OneMax in Black-Box Models with Several Restrictions

Black-box complexity studies lower bounds for the efficiency of general-purpose black-box optimization algorithms such as evolutionary algorithms and other search heuristics. Different models exist, each one being designed to analyze a different aspect of typical heuristics such as the memory size or the variation operators in use. While most of the previous works focus on one particular such aspect, we consider in this work how the combination of several algorithmic restrictions influence the black-box complexity. Our testbed are so-called OneMax functions, a classical set of test functions that is intimately related to classic coin-weighing problems and to the board game Mastermind. We analyze in particular the combined memory-restricted ranking-based black-box complexity of OneMax for different memory sizes. While its isolated memory-restricted as well as its ranking-based black-box complexity for bit strings of length $n$ is only of order $n/\log n$, the combined model does not allow for algorithms being faster than linear in $n$, as can be seen by standard information-theoretic considerations. We show that this linear bound is indeed asymptotically tight. Similar results are obtained for other memory- and offspring-sizes. Our results also apply to the (Monte Carlo) complexity of OneMax in the recently introduced elitist model, in which only the best-so-far solution can be kept in the memory. Finally, we also provide improved lower bounds for the complexity of OneMax in the regarded models. Our result enlivens the quest for natural evolutionary algorithms optimizing OneMax in $o(n \log n)$ iterations.Comment: This is the full version of a paper accepted to GECCO 201

Local search heuristics for multi-index assignment problems with decomposable costs.

The multi-index assignment problem (MIAP) with decomposable costs is a natural generalization of the well-known assignment problem. Applications of the MIAP arise for instance in the field of multi-target multi-sensor tracking. We describe an (exponentially sized) neighborhood for a solution of the MIAP with decomposable costs, and show that one can find a best solution in this neighborhood in polynomial time. Based on this neighborhood, we propose a local search algorithm. We empirically test the performance of published constructive heuristics and the local search algorithm on random instances; a straightforward tabu search is also tested. Finally, we compute lower bounds to our problem, which enable us to assess the quality of the solutions found.Assignment; Costs; Heuristics; Problems; Applications; Performance;

Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

Co-Scheduling Algorithms for High-Throughput Workload Execution

This paper investigates co-scheduling algorithms for processing a set of parallel applications. Instead of executing each application one by one, using a maximum degree of parallelism for each of them, we aim at scheduling several applications concurrently. We partition the original application set into a series of packs, which are executed one by one. A pack comprises several applications, each of them with an assigned number of processors, with the constraint that the total number of processors assigned within a pack does not exceed the maximum number of available processors. The objective is to determine a partition into packs, and an assignment of processors to applications, that minimize the sum of the execution times of the packs. We thoroughly study the complexity of this optimization problem, and propose several heuristics that exhibit very good performance on a variety of workloads, whose application execution times model profiles of parallel scientific codes. We show that co-scheduling leads to to faster workload completion time and to faster response times on average (hence increasing system throughput and saving energy), for significant benefits over traditional scheduling from both the user and system perspectives

Job-shop scheduling with an adaptive neural network and local search hybrid approach

This article is posted here with permission from IEEE - Copyright @ 2006 IEEEJob-shop scheduling is one of the most difficult production scheduling problems in industry. This paper proposes an adaptive neural network and local search hybrid approach for the job-shop scheduling problem. The adaptive neural network is constructed based on constraint satisfactions of job-shop scheduling and can adapt its structure and neuron connections during the solving process. The neural network is used to solve feasible schedules for the job-shop scheduling problem while the local search scheme aims to improve the performance by searching the neighbourhood of a given feasible schedule. The experimental study validates the proposed hybrid approach for job-shop scheduling regarding the quality of solutions and the computing speed

Variable neighbourhood decomposition search for 0-1 mixed integer programs

In this paper we propose a new hybrid heuristic for solving 0-1 mixed integer programs based on the principle of variable neighbourhood decomposition search. It combines variable neighbourhood search with a general-purpose CPLEX MIP solver. We perform systematic hard variable fixing (or diving) following the variable neighbourhood search rules. The variables to be fixed are chosen according to their distance from the corresponding linear relaxation solution values. If there is an improvement, variable neighbourhood descent branching is performed as the local search in the whole solution space. Numerical experiments have proven that exploiting boundary effects in this way considerably improves solution quality. With our approach, we have managed to improve the best known published results for 8 out of 29 instances from a well-known class of very di±cult MIP problems. Moreover, computational results show that our method outperforms the CPLEX MIP solver, as well as three other recent most successful MIP solution methods