Multi-criteria scheduling: an agent-based approach for expert knowledge integration

In this work, we present an agent-based approach to multi-criteria combinatorial optimization. It allows to flexibly combine elementary heuristics that may be optimal for corresponding single-criterion problems. We optimize an instance of the scheduling problem 1|d _j |∑C _j ,L _max and show that the modular building block architecture of our optimization model and the distribution of acting entities enables the easy integration of problem specific expert knowledge. We present a universal mutation operator for combinatorial problem encodings that allows to construct certain solution strategies, such as advantageous sorting or known optimal sequencing procedures. In this way, it becomes possible to derive more complex heuristics from atomic local heuristics that are known to solve fractions of the complete problem. We show that we can approximate both single-criterion problems such as P _m |d _j |∑U _j as well as more challenging multi-criteria scheduling problems, like P _m ||C _max,∑C _j and P _m |d _j |C _max,∑C _j ,∑U _j . The latter problems are evaluated with extensive simulations comparing the standard multi-criteria evolutionary algorithm NSGA-2 and the new agent-based model.     

Heuristic methods for the identical parallel machine flowtime problem with set-up times

We consider the scheduling of N jobs divided into G families for processing on M identical parallel machines. No set-up is necessary between jobs belonging to the same family. A set-up must be scheduled when switching from the processing of family i jobs to those of another family j, i≠j, the duration of this set-up being the sequence-independent set-up time s_j for family j. We propose heuristics for this problem and computationally evaluate the performance of the heuristics relative to lower bounds and solutions obtained using an exact algorithm.Scope and purposeWe study a machine-scheduling problem within which we have identical parallel machines, jobs arranged into families, and sequence-independent set-up times between jobs of different families on these machines. Our purpose is to develop simple, effective and efficient heuristics for this problem, and we seek to maximise the use of ideas and algorithms that have appeared previously in the literature for related problems. In our computational experiments, we seek to study the behaviour of these heuristics and uncover relevant properties of the scheduling problem. Within this experiment, we compare the observed performance of the heuristics relative to lower bounds and optimal solutions.     

Learning cluster-based structure to solve constraint satisfaction problems

The hybrid search algorithm for constraint satisfaction problems described here first uses local search to detect crucial substructures and then applies that knowledge to solve the problem. This paper shows the difficulties encountered by traditional and state-of-the-art learning heuristics when these substructures are overlooked. It introduces a new algorithm, Foretell, to detect dense and tight substructures called clusters with local search. It also develops two ways to use clusters during global search: one supports variable-ordering heuristics and the other makes inferences adapted to them. Together they improve performance on both benchmark and real-world problems.     

Developing usability heuristics with PROMETHEUS: A case study in virtual learning environments

Heuristic evaluation is one of the most widely-used methods for evaluating the usability of a software product. Proposed in 1990 by Nielsen and Molich, it consists in having a small group of evaluators performing a systematic revision of a system under a set of guiding principles known as usability heuristics. Although Nielsen’s 10 usability heuristics are used as the de facto standard in the process of heuristic evaluation, recent research has provided evidence not only for the need of custom domain specific heuristics, but also for the development of methodological processes to create such sets of heuristics. In this work we apply the PROMETHEUS methodology, recently proposed by the authors, to develop the VLEs heuristics: a novel set of usability heuristics for the domain of virtual learning environments. In addition to the development of these heuristics, our research serves as further empirical validation of PROMETHEUS. To validate our results we performed an heuristic evaluation using both VLEs and Nielsen’s heuristics. Our design explicitly controls the effect of evaluator variability by using a large number of evaluators. Indeed, for both sets of heuristics the evaluation was performed independently by 7 groups of 5 evaluators each. That is, there were 70 evaluators in total, 35 using VLEs and 35 using Nielsen’s heuristics. In addition, we perform rigorous statistical analyses to establish the validity of the novel VLEs heuristics. The results show that VLEs perform better than Nielsen’s heuristics, finding more problems, which are also more relevant to the domain, as well as satisfying other quantitative and qualitative criteria. Finally, in contrast to evaluators using Nielsen’s heuristics, evaluators using VLEs heuristics reported greater satisfaction regarding utility, clarity, ease of use, and need of additional elements.     

