A Method to Deduce and Synthesize the Dafny Programs

We propose a systematic method to deduce and synthesize the Dafny programs. First, the specification of problem is described in strict mathematical language. Then, the derivation process uses program specification transformation technology to perform equivalent transformation. Furthermore, Dafny program is synthesized through the obtained recursive relationship and loop invariants. Finally, the functional correctness of Dafny program is automatically verified by Dafny verifier or online tool. Through this method, we deduce and synthesize Dafny programs for many typical problems such as the cube sum problem, the minimum (or maximum) contiguous subarray problems, several searching problems, several sorting problems, and so on. Due to space limitation, we only illustrate the development process of Dafny programs for two typical problems: the minimum contiguous subarray problem and the new local bubble sorting problem. It proves that our method can effectively improve the correctness and reliability of Dafny program developed. What’s more, we demonstrate the potential of the deductive synthesis method by developing a new local bubble Sorting program.

Sorting path optimization of parallel robot based on improved Genetic Algorithm

In industrial production, parallel robot is often used for sorting, battery clamp is divided into two structures, the classification and sorting, for multi-target sorting problems. The motion path of end-effector is planned, the overall sorting path is planned, and the practical problem is transformed into a similar traveling salesman problem. The improved genetic algorithm is proposed to optimize the sorting time sequence, and the optimized path shortens 10.23% total distance on average compared with random sorting and 5.37% total distance compared with fixed longitudinal sorting. The shortening of the total distance can lead to higher sorting efficiency in sorting and increase productivity.

A Novel Multi-Criteria Decision Sorting Approach based on Chebyshev's Theorem for Supplier Classification Problem

One of the interesting features of Multi-Criteria Decision Making/ Multiple Attribute Decision Making (MCDM/ MADM) is that a number of techniques that can be used to solve the same problem. In general, three common categories of decision problems are choice problem, ranking problem, and sorting problem. While, the issue of choice and ranking problems is more emphasized in MCDM/ MADM, but the literature weakly consider sorting problems. Several solutions for the above problem are suggested (i.e., Flow sort, AHP-Sort, ELECTRE Tri, etc.). Theoretically, there is no reason to be limited to these techniques. Hence, in this paper we propose a novel multi-criteria sorting method that is based on Chebyshev’s theorem. More specifically, different from other studies on MCDM sorting problems, which put more emphasis on the extension of new models, this work attempts to present a general framework using the Chebyshev’s inequality, to transform the results of conventional MCDM models from ranking format to sort mode. Finally, the proposed approach is compared with three existed models. Compared results show that the proposed method is efficient and the results are stable.

Enriched preference modeling and robustness analysis for the ELECTRE Tri-B method

We consider multiple criteria sorting problems with preference-ordered classes delimited by a set of boundary profiles. While significantly extending the ELECTRE Tri-B method, we present an integrated framework for modeling indirect preference information and conducting robustness analysis. We allow the Decision Maker (DM) to provide the following three types of holistic judgments: assignment examples, assignment-based pairwise comparisons, and desired class cardinalities. A diversity of recommendation that can be obtained given the plurality of outranking-based sorting models compatible with the DM’s preferences is quantified by means of six types of results. These include possible assignments, class acceptability indices, necessary assignment-based preference relation, assignment-based outranking indices, extreme class cardinalities, and class cardinality indices. We discuss the impact of preference information on the derived outcomes, the interrelations between the exact results computed with mathematical programming and stochastic indices estimated with the Monte Carlo simulations, and new measures for quantifying the robustness of results. The practical usefulness of the approach is illustrated on data from the Financial Times concerning MBA programs.

Flexible and Interactive Tradeoff Elicitation for Multicriteria Sorting Problems

In this paper, we propose a new method for solving multiple criteria decision-making/aiding (MCDM/A) sorting problems in the context of multi-attribute value theory (MAVT), based on a flexible and interactive elicitation process. It uses partial information to require less information from the decision maker (DM), which is given in the form of preference statements. The proposed method keeps the axiomatic structure of the traditional tradeoff elicitation procedure, without requiring exact values of indifference to be set, which can be a difficult task for the DM to perform. The use of linear programming, combined with the decision rules, allows an alternative to be assigned into a class without the need to provide complete information. By being flexible and interactive, the proposed method allows the DM to monitor the range of possible classes for each alternative at any level of information available during the process, which can save time and effort. The applicability of the method is shown by solving a project management problem on sorting activities.

Capacity Random Forest for Correlative Multiple Criteria Decision Pattern Learning

The Choquet capacity and integral is an eminent scheme to represent the interaction knowledge among multiple decision criteria and deal with the independent multiple sources preference information. In this paper, we enhance this scheme’s decision pattern learning ability by combining it with another powerful machine learning tool, the random forest of decision trees. We first use the capacity fitting method to train the Choquet capacity and integral-based decision trees and then compose them into the capacity random forest (CRF) to better learn and explain the given decision pattern. The CRF algorithms of solving the correlative multiple criteria based ranking and sorting decision problems are both constructed and discussed. Two illustrative examples are given to show the feasibilities of the proposed algorithms. It is shown that on the one hand, CRF method can provide more detailed explanation information and a more reliable collective prediction result than the main existing capacity fitting methods; on the other hand, CRF extends the applicability of the traditional random forest method into solving the multiple criteria ranking and sorting problems with a relatively small pool of decision learning data.