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Advanced Algorithms for the Layout Problem
Published in Sunderesh S. Heragu, Facilities Design, 2022
As discussed in Chapter 9, optimal algorithms are guaranteed to produce the best solution (or at least one best solution when multiple ones exist) for a given problem. Heuristic algorithms, or simply heuristics, provide a solution but do not guarantee it to be the best. A good heuristic usually produces the best solution for most small problems.
Uncertainty
Published in Diane P. Michelfelder, Neelke Doorn, The Routledge Handbook of the Philosophy of Engineering, 2020
The discussion in this section will be about approaches that are used to mitigate the uncertainty caused by the basic sources of uncertainty. These methods reduce some uncertainty but then introduce their own uncertainties, which will also be discussed. Due to the nature of engineering design, the techniques used can be referred to as heuristics (Koen 2003). From an engineering standpoint, heuristics are anything that engineers use to help solve problems and perform designs that would otherwise be intractable or too expensive. “A heuristic is anything that provides a plausible aid or direction in the solution of a problem but is in the final analysis unjustified, incapable of justification, and potentially fallible” (Koen 2003: 28, italics in original). These heuristics may appear in codes of practice, may be widely used by engineers but not appear in codes of practice, or could be techniques for use in the future for design of systems like complex and complex adaptive systems. The techniques described in this section and the section on living with uncertainty are all heuristics, or more specifically engineering heuristics.
Synthesis of Downstream Processes
Published in Juan A. Asenjo, Separation Processes in Biotechnology, 2020
George J. Prokopakis, Juan A. Asenjo
Process synthesis problems are combinational in nature since they involve discrete decisions of the type: “a separation step is performed via method a or method b,” “a separation step is or is not included in the trains,” and so on. Combinatorial problems are extremely difficult to solve and in many instances a solution to a generalized formulation cannot be obtained in reasonable computational time, even with the most powerful computers (NP-completeness). Therefore, designers have devised heuristics (unproven rules of thumb) based on engineering practice to remove the combinatorial characteristics of the problem and obtain solutions that are, if not optimal, hopefully close to the optimum. The heuristic methods are one end of the spectrum of the available process synthesis techniques. The other end consists of mathematical programming techniques that recognize and retain the combinatorial nature of the problem and attempt to solve it rigorously.
Supporting teachers in supporting students’ mathematical problem solving
Published in International Journal of Mathematical Education in Science and Technology, 2022
Johan Sidenvall, Carina Granberg, Johan Lithner, Björn Palmberg
Schoenfeld (1985) showed that proficient problem solvers master four problem-solving competences: Resources, Heuristics, Control (Schoenfeld later used the term Metacognition), and Belief Systems. Resources consist of ‘mathematical knowledge possessed by the individual that can be brought to bear on the [problem] at hand’ (p. 15), for example, facts and procedures. Heuristics are strategies and techniques for making progress with problems, for example, drawing figures, exploiting related tasks, and reformulating tasks. Metacognition is defined as ‘global decisions regarding selection and implementation of resources and strategies’ (p. 15), that is, planning, monitoring, and decision making. Belief systems comprise ‘one’s ‘mathematical world view’, the set of (not necessarily conscious) determinants of an individual’s behavior’ (p. 15), and this includes views about oneself, the context, the topic, and the mathematics. Supporting students in their problem-solving process means supporting one or more of these competences. Although several years have passed since its publication, Schoenfeld’s framework is still the most comprehensive and well-cited framework for problem-solving competence (or knowledge and behaviour, as he denoted it).
Evaluating planning strategies for prioritizing projects in sustainability improvement programs
Published in Construction Management and Economics, 2020
Amir R. Hessami, Vahid Faghihi, Amy Kim, David N. Ford
Finally, heuristic algorithms are designed to find a good solution, but they do not necessarily guarantee that it is within a specific range of accuracy. With the right set of knowledge and experience, heuristic analyses can provide viable solutions for complex problems in a very short amount of time. Heuristic approaches are particularly useful during the earliest phases of program development, when precise design-level data about the projects may not yet be available. The relative simplicity of heuristic algorithms also makes them particularly suitable for supporting decisions at higher levels of management. Examples of commonly used heuristic methods include the Bottleneck Dynamics approach (prioritizing in order of decreasing benefit–cost ratio) (Morton et al. 1995), and the Tabu Search (solution neighbourhood searches with worsening moves permission) (Glover and Laguna 1998). In the current work, the researchers examined the most applicable heuristic strategies for sequencing projects in sustainability programs and assessed their effects on program performance.
Optimisation of the multi-depots pick-up and delivery problems with time windows and multi-vehicles using PSO algorithm
Published in International Journal of Production Research, 2020
Imen Harbaoui Dridi, Essia Ben Alaïa, Pierre Borne, Hanen Bouchriha
The industrial market increasingly requires the use of more effective managerial strategies to better meet the needs of the customer. One of the major problems that financially penalise companies is the transport of raw materials, which has a direct impact on the beginning dates of manufacturing. Indeed, an effective production plan includes the timely acquisition of resources. That's why nowadays, the transport optimisation and logistics performance are very important economic issues for companies. This is based, in particular, on the organisation and efficiency of vehicle routing. The Vehicle Routing Problem (VRP) is a combinatorial optimisation problem among the most known of the literature. It consists of determining the routes to be followed by a fleet of vehicles, in order to satisfy a set of requests customers (delivery, maintenance, repair, pickup, etc.). The study of the VRP and its multiple variants gave rise to many algorithms and resolution techniques. However, further to the complexity of these problems (important size, dynamics relations, multiplicity of the spatial, temporal and economic constraints), their resolution by exact methods is extremely difficult. The use of heuristic methods, or even meta-heuristics, is necessary to solve them effectively. These methods allow finding feasible solutions, in a reasonable calculation time.