Reasoning and predicting POMDP planning complexity via covering numbers

Partially observable Markov decision processes (POMDPs) provide a rich mathematical framework for planning tasks in partially observable stochastic environments. The notion of the covering number, a metric of capturing the search space size of a POMDP planning problem, has been proposed as a complexity measure of approximate POMDP planning. Existing theoretical results are based on POMDPs with finite and discrete state spaces and measured in the l ₁-metric space. When considering heuristics, they are assumed to be always admissible. This paper extends the theoretical results on the covering numbers of different search spaces, including the newly defined space reachable under inadmissible heuristics, to the l _n-metric spaces. We provide a simple but scalable algorithm for estimating covering numbers. Experimentally, we provide estimated covering numbers of the search spaces reachable by following different policies on several benchmark problems, and analyze their abilities to predict the runtime of POMDP planning algorithms.     

On look-ahead heuristics in disjunctive logic programming

Disjunctive logic programming (DLP), also called answer set programming (ASP), is a convenient programming paradigm which allows for solving problems in a simple and highly declarative way. The language of DLP is very expressive and able to represent even problems of high complexity (every problem in the complexity class ${{\Sigma}_{2}^{P}} = {\rm NP}^{{\rm NP}}$ ). During the last decade, efficient systems supporting DLP have become available. Virtually all of these systems internally rely on variants of the Davis–Putnam procedure (for deciding propositional satisfiability [SAT]), combined with a suitable model checker. The heuristic for the selection of the branching literal (i.e., the criterion determining the literal to be assumed true at a given stage of the computation) dramatically affects the performance of a DLP system. While heuristics for SAT have received a fair deal of research, only little work on heuristics for DLP has been done so far. In this paper, we design, implement, optimize, and experiment with a number of heuristics for DLP. We focus on different look-ahead heuristics, also called “dynamic heuristics” (the DLP equivalent of unit propagation [UP] heuristics for SAT). These are branching rules where the heuristic value of a literal Q depends on the result of taking Q true and computing its consequences. We motivate and formally define a number of look-ahead heuristics for DLP programs. Furthermore, since look-ahead heuristics are computationally expensive, we design two techniques for optimizing the burden of their computation. We implement all the proposed heuristics and optimization techniques in DLV—the state-of-the-art implementation of disjunctive logic programming, and we carry out experiments, thoroughly comparing the heuristics and optimization techniques on a large number of instances of well-known benchmark problems. The results of these experiments are very interesting, showing that the proposed techniques significantly improve the performance of the DLV system.     

The two-stage assembly scheduling problem to minimize total completion time with setup times

We address the two-stage assembly scheduling problem where there are m machines at the first stage and an assembly machine at the second stage. The objective is to schedule the available n jobs so that total completion time of all n jobs is minimized. Setup times are treated as separate from processing times. This problem is NP-hard, and therefore we present a dominance relation and propose three heuristics. The heuristics are evaluated based on randomly generated data. One of the proposed heuristics is known to be the best heuristic for the case of zero setup times while another heuristic is known to perform well for such problems. A new version of the latter heuristic, which utilizes the dominance relation, is proposed and shown to perform much better than the other two heuristics.     

Interchangeability with thresholds and degradation factors for Soft CSPs

Substitutability and interchangeability in constraint satisfaction problems (CSPs) have been used as a basis for search heuristics, solution adaptation and abstraction techniques. In this paper, we consider how the same concepts can be extended to soft constraint satisfaction problems (SCSPs). We introduce two notions: threshold α and degradation factor δ for substitutability and interchangeability, ( _α substitutability/interchangeability and ^δ substitutability/interchangeabi-lity respectively). We show that they satisfy analogous theorems to the ones already known for hard constraints. In _α interchangeability, values are interchangeable in any solution that is better than a threshold α, thus allowing to disregard differences among solutions that are not sufficiently good anyway. In ^δ interchangeability, values are interchangeable if their exchange could not degrade the solution by more than a factor of δ. We give efficient algorithms to compute ( ^δ / _α )interchangeable sets of values for a large class of SCSPs, and show an example of their application. Through experimental evaluation based on random generated problem we measure first, how often neighborhood interchangeable values are occurring, second, how well they can approximate fully interchangeable ones, and third, how efficient they are when used as preprocessing techniques for branch and bound search.     

