mechanism synthesis routine. Sequential transformations mapping Grashof mechanism parameters satisfying sub-type specific upper and lower constraints are used. Convergence criteria of: (i) objective function value change, (ii) mechanism parameter change, and (iii) task satisfaction are used. These criteria, combined with search restarts, ensure the synthesis of an acceptable mechanism. Example results demonstrate the effectiveness of the routine.

Solving the job shop scheduling problem with tabu search

In the job shop scheduling problem we desire to minimize the makespan where a set of machines perform technologically ordered operations unique to each member of a set of jobs. Each operation has a fixed time duration, no machine can perform more than one operation at a time, and preemption is not allowed. In this paper, an effective tabu search approach to the job shop scheduling problem is presented. The procedure starts from the best solution rendered by a set of 14 heuristic dispatching solutions. It then makes use of the classical disjunctive network representation of the problem and iteratively moves to another feasible solution by reversing the order of two adjacent critical path operations performed by the same machine. The concepts of historical generators and search restart are used in conjunction with a contiguous spectrum of short term memory values to enhance the overall exploration strategy. Computational results are presented and areas for future investigation are suggested.