Addressing the N/1 scheduling problem—A heuristic approach

The problem of sequencing n-jobs on one machine (n/1) to minimize maximum job lateness has been the subject of much prior research. Most of this research has been directed at identifying optimal solutions to the problem via algorithmic search techniques. A weakness in employing an algorithm for solving the problem, however, is that lengthy computational times may result because of the necessity of searching n! sequences. By employing a multiple heuristic approach this limitation can be avoided. An optimal or near optimal schedule can be identified in a finite number of steps.This paper describes a multiple heuristic model that is effective more than eighty-ninety percent of the time in providing an optimal schedule for the N/l/L max scheduling program. Ten separate heuristics are described, and the results of testing the heuristics over fifteen hundred and sixty randomly generated problems is presented. Three of the heuristics are combined to form the heuristic-scheduling model.     

Two-stage hybrid flow shop scheduling with dynamic job arrivals

Motivated by applications in semiconductor manufacturing industry, we consider a two-stage hybrid flow shop where a discrete machine is followed by a batching machine. In this paper, we analyze the computational complexity of a class of two-machine problems with dynamic job arrivals. For the problems belonging to P we present polynomial algorithms. For the NP-complete problems we propose the heuristics, and then establish the upper bounds on the worst case performance ratios of the heuristics. In addition, we give the improved heuristics that can achieve better performances.     

On the empirical justification of theoretical heuristic transference and learning

The solution of intractable problems implies the use of heuristics. Quantum computers may find use for optimization problems, but have yet to solve any NP-hard problems. This paper demonstrates results in game theory for domain transference and the reuse of problem-solving knowledge through the application of learned heuristics. It goes on to explore the possibilities for the acquisition of heuristics for the solution of the NP-hard TSP problem. Here, it is found that simple heuristics (e.g., pairwise exchange) often work best in the context of more or less sophisticated experimental designs. Often, these problems are not amenable to exclusive logic solutions; but rather, require the application of hybrid approaches predicated on search. In general, such approaches are based on randomization and supported by parallel processing. This means that heuristic solutions emerge from attempts to randomize the search space. The paper goes on to present a constructive proof of the unbounded density of knowledge in support of the Semantic Randomization Theorem (SRT). It highlights this result and its potential impact upon the community of machine learning researchers.     

A revisit of fast greedy heuristics for mapping a class of independent tasks onto heterogeneous computing systems

Mixed-machine heterogeneous computing (HC) environments utilize a distributed suite of different high-performance machines, interconnected with high-speed links, to perform groups of computing-intensive applications that have diverse computational requirements and constraints. The problem of optimally mapping a class of independent tasks onto the machines of an HC environment has been proved, in general, to be NP-complete, thus requiring the development of heuristic techniques for practical usage. If the mapping has real-time requirements such that the mapping process is performed during task execution, fast greedy heuristics must be adopted. This paper investigates fast greedy heuristics for this problem and identifies the importance of the concept of task consistency in designing this mapping heuristic. We further propose task priority graph based fast greedy heuristics, which consider the factors of both task consistency and machine consistency (the same concept of consistency as in previous studies). A collection of 20 greedy heuristics, including 17 newly proposed ones, are implemented, analyzed, and systematically compared within a uniform model of task execution time. This model is implemented by the coefficient-of-variation based method. The experimental results illuminate the circumstances when a specific greedy heuristic would outperform the other 19 greedy heuristics.     

Efficient stochastic hybrid heuristics for the multi-depot vehicle routing problem

The paper addresses the problem of multi-depot vehicle routing in order to minimize the delivery time of vehicle objective. Three hybrid heuristics are presented to solve the multi-depot vehicle routing problem. Each hybrid heuristic combines elements from both constructive heuristic search and improvement techniques. The improvement techniques are deterministic, stochastic and simulated annealing (SA) methods. Experiments are run on a number of randomly generated test problems of varying depots and customer sizes. Our heuristics are shown to outperform one of the best-known existing heuristic. Statistical tests of significance are performed to substantiate the claims of improvement.     

ILP heuristics and a new exact method for bi-objective 0/1 ILPs: Application to FTTx-network design

Heuristics and metaheuristics are inevitable ingredients of most of the general purpose ILP solvers today, because of their contribution to the significant boost of the performance of exact methods. In the field of bi/multi-objective optimization, to the best of our knowledge, it is still not very common to integrate ILP heuristics into exact solution frameworks. This paper aims to bring a stronger attention of both the exact and metaheuristic communities to still unexplored possibilities for performance improvements of exact and heuristic multi-objective optimization algorithms.We focus on bi-objective optimization problems whose feasible solutions can be described as 0/1 integer linear programs and propose two ILP heuristics, boundary induced neighborhood search (BINS) and directional local branching. Their main idea is to combine the features and explore the neighborhoods of solutions that are relatively close in the objective space. A two-phase ILP-based heuristic framework relying on BINS and directional local branching is introduced. Moreover, a new exact method called adaptive search in objective space (ASOS) is also proposed. ASOS combines features of the ϵ-constraint method with the binary search in the objective space and uses heuristic solutions produced by BINS for guidance. Our new methods are computationally evaluated on two problems of particular relevance for the design of FTTx-networks. Comparison with other known exact methods (relying on the exploration of the objective space) is conducted on a set of realistic benchmark instances representing telecommunication access networks from Germany.     

Perturbation heuristics for the pickup and delivery traveling salesman problem

This article describes and compares seven perturbation heuristics for the Pickup and Delivery Traveling Salesman Problem (PDTSP). In this problem, a shortest Hamiltonian cycle is sought through a depot and several pickup and delivery pairs. Perturbation heuristics are diversification schemes which help a local search process move away from a local optimum. Three such schemes have been implemented and compared: Instance Perturbation, Algorithmic Perturbation, and Solution Perturbation. Computational results on PDTSP instances indicate that the latter scheme yields the best results. On instances for which the optimum is known, it consistently produces optimal or near-optimal solutions.Scope and purposeIn several distribution management contexts, it is necessary to construct a shortest tour starting at a depot and making several pickup and deliveries. In the Traveling Salesman Problem with Pickup and Delivery, to each pickup point is associated a delivery point later in the tour. Like several routing problems, the PDTSP is very hard to solve to optimality and local search heuristics often get trapped in local optima. Perturbation heuristics provide a means of escaping from local optima. This paper describes and compares three types of perturbation heuristic. It shows that the best scheme consistently yields high-quality solutions.     

Beam search heuristics for the single and multi-commodity capacitated Multi-facility Weber Problems

The Multi-facility Weber Problem (MWP) is concerned with locating I uncapacitated facilities in the plane to satisfy the demand of J customers with the minimum total transportation cost of a single commodity. It is a non-convex optimization problem and difficult to solve. In this work, we focus on the capacitated extensions of the MWP which are Capacitated MWP (CMWP) and multi-commodity CMWP (MCMWP). Both the CMWP and MCMWP impose capacity restrictions on facilities. Indeed, the MCMWP is a natural extension of the CMWP and considers the situation where K distinct commodities are shipped subject to limitations on the total amount of goods sent from facilities to the customers. Customer locations, demands and capacities for each commodity are known a priori. The transportation costs, which depend on the commodity type, are proportional to the distance between customers and facilities. We first introduce branch and bound algorithms for both the CMWP and the MCMWP then we propose beam search heuristics for these problems. According to our computational experiments on standard and randomly generated test instances, we can say that the new heuristics perform very well.     

Min-domain retroactive ordering for Asynchronous Backtracking

Ordering heuristics are a powerful tool in CSP search algorithms. Among the most successful ordering heuristics are heuristics which enforce a fail first strategy by using the Min-domain property (Haralick and Elliott, Artif Intel 14:263–313, 1980; Bessiere and Regin, Mac and combined heuristics: two reasons to forsake FC (and CBJ?) on hard problems. In Proc. CP 96, pp. 61–75, Cambridge, MA, 1996; Smith and Grant, Trying harder to fail first. In European Conference on Artificial Intelligence, pp. 249–253, 1998; Dechter, Constraint Processing. Morgan Kaufman, 2003). Ordering heuristics have been introduced recently to asynchronous backtracking (ABT), for distributed constraints satisfaction (DisCSP) (Zivan and Meisels, Dynamic ordering for asynchronous backtracking on discsps. In CP-2005, pp. 32–46, Sigtes (Barcelona), Spain, 2005). However, the pioneering study of dynamically ordered ABT, ABT_DO, has shown that a straightforward implementation of the Min-domain heuristic does not produce the expected improvement over a static ordering. The present paper proposes an asynchronous dynamic ordering which does not follow the standard restrictions on the position of reordered agents in ABT_DO. Agents can be moved to a position that is higher than that of the target of the backtrack. Combining the Nogood-triggered heuristic and the Min-domain property in this new class of heuristics results in the best performing version of ABT_DO. The new version of retroactively ordered ABT is faster by a large factor than the best form of ABT.     

Heuristically Accelerated Reinforcement Learning by Means of Case-Based Reasoning and Transfer Learning

Reinforcement Learning (RL) is a well-known technique for learning the solutions of control problems from the interactions of an agent in its domain. However, RL is known to be inefficient in problems of the real-world where the state space and the set of actions grow up fast. Recently, heuristics, case-based reasoning (CBR) and transfer learning have been used as tools to accelerate the RL process. This paper investigates a class of algorithms called Transfer Learning Heuristically Accelerated Reinforcement Learning (TLHARL) that uses CBR as heuristics within a transfer learning setting to accelerate RL. The main contributions of this work are the proposal of a new TLHARL algorithm based on the traditional RL algorithm Q(λ) and the application of TLHARL on two distinct real-robot domains: a robot soccer with small-scale robots and the humanoid-robot stability learning. Experimental results show that our proposed method led to a significant improvement of the learning rate in both domains.     

Downward pattern refinement for timed automata

Directed model checking is a well-established approach for detecting error states in concurrent systems. A popular variant to find shortest error traces is to apply the A\(^*\) search algorithm with distance heuristics that never overestimate the real error distance. An important class of such distance heuristics is the class of pattern database heuristics. Pattern database heuristics are built on abstractions of the system under consideration. In this paper, we propose downward pattern refinement, a systematic approach for the construction of pattern database heuristics for concurrent systems of timed automata. First, we propose a general framework for pattern databases in the context of timed automata and show that desirable theoretical properties hold for the resulting pattern database. Afterward, we formally define a concept to measure the accuracy of abstractions. Based on this concept, we propose an algorithm for computing succinct abstractions that are still accurate to produce informed pattern databases. We evaluate our approach on large and complex industrial problems. The experiments show the practical potential of the resulting pattern database heuristic.     

A note on “Beam search heuristics for the single machine early/tardy scheduling problem with no machine idle time”

In a recent paper by Valente “Beam search heuristics for the single machine early/tardy scheduling problem with no machine idle time”’, Computers & Industrial Engineering, 55, 663–675, 2008, several beam search approaches are compared on a large set of instances of the total weighted earliness-tardiness problem on single machine with jobs independent weights and no machine idle time. That problem is denoted 1|nmit|_∑jhEj+_∑jwTj$1|\mathit{nmit}|{\sum }_j{\mathit{hE}}_j+{\sum }_j{\mathit{wT}}_j$. This note points out that the standard iterated dynasearch procedure applied to that problem outperforms all the literature heuristics. Based on these results and others obtained on similar problems, we conclude that dynasearch for its efficiency and simplicity, should be used as a benchmark for future heuristics on those types of single machine no idle time problems.